Let's say you really need to find reliable information about the best diet for high blood pressure, or heart disease, or diabetes. Where do you go? Do you go to a website sponsored by Big Pharma that wants to sell you pills to fix your problem? Or do you want to treat the cause? Welcome to the Nutrition Facts podcast with the latest peer-reviewed research on the best ways to eat healthy and live longer. Today we take a close look at the mighty power of vitamin C, and we start with the risks and benefits of using vitamin C for depression and anxiety. Emerging evidence suggests that higher daily intake of fiber-rich fruits and vegetables is associated with lower incidences of anxiety in adults, and at the same time greater happiness, higher life satisfaction, and greater emotional well-being. So persuading people to consume more fruits and vegetables may not only benefit their physical health in the long run, but also their mental well-being in the short run. Fruit consumption, for example, has protective association with leaving killers, like heart disease, stroke, diabetes, and cancer, as well as depression. The question is, why? Several different mechanisms have been proposed. For example, it may be the antioxidants and anti-inflammatory properties of produce, like averaging the free radicals that are involved in some of the inflammation associated with depression. If that's the case, what about just taking vitamin C supplements? The brain has some of the highest levels of vitamin C in the body, so the thought is, if we take extra vitamin C, it may have some sort of therapeutic role in brain diseases, especially given it's not just an antioxidant, but also has other critical functions in the brain, such as helping to build neurotransmitters like dopamine, so you don't know whether it actually helps until you put it to the test. One study found a beneficial effect, adding vitamin C as an adjunct treatment to an anti-depressant, while another study found no benefit from vitamin C supplementation. So there are mixed results for vitamin C and depression. Here's another study that found no benefit when it came to depression, but those randomized to vitamin C instead of placebo pills did show a significant decrease in anxiety level. And this wasn't only seen in this study. The effects of oral vitamin C supplementation on anxiety in students, double-blind, randomized, placebo-controlled trial. High school students were given 500 milligrams a day, or placebo. 500 milligrams of vitamin C is about what you find in five oranges for yellow kiwi fruit or guavas, or one and a half yellow bell peppers. Within just two weeks, the vitamin C reduced anxiety compared to placebo, along with providing a significant drop in heart rate. Given these data showing vitamin C may have anxiety-reducing effects, researchers sought to find out if only a single dose could acutely affect emotional states. And indeed, within only two hours of taking some C, subjects experienced a significant drop in anxiety compared to placebo, though only among those who started out the most anxious in the first place. As a bonus, vitamin C supplementation may lower your blood pressure for a few points, but whole fruits and vegetables can do the same thing and may even do it better for those who need it the most. As I've shown previously, even just adding two servings of fruits and vegetables a day can have psychological well-being benefits within only two weeks, and you won't be put at risk of kidney stones like you would with vitamin C supplements, though that appears to be only a problem in men. Here's a fun fact. There are now experiments that can show how much vitamin C our body absorbs and excretes. Here's the story. For many years, the RDA, the recommended daily allowance for vitamins, was just based on preventing deficiency with a margin of safety. But the minuscule amount of vitamin C, for example, needed to avoid scurvy, not necessarily the ideal intake for optimal health. So what might be the optimal intake of vitamin C? Let's ask the body. How might we do that? By seeing how much the body absorbs and excretes.  But if you take a supplement containing 1250 milligrams, your body seems to realize that's too much, and so clamps down on absorption at the intestinal lining level, and you end up absorbing less than half. So by doing experiments where you slowly ratchet up the intake, you can see when the body starts to say, OK, that's enough. And that magic level of intake appears to be about 200 milligrams a day.  But above that, your body tries to block further absorption, suggesting our intestinal vitamin C transport mechanisms have evolved to fully absorb up to about 200 milligrams of vitamin C a day. In addition, vitamin C is reabsorbed in our kidneys back into our bloodstream to maintain our vitamin C blood levels up at around 70 or 80 micromoles per liter, which is what you reach at a vitamin C intake of about 200 milligrams a day.  So based on these kind of data, one might propose that 200 milligrams is the optimal daily intake of vitamin C. You can confirm using disease data at what daily intake of vitamin C is there the lowest stroke risk, for example, apparently at about 200 milligrams a day. While dietary vitamin C intake was associated with a lower stroke risk, vitamin C supplements were not, which is consistent with the overall body of evidence showing that antioxidant supplements in general don't seem to protect against heart attacks or strokes. But wait, can you get all the way up to an intake of 200 milligrams a day without taking supplements? No problem. Single servings of fruits and vegetables may have about 50 milligrams each, so a measly 5 servings of fruits and veggies a day could get you to ideal blood levels. Finally today, what can we conclude about the role of IV vitamin C after 33 years of trials involving more than 1,500 patients? Studies in the 70s showed an extraordinary survival gain in terminal cancer patients with vitamin C is simple, relatively non-toxic therapy, and so no wonder it got a lot of attention, especially when reported by a world-renowned scientist Linus Pauling. But studies like this in the 1980s found no such benefit, and so last they were left with the inevitable conclusion that the apparent positive results in the original study were the product of bias rather than treatment effectiveness. In the 1990s though, an alternative explanation arose. The disappointing 80s research only used oral vitamin C, whereas the apparently successful 70s experiments also gave vitamin C intravenously, and we didn't realize until the 90s that the same dose