Mae'n gwybod i'r cerddau iawn ar gyfer Saeotud Rhaeg, ac mae'n byw o gweithio i'n Ghaithρwyr- Chloe. Maen nhw yw'r iawn am ei wneud. Mae daeth gweithio. Mae hynny am yn Gwychonol. Mae wneud i'n gweithio. mae'n byw i'n gweithio i gweithio. Gwrth i'n ddefnyddio Saeshau- oherwydd y fwy o Saesau, mae mwy oed yn ddefnyddio, mae'n ffans oes oed. Ond mae gallai ddefnyddio. Mae'n gweithio ar ôl, I gafodd i ni i'w fan i'w gyrfa. Dyna chi'n eu schod i gynnwys ym Ystryd bood. Dwi wedi gweld, ac rwyf wedi gweld. A oedd yn ôl. Rydywch i'n gobeithio, a dwi'n gobeithio, Gydwch chi yn eu cyllwynadon gyda'r cyfond, a dyna'r cyllwynadon gyda'r cyfond, ac mae'n gobeithio i gydwch. Gydwch chi'n cyllwynadon gyda'r cyfond, a gwnd i chi i'w gwbl, a dwi weld bod ein gweld yma.    And I said get the police and then the police come and he says he's seen this letter, he's serious. I mean the guy left his name, mobile, house address and a lot.  So when I went and seen him, I waited two days, two days I stayed indoors. And I was shitting myself. And then the police come and I said did you see him? I said yeah.  I went yeah.  I went nothing. I said until he comes to our country, I said we're not going to hang around the airport.  So I went on for a few months and I was shitting myself. And then obviously I got a letter back from him and he says okay, you've not done it for a while, I'll let you go now. I could relax then.  But he's giving you something to check on to your car for bombs? Yeah I said the police come and I said six o'clock and I said what's that? He says check on your car for bombs. I said what, if the car starts up he says yeah.  And he says be careful with your mail. If you open it it could explode in your face.  So I used to get me made Jimmy. So Jimmy, go on and take his drivers into work. I'll just have a cigarette at the moment.  I'd be like 300 yards away. I'd be like 300 yards away. I said what are you doing?


Hello and welcome to the session. I am Deepika here. Let's discuss a question which says in given figure a Gulaab German contains sugar syrup up to about 30% of its volume find Approximately how much syrup would be found in 45 gulaab Germans? each shaped like a cylinder with two Hemispherical and with length 5 centimeter undiameter 2.8 centimeter Now we know that volume of cylinder is equal to R-Sphere H and Volume of hemisphere is equal to 2 by 3 pi R cube Where R is the radius H is the height. So this is a key idea behind our question We will take the help of this key idea to solve the above question. So let's start the solution Now it is given that each gulaab German shaped like a cylinder with two Hemispherical ends with length 5 centimeter so this total length is 5 centimeter and Diameter 2.8 centimeter This is the diameter of the gulaab German is 2.8 centimeter Therefore the radius of is equal to radius of cylindrical part That is R is equal to 8 upon 2 centimeter, which is equal to 1.4 centimeter therefore the length of two hemispherical ends is Equal to 1.4 centimeter plus 1.4 centimeter and this is equal to 2.8 centimeter Now the total length of the gulaab German is 5 centimeter therefore the length of the cylindrical part equal to total length of the gulaab German minus length of two Hemispherical ends is equal to 5 centimeter minus 2.8 centimeter and this is equal to 2.2 centimeter Hence this length that is the length of the cylindrical portion is 2.2 centimeter Now volume of gulaab German is equal to volume of cylindrical part cylindrical part volume of two hemispherical ends According to our key idea volume of cylinder is equal to pi R square H into Volume of hemisphere is 2 by 3 pi R cube. Let us take pi R square common We have volume of gulaab German is equal to pi R square into H plus This is again equal to take pi is equal to 22 upon 7 into R is 1.4 centimeter 1.4 into 1.4 into H 2.2 Because the height of the cylindrical part is 2.2 centimeter plus 4 by 3 into R R is 1.4 centimeter So the volume of the gulaab German is 22 upon 7 into 1.4 into 1.4 into 2.2 plus 4 by 3 into 1.4 centimeter cube and this is equal to 22 into 0.2 into 1.4 into 2.2 plus 5.6 upon 3 centimeter cube and This is again equal to 6.16 into Take 3 LCM inside the bracket we get 6.6 plus 5.6 upon 3 centimeter cube and this is again equal to 6.16 into 12.2 upon 3 centimeter cube and this is equal to 75 point 152 upon 3 centimeter cube and this is equal to 25.05 centimeter cube therefore volume of each gulaab German is equal to 25.05 centimeter cube Now it is given a gulaab German contains sugar syrup up to about 30 percent of its volume So sugar syrup is equal to 30 percent volume of gulaab German therefore volume of sugar syrup for each gulaab German equal to 30 percent of Let us take the approximate value of 25 point zero five which is 25 30 percent of 25 and this is equal to 30 upon 100 into 25 centimeter cube So on cancellation we have this is equal to 15 upon 2 centimeter cube or this is equal to 7.5 centimeter cube therefore volume of sugar syrup for 45 gulaab Germans is equal to 7.5 into 45 centimeter cube and this is equal to 37.5 centimeter cube therefore volume of sugar syrup for 45 gulaab Germans is equal to 338 centimeter cube Approximately for the above question is 338 centimeter cube. I hope the solution is clear to you. Bye and take care


Looking, Hennessey throws, ball up in the air, intercepted, fired! Now feeling some pressure, flush to his left, throws back shoulder, intercepted, fired! 45-40, fired to the 35! He's an all-pro, and he's an old hand now with the Hennessey Titans, which is hard to believe. Number 31, Kevin Byrd. Welcome to Titans All Access, and thank you for being our Nissan insider on the first show of the year. Thanks for having me, Mike. Before we talk about the Giants, can we talk about MTSU retiring, your number, and them telling you last month about that? Has that all sunk in yet? A little bit. I think it'll really sink in when I go back to, obviously, Floyd Stadium on September 30 against UTSA. Stand out there on the field with my family and kind of go through all those moments. It'll really sink in, but still, to this day, it's just kind of unbelievable a little bit. But to get your jersey retired is something that's special, obviously something that's going to live on long after I'm gone. You've only been with the Titans since 2016, but it feels like a lifetime ago, doesn't it? I had guys in the locker room, when I was a rookie, that was year six, year seven, I was like, man, it's going to fly by, it's going to fly by. And, you know, as a rookie, you're not really paying attention. You're like, yeah, yeah, this rookie year is pretty long right now. But going into year seven, man, it feels like it's just flew by, obviously seeing the change over in the locker room. But it's been incredible. It's been an incredible journey. Hopefully, I got another seven years still left to play. How did you feel like preseason and training camp went for Kevin Byrd? I think every year it's a progression for me with this year being in a legit leadership role in my room, being the oldest guy in the room. Not only working on myself in my game, but also working with the young guys. These young guys want to be great. They have a lot of big things they want to accomplish and the standard is very high. So not only am I just, you know, focusing on myself, but focusing on the group, the whole team as a whole to make sure that we're all, you know, clicking on all cylinders, you know, every time we're on the field. Does this have a chance to be a great defense? I absolutely think so. Just the guys that we have in our locker room, starting from the front seven, all the way to the back end. We understand the magnitude of the talent that we have on our team and on our defense. We all have Super Bowl aspirations, so we have to take everything day by day and just try to win the Super Bowl. Who's the guy in the secondary that's going to jump out at us this year? And maybe I don't want to say surprise, but take a step. I definitely think Imani Hooker is going to take a big step this year. He obviously was a full-time starter, had a really great year, but I'm expecting big things from him. And Christian Fulton as well. Christian Fulton took a step last year, but I think for him, I've talked to him multiple times this offseason saying, I think you have to be the X-Factor for us on defense. He's the oldest guy in the cornerback room, only in year three. So he has to make sure that you're setting the tempo every single day and leading those guys the right way. Does it feel good that they're sort of building the secondary around you? Yeah, it feels weird. It feels weird. But I just think it's just one of those things where I've made plays in this game. But the way they're building it, we have some guys that can really play some man coverage. We have guys that can play zone. But I think for me, it helps me be able to be a freelancer out there. I can play free. I can focus on getting my eyes on the cornerback, trying to make those interceptions like I always do. So hopefully they continue to keep building after me, honestly. The Giants, the opponent, new head coach, new coordinators, the whole thing. How hard is it to get ready for a team like the Giants in an opener when you really don't know exactly what they're going to do? It's always tough because you really don't know what the other team is going to do. But that's what I've been doing, watching a lot of stuff that Josh Allen did and was successful against us on watching those things, making sure we're staying on top of those things. But I've been watching a lot of just personnel.  And obviously, starting with 26, Saquon Barkley is the guy who we have to stop. Yeah, Saquon Barkley, he's a big back, an excellent runner, but he's really a good pass catcher.  You know, a lot of times when you have teams, but they put these backs out there in empty formations and, you know, cornerers out here, really not cover them that much. But a guy like him, you have to cover like a receiver. He has great hands. Like I said, great explosive speed. A guy that's really built lower body. A guy that you can't really, it's going to be hard to make a lot of one-on-one tackles with him. So everybody has to be the point of attack. And like I said, just excited to get the season kicked off. What do you tell the young guys who haven't done this before? You know, I just tell those guys, man, study as much as you can. But when you get out to game day, play loose, relax. Don't be too tensed. Obviously, you know, for some of these guys, as rookie, it's going to be your first time at NFL Stadium playing. It's going to be loud. It's going to be intense.  He's played at Alabama. He's played at Auburn. He's been in these live stadiums. So I'm going to spend the guard there and just play cool. Don't get too high. Don't get too low.  Kevin Byer, thank you so much for being with us on Titans All Access.


Ahead of the 2023 elections, presidential last-person, Kingsley Marlowe, on the platform of the African Democratic Party, has met with the former chairman of the Independence National Electoral Commission, Professor Atahiru Jega, over the need for a viral third force movement. A foremost political economist, Professor Pat Otomi N. Jega, among others had in October last year, unveiled a non-partisan coalition under the aegis of the National Consultative Front, designed to govern our support for legislation for the electronic transfer of election results. But just last week, Wednesday, Jega had said that Nigeria is in the process of total collapse, described in the 2023 January elections as critical for Nigeria's unity. Meanwhile, Marlowe, who is a former central bank of Nigeria's deputy governor, had declared his intention to contest the 2023 presidential election under the African Democratic Congress platform. We're now being joined by political affairs analyst, Oluqai Adi, Sadako, many thanks for joining us on the news now. Yeah, thank you very much for having me on the show. All right. Good evening to you. Yeah, good evening to you. Yeah, we do appreciate your time. Let's talk about this third force movement now. You know, the former deputy governor of the CBN has met, you know, with the former INH chairman Atahiru Jega to strategize on just direction this particular movement should go. In your opinion, what are the tasks ahead of this particular movement? They seem to want to salvage Nigeria from the doldrums they say that time the country has fallen. The idea of floating the third force political movements has never been in doubt, a bad one. It has always been a child of necessity for Majula's democracy, because normally democracy is supposed to be about competition, political competition, you know, giving rooms for more competitive tendencies. And to engender more involvement, free will involvement of Nigerians. So those that have promoted the idea of third force are not wrong. That is what the tenet of democracy is all about. It is allowed and it is in order. But as far as I am concerned, they need to do more work because the nature of the, the peculiar nature of Nigeria's democracy has to do with not just promoting the idea of floating the political movement or party or social media or TV, but getting it to go down to the consciousness of the grass-toothed people in Nigeria. And that is the power that the APC and the BGP have been able to gather for themselves as political parties in Nigeria. On the lips of every Nigerian, let me say, common Nigeria today, grass-toothed Nigeria today is the name of APC and BGP. The common Nigerians, grass-toothed Nigerians are not familiar with the names of any other political party above from APC and BGP. Whereas more than 18, 19 political parties in Nigeria legally, legally- Registered by Ireland. Recognized political parties in Nigeria. But on the lips of every Nigerian is the APC and BGP. So those that have promoted the idea of thought force should go beyond coming on TV and going on social media to promote the idea. All right, Mr. Salakor, if I have to vote in now, Mr. Salakor, he has a name as well. All right, yeah, Mr. Salakor, can you hear me? All right, Mr. Salakor, if I have to vote in now, you've talked about him, the third force are going beyond doing the activities on social media. But one day on Vail Time Time in October last year, specifically they say or they said that the third force would be a non-partisan coalition in under the age of the NCF, that's the National Consultative Front. But right now, you have rightly said that on the lips of most Nigerians, the political parties, that they know or recognize other PDP and APC. Just how do you think that this new front, that the NCF can actually champion their cause without being partisan, as it is, because if we'll talk about them elections in 2023, they have to maybe sort of push their agenda through a political party. Just how do they go about this? You see, for any political movement to be well-accepted across the length and breadth of Nigeria, to get down to the consciousness of every Nigerian, every look and cranny of the country for wide and expansive acceptance and support, approval, it must have the element of those money bags, let me say money involved. Nigerians, obviously Nigerians don't associate or identify or patronize political parties which won't be able to pay, bring out money to pay for their involvement and patronage. And that is why it has been very, very difficult for other political parties. I was a time in Nigeria when we had over 90 political parties. Why were Nigerians not patronizing those political parties? Because certain money bags, Nigerians, not involved in the running of those political parties. So for this not-false political movement to be well-accepted, to be a political party that could be reckoned with by the wider acceptance of Nigerians, then I think money has to be involved. They shouldn't just, they shouldn't just stay on advocacy, talking, consulting, meeting people and talking to people. They should know that politics has to do with money. There are some Nigerians they must have to bring in to bankroll the financial expenses of the survival and expansion of the party. The third force is a very good idea. I'll not be telling you this. That idea of the third force was the idea of two people, two people in Nigeria in 2014. And that is this Oluqai O'Rizalakor that is talking to you and veteran O'Rizalakor. It was the idea of the two of us in 2014. Veteran O'Rizalakor and Oluqai O'Rizalakor, we mutated the idea and we tried to reach out to a lot of Nigerians who were meaning Nigerians, politically conscious Nigerians to be part of it, to buy into it. But unfortunately, we realized then that a lot of Nigerians were not interested because the factor of Oluqai Bankroll, the financial expenses of how to grow the party, the movement was not involved. So, mutated the factor. And getting certain Nigerians, politically prominent Nigerians also to come to the side of the third force political movement is also the factor. Alright, Mr. Oluqai O'Rizalakor, let me take it one step further. Mr. Oluqai O'Rizalakor, if I should take it one step further, you have identified the issue of bringing prominence in Nigerians, the issue of funding and bankrolling the movement. But then again, how did they circumvent all of these issues of zoning and all of that that is plaguing the countries and most political parties right now? Because from what we have just read, the NCF is partnering the ADC and that they're actually demanding a power shift to the South East. Sorry. On moral grounds, hello, can you hear me? Go ahead. On moral grounds, the South East is justified to be agitating for power shifts. The presidential power to shift to the region. But the fact of the matter is the peculiar nature of the Nigerian politics is beyond that sentiment at this very point in time. The South East has been playing their national politics because the inside one of the two prominent political parties in Nigeria and that is the BDP, the People's Democratic Party in Nigeria. I would have preferred to be comfortable for the BDP to keep president of the leadership of BDP to reward their loyalty their loyalty over 20 years in that party with the ticket, the presidential ticket of that party at this time. Not in a party where BDP is not strong. Besides that, the South East politicians have been playing their politics well. Then it will be a problem for any of the two political parties to willingly give them tickets. All right. The HPC is not willing to give South East. The BDP is not willing to give South East. Then South East will sit down and think that there is something wrong with the nature of their national politics. Under normal circumstances, the BDP is supposed to be willing. Notified about fresh news updates.


Hello everyone, welcome back to another Photoshop tutorial. This one is going to show you how to create text. That has a stroke, but it has no fill in it. So it's kind of old school, but it's only stroke, no fill. There are a few fonts that can do this by default or try to do it, but I can show you how to do it to any font, any textile. Let's go, let's just start from scratch. All right, cool. So we've got a black background. I'm now going to go click on the text tool or the type tool and I'm just going to type something in. So I'm going to type in my name, Curtis, by Perfect Beauty. All right, I'll move this somewhere around the center just so you can see it. Bingo, here we go. Okay, the next step and it's a crucial one. You want to right click on this and we're going to convert this into a smart object. You have to do that in order to get to this stage. Now I'm going to go ahead and right click or I'm actually going to double click outside beside the name right here inside this layer. So I'm going to double click and this opens up the layer style panel. Two things we need to do. The first one is we're going to apply the color. So we're going to actually apply the stroke. So let's apply a stroke. So I've select clicked on stroke and let's make the stroke, I don't know, something like eight pixels, okay? And we're making it red outside, but this doesn't matter. It's just to show you the technique. I'm going to go ahead now and click back on blending options and this is where the money comes. What you want to do is you want to go to blending options, advanced blending, pull the fill opacity down to zero. Now when I click on okay, this is a basically it's text without fill and it has a stroke. That's how you do it inside Photoshop. Thanks for watching.


Y'all This is my second time recording this entire chit chat Truth be told I think my camera is on her last leg. I think she's got done because It's not recognizing memory cards when I'm telling you if it's over I'm not gonna be in the mood to buy new equipment y'all. I can't I'm not gonna be in a mood to do it I'm just saying so we're gonna pray for our camera. You know what the body has father Lord we ask you right now father to go ahead and heal this camera dear Lord You are alpha and Omega see her through and this I pray amen amen you receive that y'all Let me stop playing um cuz we don't play with God not around here. So you guys We are headed into July I Am overwhelmed. I'm excited for the remainder of the year a quick testimony Those of you who follow my vlogs you will get this in my blog too. Yeah, girl Got an email last week from my human resources HR. They basically said I am up for a What do they call it a workplace? Adjustment Basically, I think what they what that means is they look at other positions or other people who have similar positions in my area And I need to be adjusted a little bit more. Hold on. I don't know if that means if I'm gonna get less No, no, we ain't gonna do that. I'm gonna get more. So, yeah, I want to make sure y'all paranoid. I'm paranoid Yeah, you have been identified to receive a compensation increase ain't got good y'all Again, I'm gonna be explaining this in my vlog, but I literally was just talking to my husband too And I was saying how you know again being disobedient and not really Thinking that I could you know pay the mortgage on my own and I verbatim said now if I get a promotion I'll be okay and look at God like that. Okay, so thank you Lord. So That's going on But anyway, y'all know how we do it these chitchats we talk about what's going on my personal life effect Which I started talk about when I'm watching on YouTube and then we talk about what I'm watching on TV Nice end of the day. I have me a little drink you drink. I see my nails. Yes These are some nice my these are not staying on. Well, you guys So personal life is what I'm gonna talk about first. I've been doing my nails, but they're not staying on right So I have advanced to doing My own press on nails and this go around I'm gonna use this cute little foil. Let me see if this can zoom in. Do y'all see this is Miss adorable Little bitty angels a red and green background and what I think I'm gonna do is I'm gonna do a white and Green with a little bit of sparkle for my nails and I'll show y'all what that looks like Of course, I always post it on Instagram, but you have to understand. I'm a girly girl like Most of the man who see me or most of the most of the man that have tried to hit up on me Before and after I was married one thing they say me even my husband Even though he's not really big into that is that, you know, I've always gotten me from the opposite sex You are not necessarily how maintenance. I do think I'm a little hot maintenance But you're put together from top to bottom. I'm like that. I've always had my nails on my feet stay done I just you know, I'm just like that hair stick when I when I am going somewhere. I Clean up me girl. I posted on Instagram my mommy uniforms Y'all see this is what I have on my mommy uniforms. They make them now at Walmart with pockets Y'all saw me I posted a video on my Instagram those of you who follow me on Instagram baby when I saw that Excuse me. I didn't notice it till I got at home when I tried it on I was so excited y'all That really made my week and so when my husband won't kiss ass up cuz he doesn't like these things He ain't here, but I'm whispering. He don't like these. He don't like it when he woke up. I was a hey Do you see this they got pockets now and he's looking at me like what I said, yeah They got pockets. This is a game changer. Y'all he just looked at me He just looked at me and started shaking his head. He's like, what do you mean? It's a game changer. I said, um This means this is me. This is what I'm wearing all day. Thank you You we got at least another 40 years in this piece and he's like, no Yeah, he started shaking his head. I'm like, look he even said I don't know if y'all caught it on the video or something Instagram I wanted to edit out.   Use your imagination. Alex. This is a tease. This is It has come to my awareness recently like the past two weeks I have discovered that I am not really five four This is the thing I have a Napoleon Napoleon complex. I view myself bigger than honestly in my head I I'd be telling y'all I'm five four and I really did think I was five four But when I was five four in my head, I thought I was five eight answer like seriously that's Baby The only way only reason excuse me while I re-measure myself is that JB is tall for his age. My baby's four seven So I was like, let me see what's the difference between between us. So I put myself up against the wall. I put a little sticky note up there, right I put my I put him up and put a little sticky note and I we both turned around and looked at it And he burst out laughing. He said mama. You're just only this This much in between me. I said, no, no, no, that's not right. Something's not right. Let me go ahead Let's get the tape measure out. Let's go ahead and officially measure you and then we'll measure myself Oh, my baby's this dyslexia. So I'm like make sure you read the first The first number and then the second number baby. He said, okay, mama He said, oh, it says you five three.  So We have found a real estate agent out here in phoenix. So as you are not aware, we've found a movement back to texas Hopefully in the springtime of next year and we're now trying to find a real estate agent in the dfw area area If you know of any great good real estate agents in the area, please drop it down below We are looking for recommendations And we want someone who's familiar with the farney area that is headed towards east texas. So that's going um on We're starting back school. We're doing a little bit of summer school for the next two weeks We're going hard with it Just a review of second grade for jb And then i'm going to give him just a few days off and then we're going to go into Reading and math until the end of august. I'm trying to figure out when I want our Next school year to start. I think what I want at the end of august And so that's what I'm going to be really busy doing is planning our next Our next school year So one of the things that I'm finding is absolutely necessary as a teacher because I don't know y'all This is what was my first year homeschooling has said it's absolutely necessary to review Previous lessons and to build up on what was already taught because they just need that repetitive. So um, for example I just can't pull out a Working and say okay go ahead and and Find all of the different adverbs.  Um, as far as grammar goes I just can't say okay go ahead and find out the adjectives, you know something that's not as common But once he gets it and I remind of what it is. He's good y'all With my husband out traveling and I think I've briefly mentioned this He's going to be a traveling med tech. He's not going to go do a traditional eight to five job That way he can spend, you know, take three Whatever how long three to four months being a traveling med tech take a month going back over to kenya Um, and then come back and work and we will actually also be going back and forth with him too Um, not back and forth a lot, but as a family, we're gonna make a trip to kenya as a family Probably in the summertime in two more years. So yeah, that's what's going on So y'all that's it with the person stuff everything's going well Justine still doesn't like that. I show up to people houses on and Have a neighbor. Yeah, first of all So when the pandemic first hit the way I am on here, baby is the way I am in person So when the pandemic first hit I will go over to miss lori's house a lot because they didn't have a lot of visitors And we were the only ones that was our place. And so another neighbor was like I understand that there's a certain person that shows up to people houses unannounced And she just barges in and be loud girl. I was acting like push. I'm like, who's that? Who did that? So she made another comment recently that well, at least I'm not like Somebody who just shows up unannounced child That's why I said you guys There will always be as bubbly as my personality is and I think I'm a likable person But there will always be some people who don't like you and that's okay. That's okay Anyway, y'all, okay, so what I'm watching on youtube girl nothing now I don't watch married to medicine, but child.  I will say that she's very entertaining and like I said I don't want to show anymore But baby, I think she may be talking a little bit too much sometimes because They can't be revealing everything on the show. So she's very smart. I think that dr. Hevelling and this is a intelligent woman and I think it's smart that she reviews her own show. So I like that. So I do watch her reviews of the show um I recently described I recently subscribed to her brother named carlos king and he does reaction videos y'all Have y'all been reading about this ppe loan scams going on? So there's this sister. Her name is patricia What is her name? I've just subscribed to her. I can't find her y'all Let me see if I can find her I think her name is patrice patrice steward very intelligent very smart woman. So she hacked this video, but This is what people or uh, what who he was reacting to. I'm sorry her video So I guess people decided that they would have these fake companies Hire fake employees stating that they make a hundred thousand dollars. Whoever feels like the application is feeling this information out, right? You pay that person who feels like your application $5,000 they say that you got some Uh company where you make a hundred to two hundred thousand dollars a p e loan. Are y'all crazy? So you got people getting twenty thousand dollars I I read another comment where someone said that they knew someone who got like over a hundred thousand dollars Or you serious? Y'all gotta be careful.  The girls started watching a little bit of ta ti Ta ti is a makeup artist started to watch some of her videos. Y'all Nancy told me she was only 30 something She looks older than that. I thought she was in her 40s. Um, she's very talented I was watching the video where scott was doing her makeup And he's very talented too. He does makeup almost like an artist and she is his canvas. He's very very talented Um scott What is his last name scott borns?  Yes, I said it She's an entertainer, but she can't act. She cannot sing. That's about it. Um Uh Nothing else i'm watching on youtube girl. I was having issues with my computer and um, the guy was trying to Take off McAfee on my system and I just remember That john macabee is his name. Yeah, john macabee supposedly committed suicide. Do y'all believe that? Hmm, I don't believe that man committed suicide. I really don't I now I do think that he did kill his um Neighbor, there was like some scandalous Stuff that happened a couple of years ago and he's been island hopping now Was he the one that had the island where people like epstein and I think even clinton name was in it He had like a private island macabee had this private island where he would have certain type of parties So I think he's in that lifestyle. Oh by the way, his wife was black like he married a sister I don't know if she's african-american, but she's black. It's my whole point Um, they had a video still on youtube. I believe her name begins with a jay It's either jane or jannis john macabee lost a lot of money He wasn't worth as much money as I thought he was at one point. He was worth a hundred million dollars. Not so much Um, so yeah, girl. He apparently committed suicide, which I don't believe I don't buy it Um, what was he at was it brazil believed at one point? I think he was even He said that people were trying to kill him and believes what is that aboard the south Very south america. My girlfriend's originally from belize. Y'all know who's else from belize? I know I'm all over the place. Um Deep deep voice. He has a deep voice. He was sort of shun PDD in them his name begins with an s Sean yeah, that was his name. Yeah, his butt was from belize. My girlfriend used to date a brother from belize So anyway, y'all um poor mackafee. Yeah his his time He even said so you you can't play around with this He even said a couple of years ago I think it's been about five years that if he wanted to He could spill the dirt on on the government if you wanted to he could don't don't say that Don't don't do that. So y'all my battery light is blinking. Let me hear up and tell you when I'm watching good girls Childly counsel good girls Let me tell you something after the second season the rat the writing was trash We wanted a rio. I told y'all I wanted rio and bev to get together and it was just trash They couldn't the story lines just went downhill after the second season I watched the show. I believe it was on hulu called false positive With pierce Brosson the irish actor good. Look, he's still fine girl.  I'm watching a new series on netflix called manifest. It's okay, but hmm Luca we saw the disney movie. Luca was so cute I started to watch the trial of gabriel finandez when I tell you I can't do it 10 minutes into it. I was a mess We're gonna keep going.  No, I'm short. I'm I'm taller than him. Um What is his name y'all kevin heart and fatherhood? So I know I'm kind of rushing this but my battery is low. That's what I'm watching. What are you watching on tv? There really ain't not not a lot going on. So that's it everyone. Thank you so much for watching. Take care. Bye


Hi everyone, Joe for Jaspy's casebreaks.com here with a nice break, 2022 Panini National Treasures Baseball. Pick your team 30. A lot of pick your teams here. So thanks everyone for getting it done, appreciate it. Big thanks to everyone who bought their spots here on a Wednesday. Stephen K, you ended up with last spot mojo before I pulled the remaining teams for that random number block randomizer. And here are the results of it here. We did that in a different video. Numbers applying only to those teams here. Let's keep that two to my side over here. All right, and there's the case of 2022 National Treasures Baseball. Good luck. All right, let's see what we got. Good luck everybody. There's that blank card right here to slow play the hits a little bit. We got Travis Demarit leading us off to 99. That will be for Atlanta, Jason K with the Braves. Got a Vidal Bruhan for the Rays. That'll go to, that's a number block team. So it's 91 out of 99. So we go by that digit right here. And that will be for Carl in one. And you got Vince Coleman, retro materials. Five out of 25. Mets are a number block team. Carl, number five. Beer, Seth Beer. 49 out of 49, die cut material signatures for Raymond. And the Diamondbacks, got the Diamondbacks straight up. There's Rake Myers, not Jake Myers, but Rake Myers. 30 out of 49 for Astros. For the Astros, goes to Astros zero. That'll be for Tristan. We got the Chasmanian Devil. I see what they did there. 74 out of 99. It's another one for the Strohs. This time Astros four. That's for Nick Oh. Houston four. Nice patch here, Kyle Muller, six out of 25. Jason K with the Braves. And we got a Ken Griffey Jr. Nice, Hall of Fame materials signature, 17 out of 49.  That's awesome. Got a piece of his lumber, excellent penmanship. Real nice, congrats. We got a one-of-one quad relic and autograph Ryan Bliss for Arizona. It's Raymond L with the Diamondbacks. Congrats, Ray. You got a bit of the snake logos right here. That's awesome, man. Out of fives and under. All aboard the Big Head Express. And the book is gonna be a legend. It is Joe Cronin, 17 out of 49. Those old burlap sack jerseys. Boston, Ed P with the Red Sox. All right, box one in the books. Next box, Dallas Mavs in LA. Playing the Clippers. Kyrie's debut. Forgot that Luca is injured. I thought we were gonna see both of them play, but Luca's still working through an injury. Next box, we're gonna start off with Elias Diaz, 29 out of 99. Rockies, relic for Carl and the number nine. We got Field Gear, Zach Ranke.  Royals are a number block team. Ranke, I think, re-signing with the Royals recently. That's 72 out of 99. Royals two, Kenneth with number two. Field Gear, Albert Pujols. Looks like 27 out of 99. And that'll be for Jeffrey. Picked up the Cardinals straight up. Tyler Freeman, three I-25, three color patch and autograph. That's for Cleveland three. To me for Tristan. Cleveland, this is for you. We got Reese Nair, die-cut material signatures. Nice patch in there, 21 out of 25. Calvin with the Padres. Die-cut material signatures. Ryan Malkassel, 40 out of 49. Kevin with the O's. We got Thomas Zabuki, nine out of 25. It's an awesome Mets patch right there. That's gonna go to Mets nine. That'll be for Carl. The big hurt, 23 out of 49. You got a piece of his lumber and autograph. Holofame material signatures. White socks, that's gonna be Ed P. Trust me, Ed, she'll like this card too. The book is Lars Knutbar, nine out of 10. Lars, ooh, look at that. At the D of Cardinal. Lars Knutbar's on-card autograph. Nice letter patch right there, nine out of 10. For the Cardinals, that's gonna be Jeff and the Cardinals. Nice hit. And the one on the bottom is Triss Speaker, 21 out of 99. Treasured stats card for Ed and the Red Sox. All right, halfway through this four box break. Box three, more top loaders there. And we got Yusei Kukuchi, to 99 for Toronto. That's 17 out of 99, so Toronto seven will be for Nick. Red, white, and blue relic, 16 out of 49. Cedric Mullins, Kevin with the Orioles. Piece of his lumber. One of one, Roger Maris. Piece of his bat. That's Carl, Yankees one. That's awesome, Carl. All aboard the Big Hit Express. Woo-hoo. A little bit of history there. Otto Lopez, an Otto Otto. Seven out of 49, Toronto seven for Nick. Got Jesse Winker, 53 out of 94. Seattle, Rob with the M's. Got a piece of the Jersey. Nice, a lot of graph. Ooh, that looks pretty cool, but it's Trevor Bauer. 18 out of 99. This is for the Dodgers, that'll be for Ryan. Jaren Duran, Duran, 56 out of 99. Three-color patch and autograph. Ed with the Red Sox. Got Orlando Cepeda, 21 out of 25. Lumber and Otto for Ed and the Giants. And the book. A legend, Miguel Cabrera, definitely a legend. 18 out of 49. Tigers are a number block team. Detroit eight is for Carl. All right, final box coming up. And we don't have more national treasures at the moment, but we do have some flawless baseball. So if you like what you saw here, you're also gonna like, think you're gonna like flawless a lot too. All right, we got a six out of eight. Tyler Stevenson, Chris with the Reds. Joe Ryan for the Twins, four out of 99. That'll be for Oliver and the Twins. 49 out of 99, Vlad Guerrero Jr. Field gear, Jersey. CO Turtle Outdoors. How are you? Doing good? Toronto, Toronto nine. That's gonna be for Carl. And there's, use the fullest Luke. Luke Williams, 10 out of 25. Jason Kay with the Phillies. You got Joey Gallo, Dodgers edition, 10 out of 10. Ryan with the Dodgers. Let's see how the, I don't know who's gonna pick up Joey Gallo. Let's see how the banning of the shift helps. Some argue that it's negligible. 22 out of 25, Robin Ventura. Jersey and autograph, treasured material. Ed with the white socks. This top over here. We're using a different kind of penny sleeve here. It gets wrinkly a little too easily. The larger top over here, that's gonna fit better. All right. Ooh, a one of one Royce Lewis. Majestic patch and autograph. It's an RPA. Oliver Soria picking up the Twins straight up. There you go, Oliver. I don't know when the last time we had a, we had a train whistle. There you go, Oliver. Oliver. All aboard the Big Head Express. Woo-hoo. Andrew H. Hi, Andrew. We, there are a number of Andrew H's. Which Andrew H are you? Jackson Holiday. Holiday, 79 out of 99. Number one overall pick. Oh, Andrew Herman. Hi, welcome. Long time no see. Kevin with the Orioles. There you go, getting the Jackson Holiday. The book. Legendary material, duals, stat line. 10 out of 10. Ooh, nice. Dave Winfield. There's your dual relic. There's the cut signature. Yankees are a number block team. Yankees zero. Tristan, there you go, Tristan. Tristan's a big Yankees fan. Nice. And finally, we got a die cut material signature Luke Jackson, 46 out of 99 for Atlanta. That's gonna be for Jason K. Use the force, Luke. There you go, gang. That's a no randomizers. That's a really nice break of 2022. Panini National Treasures Baseball. Thanks everyone for getting in. I'm Joe. I'll see you next time for the next one on jaspyscasebreaks.com.


Welcome to the 30 paintings in 30 days project. So every day of this month, at least 30 days of this month, we are gonna create a little painting a day and we're gonna see what happens. I'm gonna experiment mostly with watercolor and gouache and let's get to painting and I will see you at the end. Hey guys, welcome to 30 paintings in 30 days and we are on painting study number 19. I can't believe we're there. All right, so we are going to turn our inspiration book here to another page that I find interesting, that I wanna work from today and then we're gonna get started. So, you know, I love these sunset pictures, don't you? You know, there's something about this one where you just have a little peek of it in the blue sky and then that one, maybe. Maybe, maybe. I do think we wanna do sort of a sunset thing. So let's do that. So let's leave it here. I love sunset skies and I go on these tangents where, you know, for weeks all I do are like sunset paintings. I know it's crazy. And you're all probably going to another one. It's a great way to experiment and play with color though and so we're gonna get started. We're gonna work right here in this square.  My water is disgustingly dirty. I'm going to just add a little bit of it. It's a little bit on the green side, but that's okay. I'm gonna add some water and I'm gonna spread that pigment out in a sort of haphazard manner and then I'm gonna give it a dry. I did wipe my palette off because that was nasty and while that color works right here, it's, yeah, not good. So, okay, so we're gonna go in and I'm gonna take some of the Van Gogh Cerulean blue which is very well pigmented and I'm just gonna grab the tiniest tiny bit of it and I'm gonna mix it with some cobalt blue and it'll sort of green up the cobalt blue and give me a nice happy medium and I'm going to put some of that on here and I'm sort of using the parts where that bluish green that was on the palette was darker than others to use that as the parts I wanna make darker and the parts that are white or the lighter green color, I wanna preserve them if I can and leave them lighter and sort of just follow with what naturally happened with the water as far as suggestions about where to put the shadow. Okay, and then I'm going to grab some, the Jane Davenport Royal, which is a blue purple and again, I'm just gonna add a little bit because that's a really purple purple and you can always add more but you can't take it back. Okay, that's good. I'm gonna add a little bit of that to the paint here. A few spots. Purple's a great sort of shadow color. Ooh, I like where this is going. Okay, we're gonna give that a dry.  I'm gonna grab some of the Jane Davenport yellow color here that's called Buzzy. That's a very, very bright yellow.  I'm gonna put this over some of the white parts.  Now, you can't always lift off watercolor paint. Some colors will stain right away and they'll stain heavily and they won't lift but it's always handy to have a rag, a Mr. Clean Magic Eraser works. I have it handy and you can at least try and you may not be able to get all the pigment off but you may be able to get some of it off. Okay, so just like that. And then I'm gonna take some of the orange. What is this? Whole-Bind Permanent Yellow Orange. I'm gonna mix it with that yellow that was on here and I'm gonna just, again, add some more water. I'm gonna put just a little bit. Cause again, I don't want a ton. You can always add more pigment but you can't really take it back. I said that already in another video. I say it all the time with watercolor. You can't always take it back. And I'm just doing an abstracted sort of stormy sky, sunset, sky thing inspired by what I see in the photos I took. Okay, then I'm gonna grab a little bit more of that orange but without watering it down. And I'm gonna put some of that on the page and then I'm gonna add some water. Then I'm gonna grab some pink and this is Jane Davenport's pink color called Best Friend. It's a really pretty pink color. And I'm gonna, again, blend out some of those marks with some water. Gotta kind of work quickly with these Jane Davenport paints because they dry fast, which is one of the reasons I didn't dry the paper. I want it to sort of blend a little bit. And there we go. I like the way that looks. Now let's give it a dry. Okay, let's lift the tape, shall we? Now I do admit to you with this blue tape, it is a little bit distracting to get past the blue color of the tape when you're working on your paintings. Sometimes the blue sort of interferes with the colors I'm seeing, if that makes sense. So if you find that, you're not alone. Look at that, that is cute. I like that one. So there we go, painting number 19. Speed Fruit Through version, sorry. If you'd like to support the free content here on Facebook or in the, here on Facebook, Holy Cow. If you'd like to support the free content here on YouTube or over in the Facebook art groups, I certainly would appreciate that. You can of course join Patreon. We do have YouTube membership here for a small fee. And also I have an Etsy shop and I have PayPal tip jar and all that stuff. So check out the video description. Relevant links will also be down there. And yeah, don't forget the most important things.  Do share your work with me. I would love to see what you're doing. That's it for now. See you later. Bye guys.


Regarding insulation, I think this is also one of the favorite topics as far as undergraduate heat transfer courses are concerned, critical radius of insulation and what we do with that. Insulation essentially we have seen or from intuition we know that it is used to reduce the heat transfer. So, by adding more and more insulation, we have almost always thought that the temperature I mean the heat transfer rate is going to decrease. Therefore, how much ever you had it is not going to matter in the overall scheme of things, but that is not the truth because if you look at I will just quickly in couple of minutes draw these and go ahead. So, if I take a plain wall, this is the wall of thermal conductivity k and if I have an insulation with thermal conductivity k i n s and this is this temperature is T 1 and this is T infinity here. I have Q according to Fourier's law is T 1 minus T infinity divided by summation of R thermal, where R thermal is essentially L wall L insulation. So, L wall by k a plus L insulation by k a plus 1 over h a. This 1 over h a and L wall by k a are going to be there irrespective of whether we put in this insulation or no. So, these two are constants. This quantity L insulation by k insulation a is going to increase increase in thickness. So, as L insulation increases logically we are going to see that the overall total thermal resistance increases and therefore, Q is going to drop nothing great about it it is not a problem. And as we saw in from the morning for a plain wall the area associated with heat transfer is constant whether I take this surface or this surface or this surface the normal area to heat transfer is the same a. So, because for a plain wall a is constant along x direction Q is constant as well as Q double prime or heat flux is also a constant meaning it is invariant with respect to x. This is something which we have to understand and appreciate very clearly. In fact, students should be tested on this concept simply because we use heat flux and heat transfer rate interchangeably in numerical problems, but for a plain wall it does not matter whether we use heat flux or heat transfer rate we are going to have there is no effect of the area as a function of the cross sectional or as a function of the axial location, but if I look at a radial system like a sphere or a cylinder what is going to happen is the following. So, let us take this is a cylinder and whatever I do for a cylinder is valid for a sphere. So, this is t 1 and this is h comma t infinity and this is just a wall a pipe which is carrying steam is going to lose heat from here to here. So, this is the direction of heat transfer. So, I can write Q is equal to t 1 minus t infinity please note I have this resistance inside for steam flow is also constant. So, I am not taking that I am writing this temperature difference. So, I am writing the temperature difference t 1 minus t infinity. So, I will have the resistances associated with conduction through the wall and convection. So, this will be log R 2 by R 1 by 2 pi L k wall plus 1 over h a surface.  So far so good no problems now I am going to put an insulation material to this pipe. So, R 1 R 2 and R 3 and we have the same h comma t infinity this surface is maintained at t 1. I can clearly say that I am going to have an additional resistance this is the conduction resistance for the wall this is the conduction resistance for the insulation and this is a convective resistance for the heat flow from inside to outside the direction of heat flow is fixed. We have an additional resistance in the path. So, I will write Q is equal to t 1 minus t infinity log R 2 by R 1 2 pi L k wall which is also constant plus these are the two important terms log R 3 by R 2 2 pi L k insulation plus 1 over h a 3. These two terms have come in instead of this one term what is what are these two terms log R 3 by R 2 divided by 2 pi L k insulation plus 1 over h 2 pi R 3 L. This is with insulation and without insulation it is going to be 1 over h 2 pi R 2 L without insulation. Every other resistance in the problem is constant if there is a convection on the inside of the pipe any other material associated with the pipe wall we do not care everything else is a constant what is changed is these two quantities. So, t 1 minus t infinity divided by something plus constant value plus 1 term in case 1 which is equal to in second case with insulation t 1 minus t infinity constant plus term 1 plus term 2 two additional terms which are given by this. Now, I cannot say what is the effect of keeping on adding insulating material why if I keep adding insulating material this R 3 is going to increase this conduction component of the resistance this conduction component. This is R conduction of insulation this is R convection on the outside of the insulating surface surface area for a larger cylinder is larger. So, when the radius was R 2 2 pi R 2 L R 2 is smaller than R 3. So, this area is going to be smaller. So, the resistance here is larger whereas, here this resistance is going to become smaller because R 2 is smaller than R 3 1 over h 2 pi R 2 L is going to be larger than 1 over h 2 pi R 3 L obviously. So, what is happening the bottom line is I am adding more and more insulation the thickness is increasing conduction resistance is increasing because this term is getting bigger and bigger. But I am going to see a drop in this quantity with additional resistance being added and when I keep doing this adding of insulation I will come up with a situation where I might actually see a increase in the heat transfer as opposed to a decrease in the heat transfer. So, if I plot these two resistances this is the x axis is resistance this is the thickness of insulation or thickness of insulation. So, or R 3 if you want to say as R 3 increases R convection decreases R conduction increases and you will come up with a summation of resistances which look something like this and all this has been illustrated here most of us are familiar also. So, additional insulation increases the conduction resistance of an insulating layer, but decreases the convective resistance of the surface because of the increase in the surface area. And heat transfer of the pipe therefore may increase or decrease and this happens because of the fact that in radial systems though q is equal to constant that is sacred we cannot change that. So, q at any cross section is the same how many watts is coming out from inside is what is going to go out, but heat flux is not a constant that means heat flux as R increases surface area increases heat flux progressively decreases as R increases means a is equal to 2 pi R L or a equal to 4 pi R square does not matter you go outer and go to the outside surface of the cylinder progressively from the inside the associated area for heat transfer is more. Therefore, heat flux is going to be progressively decreasing. So, that is the reason for this concept. So, all this is illustrated here in case of a cylindrical pipe this is the additional resistance which is there and as I told you all other resistances are constant these are the two resistances which are going to play a role conduction of the insulation convective resistance on the outside of the insulation. So, if I want to optimize if I want to have q R as optimized value then I should have an optimal thickness of insulation which can be obtained by differentiating this expression d q basically differentiate this one when this is minimized q R is going to be maximized so on and so forth. So, all of us have done this mathematically where the independent variable is now going to be R 2. So, d by the R 2 of this denominator expression differentiate set it equal to 0 you will get critical radius of insulation of cylinder is k over h and for a sphere it will come to k over h. So, what it tells me bottom line is the rate of heat transfer from the cylinder increases with the addition of insulation until where until the point where you reach critical radius of insulation. So, from a bare cylinder you add a little bit of insulation the heat transfer is going to increase as long as the value of the outer radius is smaller than the critical radius calculated this way it reaches a maximum when R 2 equal to R critical starts to decrease beyond that point that does insulating a pipe may actually increase the heat transfer rate instead of decreasing when R 2 is smaller than R critical.  So, as the resistance progressively summation of the resistance progressively decreases your heat transfer rate is going to increase. In fact, that is what is plotted there the reciprocal is what is plotted the heat transfer rate increases between the bare surface to the location of R equal to R critical and then you see a drop in the heat transfer. So, this is something which all of us know critical radius of insulation people derive ask questions on that, but we need to keep in mind that this portion involves increase and where do we use this do we need to ignore this or do we have to be so careful in doing this we should put insulation little beyond R critical how much you have to put we have to be very careful. So, yeah the next transparency essentially will give you a feel of how important this aspect of critical radius is. So, value of critical radius will be largest when k is large and h is small as seen by these expressions k over h or 2 k over h here. So, lowest value of h typically we see in natural convection situation which is about 5 order of magnitude we are not talking of actual numbers around 5 in gases natural convection gases and insulate common insulating material let us say it is 0.05 watt per meter square Kelvin we are talking of a critical radius of insulation of about 1 centimeter or 10 mm. So, if you have radiation effects this value is going to be even smaller. So, what we are saying is though there is a curve which is shown like this this is the bare surface this is the critical radius essentially this portion is hardly 1 centimeter. So, even when we apply insulation we are almost always beyond this portion. So, that is something which we need to appreciate that is why in most general situations we do not care about critical radius of insulation that much when we are doing things practical. So, in case of force convection this is still lesser critical radius would be much less than 1 mm because of the larger h value associated k over h therefore, we can insulate hot water or steam pipes freely without worrying about the possibility of the increasing heat transfer by insulation of this pipe. So, the logic that we use for plain wall just more the insulation merrier is probably valid here electrical conducting wires where you want heat dissipation to be more you would want it to be below the critical radius of insulation. Therefore, plastic electrical insulation may actually be used to enhance the heat transfer from electrical wire and thus keep the steady operating temperature lower and at safer levels. So, this is with regard critical radius there is a small example problem which will solve this is a 3 millimeter diameter 6 meter long electric wire is tightly wrapped with a 2 millimeter thick plastic cover whose thermal conductivity k is 15.15 watt per meter Kelvin. Electrical measurements indicate that a current of 10 amperes passes through the wire there is a voltage drop of 8 volts along the wire. So, when there is a current of 10 amperes there is a voltage drop of 8 volts. If the insulated wire is exposed to a medium that is offering heat transfer coefficient of 12 which is typical natural convection value and temperature is 27 degrees centigrade determine the temperature at the interface of the wire and the plastic cover in during steady state operation also determine whether doubling the thickness of the plastic cover will increase or decrease this interface temperature. So, it is a straight forward problem on insulation multiple resistances and we have to also deal with critical radius. So, if you look at the diagram this red portion represents the current carrying conductor whose diameter is 3 millimeter radius 1.5 millimeter length is 6 meters here then there is a plastic cover this blue one is a plastic cover material of thermal conductivity 0.15 this insulating material. And when you pass the current of 10 amperes voltage drop is 8 what it means is that electrical heating kind of situation is given in terms of voltage and currents. So, power is equal to V times I V and I are given. So, power or wattage can be obtained this heat has to be dissipated out. So, if the insulated wire is exposed. So, the heat is being carried away by a fluid which is basically air probably which is giving a heat transfer coefficient of 12 and a temperature around of the medium is 27 degrees. So, the resistance diagram here why have we drawn only this part of the network we have drawn this part essentially because we are dealing with the insulating plastic material that is the blue portion that is air plastic and air convection represents the outside convective heat transfer or resistance. For this wire it is a heat generating problem we cannot apply we cannot draw a thermal resistance directly because this is having a situation where q is not a constant there is a volumetric heat generation whatever heat is coming out that is what is generated that is going through this insulation and the conducting medium. Therefore, this q what I what we have shown here is V times I, but that resistances associated are this plastic and the convective part T 1 represents the temperature at the interface of the conducting wire and the plastic. This is what we have to find for this q T 1 minus T infinity T infinity is known if I calculate these two resistances I can apply my basic equation which gives me the appropriate answer, but again we follow a certain methodology. So, we have a list of assumptions that we have to write first thing is we have thermal conductivities which are known and constant there is negligible contact resistance at the interface between the wire and the plastic material. There is negligible radiation and even if there is any all the heat transfer coefficient value takes care of it one dimensional radial conduction. So, that is very important because we are studying only radial conduction at this point and it is steady state environment steady state system because there is no change with respect to time. So, after all this we get q is equal to 80 watts and a 2 which is the area associated with this surface that we have calculated 2 pi r 2 l. So, r convection can be calculated r plastic is conduction log r 2 by r 1 calculate the value at these 2.78 degree centigrade per watt. Therefore, the interface temperature is unknown T 1 I can calculate this as 89.4 degree centigrade. So, next part of the question was if the thickness was doubled what would happen that is also determined whether doubling the thickness of the plastic cover would increase or decrease this interface temperature. For doing that we first have to calculate the critical radius the critical radius comes to be 12.5 mm. This critical radius is definitely is larger than the radius of the plastic cover. Therefore, what is the radius of the plastic cover radius of the plastic cover is you have seen this here 2 pi r 2 l 0.0035 that is essentially 3 mm plus thickness which is been given to you already 3 mm of the diameter of the wire and 2 mm plastic. So, half of it would be the radius. So, 0.001 1.5 plus 2 1.5 is the radius 2 is the thickness. So, 3.5 mm. So, 3.5 mm instead of that if I make this thickness double I would be adding another 2 mm. So, 4 plus 1.5 which will be 5.5 mm. So, this which is larger than the radius of the plastic cover. Therefore, increasing the thickness would enhance the heat transfer until the outer radius reaches 12.5 mm. That means, we are in this part of the curve let me go back here we are somewhere here I have increased this is this number is 12.5. We are here at 3.5 if I make it 5.5 also we are in this part of the curve therefore, increasing the radius increasing the thickness of this plastic sheet will actually increase the heat transfer in this case rather than decreasing it. So, that is something which we have to keep in mind. And as a result the rate of heat transfer will increase when the interface temperature is held constant or T 1 will decrease when power or voltage times current the word power is missing T 1 will decrease when power is held constant which is the case here V times I is held constant. So, you can calculate whatever if the power is held constant you can calculate the temperature and I think it comes out to be 71.14 or 77.54 whatever. So, this is a plot which has been made to illustrate the temperature at that interface and the radius of the insulation. So, you have this plot which is essentially obtained from this equation which we have used. This summary we have already covered plane wall V square T by dx square just for even though we are repeating we do not mind doing this simply because we have to understand take home as we say at the end of this student what he what he or she takes home is this finally, what is going to be asked in the exam I think this is what most students will ask essentially if you remember all this we are in good shape and we do not have to memorize everything. Heat flux remains constant heat transfer rate remains constant for a plane wall heat flux not a constant for cylinder not a constant for spherical wall heat transfer rate is constant irrespective of the radius for both these cases thermal resistance conduction L by k a this one for cylinder this one for sphere convective resistance 1 over h a temperature distribution. We do not have to memorize it but point to be noted that this is the linear temperature distribution when you have no heat generation it is a straight line distribution whereas, this is logarithmic and this is some other functional form for spherical wall. So, we have left out one problem in the middle which we remember we will take it up tomorrow from now on till about 530 we are open for any questions across all the institutes preference will be given to people who have not asked any questions so far but we will try to accommodate everybody. So, S V N I T Surat yeah your question please. Sir, in case of the insulation thickness what would be the better 10 meter in case of the insulation thickness of the wall what would be the better heat transfer case 10 meter 1 wall or the each wall of the 1 meter 10 wall of each meter. Please rephrase your question. The thickness of the insulation the 10 meter and the second case is the 10 wall of the 1 meter so which one would be the give heat based heat transfer. The question is this the question asked by one of the participants is that if I have an insulating material is it good idea to take 1 meter whole as 1 insulation or I will break them into 10 pieces and then add one after another. So, that is the question. I think the answer is if you have 10 pieces added will add the interfacial resistance so that would be better but then I do not think it is fabrication wise or putting insulation wise putting 10 times is easier. So, we usually put whatever is available in the market we directly put so typical thicknesses whatever are available we directly put them but we cannot fragment them for 1 mm 1 mm 1 mm and then put them several times. Yes theoretically if you put several times interfacial resistances are increasing so definitely putting multiple layers is better than one layer no doubt about that but practically I do not think it is always possible if you are imagining a complete power plant and we have to insulate the complete power plant one of the heat exchangers of a power plant it is not going to be easy. Yes in a lab scale if you want to do something we can definitely do that. Gopal yeah please go ahead. Yes sir question is the regarding energy generation because this is the equation of energy conservation here why we are writing it yeah energy generation because there will not be any generation of consumption by a material if there is a reaction take place a chemical reaction in which generation of energy is taking place they are supposed to be a consumption of energy also will be that means energy generation may be a positive or negative or it will be a always positive. To rephrase this question there is a question on energy generation the thing is why is there energy generation considered in the equation I think the he is saying that there will be only energy in the reaction there will be conversion from one form to another or something like that is the question. But what we are saying is the heat diffusion or conduction equation is a very general form of equation and mind you chemical energy a chemical reaction we are not concerned with chemical energy or any other form of energy we are concerned with heat energy only. So, this is a heat balance equation if if the reaction is not generating any heat and it is proceeding like that H 2 H 2 plus O 2 is giving you two molecules of water we are not and if it is a non exothermic or non endothermic reaction that is not going to feature in the energy budget. So, when a reaction gives out or takes in heat energy in the form of heat that is what we are going to take in the energy generation term. So, we are chemical reaction nuclear reactor all these things where thermal energy is associated we are dealing with thermal energy only. So, actually to add on we can imagine like this in this room in your room whichever room you are sitting. So, if there is an electrical heater at the center of the room that is the energy generation term or otherwise if someone is spraying water on to us then that is the energy generation in this case will be negative. So, energy generation does not mean always it is positive the second part of your question. So, energy generation can be positive energy generation can be negative it depends on the process or it depends on the case by case as I said there are two examples in one of the examples electrical heater energy generation is positive if you are spray cooling if it will be energy generation will be negative because you are cooling. So, energy generation can be either positive or negative depending on the situation. So, any energy generation typically would involve conversion from one form to thermal energy if it is conversion from chemical to mechanical energy we are not concerned with that we are concerned with transformation we do not even care what is the source we just want to know whether in a given problem there is going to be thermal energy coming generated or thermal energy lost because of a process. Very good question this is only about thermal budgeting this is only about thermal budgeting. Not any other form that is why it is called heat diffusion equation not energy balance general energy balance equation common call it Salem yes please go ahead. As I said thermal conductivity is the property of material please elaborate the relation between thermal conductivity of material and its temperature. Thermal conductivity varies with temperature now whether it is going to vary linearly non linearly whether it is going to increase decrease is all dependent on the molecular structure associated with the material. So, there is no general rule or general relationship for any unique answer for this question actually. So, for a given material what is the variation you can find out next I think there is one more question quickly. The variation of heat transfer rate with radiation. It is what is the amount of heat that is here sir. Sorry your audio is really bad we are unable to hear anything there is lot of disturbance something related to 2.16 ok. Yeah yeah. Ok. This figure is common for both cylinder and radius. Yes yes. Qualitatively. Qualitatively this is not mathematical function it is a qualitative representation ok nature of the curve is like that increasing decreasing curve with a maxima. But the critical radius is going to be different for cylinder and sphere for cylinder it is going to be k by h and for sphere it is going to be 2 k by h. But the nature of the curve initially increase and later on decreasing and a maxima existing is going to be same for both cylinder and sphere ok. Ok. Thank you sir. Thank you very much. Sheerpur college over to you. Sir I have a small question in the equation of critical radius of insulation we got for the cylindrical system as k by r c is equal to k by h 0. And during your explanation through graphs you said that at this condition the heat transfer rate will be maximum. So how we can say that the heat transfer rate will be maximum. Will you please elaborate it to some mathematical expression over to you sir. For this we will have to go back to what we had done before on the white board. See this what will happen is as I keep adding insulation the surface area for convective heat transfer increases and this causes the convective resistance to decrease what is the convective resistance r convection is 1 over h a ok. This is going to drop as r increases that means as I add insulation conduction resistance is going to increase because you are adding more material. So greater the thickness conduction resistance is going to increase as r increases. So the summation of these two would give you a curve which looks qualitatively something like this r total and it comes to a minimum value somewhere which we essentially is what we call as the critical radius of insulation. How did we get this? It is the summation of these two curves and if you write q is equal to delta t divided by r r total and in this case all resistances except these two are constant. If I say d by d outer radius which is the variable of r conduction plus r convection is equal to 0 I come up with that so called critical radius of insulation and that is this point. This point represents the point of minimum resistance and therefore a point of maximum heat transfer rate. So for the application we have to put the insulation much much larger than this critical radius of insulation. So we cannot we are not supposed to put the insulation thickness equal to critical radius we have to put much larger. Our concern is by chance if we put our insulation much lower than the critical radius that is the concern. In the next transparency professor told us that typically for all applications it is around 10 mm. Typically any insulation you will not put anything less than 10 mm you will definitely put more than 10 mm. So most of the times this care is taken care of. However if one wants to do the calculations and show we have to ensure that our critical radius of insulation is much sorry our insulation thickness is much larger than the critical radius of insulation that is the concern. Yeah go ahead. My question is the same again on critical radius of insulation the graph you shown of q max versus R critical. If the situation is of adiabatic type then for which practical application how will we vary q with R? For adiabatic situation then for what critical radius of insulation we show. Let me ask you back the question how do you generate an adiabatic condition the question asked by one of the participants is how do I calculate or what is the usage of this critical radius of insulation under adiabatic situation. My question back to the participant is how do you generate adiabatic condition? Professor please tell me how do you generate adiabatic condition in any heat transfer application for example heat exchanger. How do you generate an adiabatic condition? No sir adiabatic it cannot be generated but we can provide insulation but I mean to say that how much by insulation we can go down for the heat transfer. Okay and for that what should be the critical radius that curve is going on decreasing up to what we can go. Okay see the question now I understood the question asked is to generate adiabatic condition what should be the radius of insulation. Okay to answer this question there is no way that you can make you can get purely adiabatic there is going to be heat loss no matter how much thickness we put there is going to be heat loss all that we are saying is that the temperature drop across the insulation is going to decrease with the thickness but there is going to be heat loss heat loss is bound to be there. See if you put a sweater if you put a sweater aren't we feel aren't we not feeling going to feel cold at all it's like asking how much thick sweater I should wear so that I am not going to feel cold at all. No matter how thick sweater I use I am going to use I am going to feel the cold but the temperature difference between the outer surface sweater temperature and my body temperature is going to decrease. There is going to be heat loss it is quite difficult or almost impossible to generate adiabatic condition just by thickening the insulating material. Good evening please ask the question we are able to hear you. So my important question is why suction lines are always insulated and whether it is to be insulated below critical radius or above critical radius. What lines? Suction lines of compressors in case of refrigeration systems. The question is why do we insulate only the suction lines of refrigeration equipment and if at all if it is insulated on the suction side whether that insulation should be above or below the critical radius. This is the question asked by one of the participants. So I don't think we should be insulating only the suction side. Why not on the pressure side? I think all the heat exchange equipment whether it is condenser or evaporator. Compressor. Compressor we will have whether on the suction side or on the pressure side whether it is evaporator or the condenser both have to be insulated and definitely whether it is condenser or evaporator the insulation thickness has to be more than the critical radius of insulation. He is talking about are you specifically asking about compressor? Suction line of suction line joining from the evaporator to compressor it is always insulated. I am interested to know why it is insulated and what is the criteria in case of refrigeration system it is always insulated and condenser is never insulated in case of the refrigeration system. My take on that would be the following. See evaporator typically operates at lower temperature. Compressor inlet has to be as close as possible to a liquid state because compressor power is directly proportional to this specific volume of the fluid. So, if there is a phase change and it becomes starts to become a vapor then you are going to talk of a larger power consumption because you are going to handle gas. Yes, you are going to handle some amount of gas but even the inlet therefore you do not want to increase the temperature as much as possible. That is probably the explanation I can think of at this moment. Yes. My question is you have spoken at length about the various forms of heat transfer the conduction, radiation and convection. Now I would like you to elaborate on heat transfer during orientation changes. For instance in equinoxes there is actually a tendency on people that there is an increase in radiation during equinoxes. So, what exactly is the reason? Is there an inclination of the range of what exactly? Equinox. Have I heard you right? Exactly. Second question? Yeah, the second question is you have given a very nice example, a very practical example of this various forms of heat transfer through a cup of coffee. So, give me more practical sort of an example while explaining the relationship between viscosity and temperature. Viscosity, we can easily give an example. Viscosity usually increases with the increase of temperature in case of gases and viscosity decreases with the increase of the temperature in case of liquids. This is general and we also explain that through cohesion and adhesive forces because in case of gases what happens is that the intermolecular interaction or the collisions increasing with the increase of the temperature. So, the viscosity or the resistance increases in case of gases. On the other hand in case of liquids it decreases because the cohesive forces the bond decreases because of the increase of the temperature. So, viscosity we can explain but I do not know your first question. First question I will take a short at it. Equinox. The question is whether it is equinox or whatever be the situation. Probably what I think happens in an equinox I have forgotten the actual phenomena. I know that it is the day when the when the day and the night are equal to 12 hours each. But I think it is to do with the relative position of the sun with respect to the earth. So, I think that is the time when probably from radiation point of view the distance is either minimum or minimum. So, that you are going to have a larger radiation component. Because the temperature of the sun is fixed the temperature of the earth is also roughly the same at a given location probably it is the relative distance which is going to matter. And we cannot we have to fix the location. So, if you are at a particular place probably what you are saying if it is true the only reason I can think of is the relative orientation of the two celestial bodies that is the earth and the sun. I do not have a better explanation than this. You know. Question number one, what is the influence of thermal diffusivity and kinematic viscosity on heat transfer when the heat transfer is taking place between the surrounding and spherical cell? Assume that there are some fluid inside the spherical tank. What are the influence of thermal diffusivity and kinematic viscosity of the fluid on heat transfer? Number one, question number two what are the factors which influence the overall heat transfer coefficient when the combination of convection and conduction is taking place? We will take the second question. There are two questions we will come back to first little later I will rephrase question number two. His question was what are the factors which influence the overall heat transfer coefficient which involves conduction and convection. The factors that influence overall heat transfer coefficient u are essentially the factors which influence the convective heat transfer coefficient and the conduction resistance. So, from definition we know u is equal to u a is equal to reciprocal of the thermal resistances. So, it depends on the nature of the fluid, it depends on the nature of the flow, it depends on the type of geometry that you are dealing with. So, exactly the same parameters which influence h the same parameters influence u, the same parameters which influence the resistance associated due to conduction that is what is going to influence u. So, it is a combination of these two which is going to influence u. The first question could you please elaborate again. The ambient is air at room temperature. What are the influence of thermal diffusivity and kinematic viscosity that is transport properties of a fluid on heat transfer. For example, if the more heat is transferred from the ambient to the inside the spherical shell for example, liquid nitrogen is available because of the transfer is there because of the change in properties transport properties. Then the evaporation rate will be higher, then there is a chance for the explosion of liquid nitrogen. Thank you. Actually we have not there is a question on influence of thermo physical properties that is alpha and nu on liquid nitrogen or spherical shell situation. We have not understood the question very well, but we will try to explain it with the problem that we have illustrated. So, see if we have to see that whether the leakage or the leakage loss is more all that we can say is that these resistances should be as less as possible. So, that means the heat loss can be high only when the resistances are less. So, I can see only when the resistances are less means the convective resistance can be made less only when the heat transfer coefficient is high. So, but then I cannot make inadvertently this heat transfer coefficient high. Yes, I think now perhaps I am understanding your question what you perhaps mean is yes, compared to natural convection if I have a forced convection let us say I put on a fan in front of my container then my convective resistance decreases and then my heat transfer rate increases and the leakage loss rate will increase. So, essentially it is boiling down to the resistances. So, to answer thermo physical properties that is the new coming in here is only in terms of Reynolds number if it is a forced convection. So, other than that I cannot see directly the kinematic viscosity effect coming in here and affecting the heat loss rate. If it is natural convection yes it is going to be Rayleigh number which is G beta delta T divided by alpha nu. So, as the nu increases my Rayleigh number decreases the natural convection effect will decrease. So, essentially whether it is natural convection or forced convection the thermo physical properties that is the kinematic viscosity is indeed having an effect, but ultimately this effect will be on H only. So, that is how I think we can understand this problem. There are some cases practically cases where the inside the spherical cell some fluid is there, liquid is there there may be a chance for turbulence while traveling. So, if the turbulence comes to a picture then the Reynolds number is also increasing. In that case what is the effect of thermo physical properties on heat transfer? See the question is the question asked is what if there is a turbulence inside the container of this problem inside the container of this problem. Yes professor had told that we have neglected the resistance because of the container because inside the container of the fluid. If there is turbulence inside ultimately what will happen there is no flow it is a container. If there is a turbulence then there can be some natural convection occurring inside. So, there is a resistance added on if there is resistance added on actually the heat loss rate should decrease. So, it is going to be a good situation if there is turbulence inside the loss will definitely decrease it is not going to make my life difficult. It is only going to aid my heat loss in terms of heat loss. How thermal conductivity varies with density of solids liquids and gases. See thermal conductivity is directly related with the density only. See why is for example if I ask myself a question why is thermal conductivity of solid I keep saying I have been telling this since morning twice or thrice thermal conductivity of copper is 400 thermal conductivity of water is 0.6 thermal conductivity of air is 0.02635 watt per meter Kelvin. So, if you see here solid is hundreds liquid is points one one decimal and gases is two decimals. So, why is this answer is in your question itself that is density. So, the density of solids is very high the density of solids is of the order of 8000 this density of liquid is of the order of 1000 that means density has decreased around 10 times. Now, if I go to the density of air it is almost 1000 times lesser. So, that is how even the thermal conductivity is also decreasing how closely my molecules are spaced so that the molecular diffusion or the molecular interaction is aided or abated decides my thermal conductivity. So, thermal conductivity and density are directly related. I am not comparing conductivity of metal solids liquid and gases, but in the same solids suppose we are taking more dense material then thermal conductivity will be different. So, within the same medium itself what is the effect of density? Same answer is again same if I have a denser material thermal conductivity of denser solid material will have higher thermal conductivity as opposed to again solid whose density is lower. Let us take an insulating material if you go on packing it densely the thermal conductivity of the insulating material will be very less but if I pack it loosely then the porosity has increased so thermal conductivity may not be very high. So, basically thermal conductivity of any material depends on how densely I pack it. Okay, thank you. Over to Vijay T.I. Yeah, my question is? Yeah, go ahead. The temperature varies with temperature. Question is how does the thermal conductivity of an alloy vary with temperature? Again, we cannot give an unique answer and say that thermal conductivity for all all alloys is going to increase with temperature or decrease with temperature. It depends on the material. It depends on the material but one question has been pending since morning is why the thermal conductivity of an alloy is lower than the independent materials? That question we have kept it as pending. We will look at that question and come back but there is no unique answer for this temperature variation of alloys. Back to you. Particularly for nonferrous alloys how the thermal conductivity varies with temperature? No, why only nonferrous alloys? For any alloy thermal conductivity is going to vary with temperature. It is going to be varying with temperature but I have no idea about nonferrous alloys separately or any other alloy for that matter. We have to look at, look into it. We will come back on the Moodle forum or during discussions in the morning tomorrow on this question. Yeah. My question is with critical thickness of insulation. Is there any relation between economic thickness and critical thickness of insulation? Okay. See, yeah, this is a question is is there any relation between economic thickness and critical radius of insulation? There is no unique answer. Definitely, yes. See, as we can see in the previous problem see if we see in the previous problem as let me answer this in a very generic fashion. First, first answer is that our insulation has to be definitely more than the critical radius of insulation so that my heat loss is less. But over that how much I should be putting is a question, open-ended question. So it depends on how much I can spend and how much heat loss I can afford to have. Definitely, as I said in one of the previous questions we cannot have zero heat loss. That is definitely not possible in any practical situation. We have to live with the heat loss but only thing is that we have to, we can minimize the heat loss with the increase of the insulation thickness but how much you can put that is decided by economics. If you take a power plant and even if you increase the thickness of the insulation by 1 mm, the heat exchangers are as big as one huge building. So if you increase the thickness by 1 mm the cost may turn into crores. So it is not always space. And also space, we need to have space to increase the insulation. So there is nothing like optimum economic thickness. It is all depends on how much money you have how much space you have how much you can afford to put. That is all. So there is nothing like optimal economic thickness. Only we have critical radius insulation. All that we need to take care is that the real insulation we put has to be more than the critical radius of insulation. Yeah, one more question I think. Yeah. Okay. Sir, I have a question. Is thermal conductivity of a material related with the valency of the atom of that material? Yeah, actually they might be related because it is related to free electrons. Free electrons which are there. They might be related directly if you ask me how directly they are related. I think number of free electrons dictate the thermal conductivity vaguely that is what I think. Number of free electrons, sorry the question asked is one of the by one of the participant is the valency is related to the thermal conductivity. The answer is yes I would think so. Why? Because the valency decides the number of the free electrons in any material. So, but how the valency and the number of the free electrons are related I have no idea we have to look into it. Okay. Because I perhaps feel that the answer of the answer of dependence of thermal conductivity with the alloying element I guess they are actually related. That's why I asked this question. If you have any idea please go ahead and answer that. Okay. Probably you are saying there is a decrease in the number of free electrons. It was just a guess I do not have. We also do not have clearly because in regular UG books I am not getting that. Probably true. It might be true. It might be true because We have to see that and Each parent material may have certain number of free electrons but when it is forming an alloy it might be lost completely or it might be reduced so much that the number of free electrons would be very less. Probably. Probably. Because we are not We are not seen. We have to see it and then corroborate. Yes. Yes. I. Yes sir. I also feel so. We will look in that direction. We will definitely look in that direction. It's a one clue for us. Yes sir. Thank you very much. Surat. Yes. So far we have been talking about the thermal conductivity and its variation and independency on the temperatures and the temperature. Yes sir. But my question is the material which is tested upon the Earth's surface which is at room which is at one atmospheric pressure if the same material is been capped in the space for which we are having very low pressure and temperature and suppose at the same time we are having the Mach condition of greater than 1 or greater than 5. At that time we are having the atmosphere which will be generating electromagnetic waves. So do we considering that kind of do we considering that kind of thermal conductivity variation for the space application? We have to. We have to definitely take care of there will be influence of pressure. See the question asked by one of the participants is he is the thermal conductivity going to be different he is going to be different if I measure in Earth and in space because the pressures where space and Earth are different so in space I am moving at a high Mach number that is the question asked definitely the thermal conductivity will be different dependent on pressure but how much depends on the amount of the pressure what we operate but there is no close form answer again for this question but all that I can say is that the thermal conductivity like it is dependent on temperature it is also dependent on pressure but it is not maybe as strong function as temperature. And any testing which is done has to be done at situations where it is going to be put in use so for space situation applications if you are if you are done calculations and obtain some value of thermal conductivity which is at room temperature definitely it is not going to be valid I think we are question is coming from Columbia accident where that there was a peel off because of the brick had to be peeled I mean fell off because unable to withstand the heat probably from that you are coming definitely will have to take care of the operating conditions which would be high speed pressure and all these also will translate to heat directly high speed will translate to heat I think directly so you will have to test it in those conditions in the lab simulate those conditions and that is what happened in even in the failure of challenger shuttle Dr. Feynman looked at the what was the reason for the failure of the challenger shuttle the gasket in the rockets which was being used was tested under ambient conditions but actually it was supposed to be used in cryogenic rockets which are operating at cryogenic temperatures and pressures different so definitely the conditions under which they are being used and under which they are being tested have to be same similar back to Hemant Sir my specific question is is there any is there any body force is effect on the solid material conductivity the last question you asked was is there any influence of the electromagnetic force on the thermal conductivity body force that is the body force electromagnetic force electromagnetic force that can be considered body force that can be considered as body force so the question is whether electromagnetic force which is a body force he is having an influence on the thermal conductivity on the face of it I cannot imagine any effect of the electromagnetic force on the thermal conductivity but honestly I do not know the answer if it causes rearrangement of the molecules then yes I do not know see it is a hand waving answer again so that is what professor is saying is that if structural rearrangement structure is going to change because of the application of the electromagnetic forces on my solid then only my thermal conductivity is going to change my molecular structure is not going to change why should my thermal conductivity change but then this is a vague answer we have no answer for this we have to look into it specifically Hemant why do not you come back with some answer yeah definitely sir I will get back to you later with the answer yeah okay yeah I think we are okay that is for the day