given IV can lead to dramatically higher levels in the bloodstream than if taken orally. So maybe high-dose vitamin C does help in terminal cancer, but maybe only when given intravenously. Encouraging case reports continued to be published. Here there was a regression, remission, and cured, documented, and individual cases of advanced kidney cancer, bladder cancer, and lymphoma. But that's three success stories out of how many. I mean, if it was 3 out of 100 or even 3 out of 1,000, well, okay, if the treatment is sufficiently non-toxic. But there's evidence that IV vitamin C is widely used in the alternative medicine world, as in 86% of practitioners serve it. Just those 172 practitioners alone treated about 10,000 patients a year, and you ask the manufacturers, and they're selling hundreds of thousands of vials of the stuff in the US. Now it's not all being used for cancer, but presumably at least thousands of cancer patients are being treated every year with IV vitamin C. Making the publication of three remarkable case reports seemed less impressive. So no matter how amazing these cases seemed, it's possible the cancer's just spontaneously regressed all on their own and was just a coincidence that happened after they were given vitamin C. To know for sure you have to put it to the test. To date, there's been some small pilot studies, and the results so far have been disappointing. The good news is that even insane doses of IV vitamin C seem remarkably safe, but failed in this study of two dozen patients to demonstrate anti-cancer activity. Similar small studies have been published all the way through to the present, with tantalizing but inconclusive results. What we do know is that the present state of cancer treatment is unsatisfactory. People have this perception that chemotherapy will significantly enhance their chances for a cure, but put all our cancer killing chemo together, and the overall contribution to five-year survival is on the order of two percent. All those side effects for 2.1 percent, at a cost of maybe $100,000 per patient per year. So it may be worth looking deeper into therapies like IV vitamin C. However, the lack of financial reward, since vitamin C can't be patented and sold for $100,000, and bias against alternative medicine could dissuade conventional investigators and funding agencies from seriously considering this approach. So decades later, what can we conclude? After trials which have included at least 1,600 patients over 33 years, we have to conclude that we still don't know whether vitamin C is any clinically significant anti-tumor activity. Although there is currently no definitive evidence of benefit, the Mayo Clinic randomized controlled trials did not negate the potential benefit based on what we now know about the oral versus IV routes of administration. So we're kind of back to square one. Does it work or not? There are highly polarized views on both sides, but everyone's working off the same incomplete data. What we need are carefully controlled clinical trials. The question is, what do we do until then? If it was completely non-toxic, then one would argue, well, buddy, you've got to lose. But it's not. It's only relatively non-toxic. For example, there have been rare but serious cases of kidney injury reported. After all, if it's so safe, why did our bodies evolve to so tightly control against excess absorption? It can also be expensive and time consuming. Each infusion costs $1 to $200 out of pocket since insurance doesn't pay for them, which can be quite a boon for alternative medicine practitioners. About 90% of the millions of doses of vitamin C being dispensed are in for-profit arrangements. So there's financial pressures pushing in both directions for and against this treatment. Now, given the relative safety and expense, though, if controlled studies even find a small benefit, it would be worthwhile. And if they don't, okay, fine. The vitamin C question can be put to rest once and for all. But in cancer treatment, we don't have the luxury of jettisoning possibly effective, relatively non-toxic treatments. We should revisit promising avenues without prejudice and with open minds. We would love it if you could share with us your stories about reinventing your health through evidence-based nutrition. Go to nutritionfacts.org slash testimonials. We may share it on our social media to help inspire others. To see any graphs, charts, graphics, images, or studies mentioned here, please go to the Nutrition Facts podcast landing page. There you'll find all the detailed information you need, plus links to all the sources we cite for each of these topics. For a timely text on the pathogens that cause pandemics, you can order the e-book, audiobook, or hard copy of my last book, How to Survive a Pandemic. For recipes, check out my second to last book, My How Not to Diet Cookbook. It's beautifully designed with more than 100 recipes for delicious and nutritious meals. And all the proceeds I receive from the sales of all my books goes to charity. NutritionFacts.org is a non-profit, science-based public service where you can sign up for free daily updates on the latest in nutrition research via bite-sized videos and articles. Everything on the website is free. There's no ads, no corporate sponsorship. It's strictly non-commercial. I'm not selling anything. I just put it up as a public service as a labor of love as a tribute to my grandmother, whose own life was saved with evidence-based nutrition.


Welcome from Intagio 2019 here in Stuttgart. The opinion leader talk with Karen Weiss. Thanks for joining us. Senior Industry Manager for Civil Infrastructure at Autodesk, one of the three sponsors of Intagio. Nice to meet you today. Nice to meet you. Let's talk about BIM. You did a keynote about BIM a few minutes ago. BIM is not a new keyword in the geospatial branch, but it becomes more and more important. First of all, what is BIM? What does it mean the same than a few years ago? So I think what people have traditionally thought about BIM is that it's a software for designing buildings. But in reality, really, BIM is a process and it's for buildings and infrastructure. So it could apply for roads, bridges, wastewater treatment plants. It's really a process for creating and exchanging digital information throughout the life cycle of an asset. So it's about attaching information or attribution to digital 3D models. So that's essentially what BIM is. Let's have a look at the reality, the status quo of BIM first in an international perspective. Yeah, so I think internationally, a lot of the BIM adoption and implementations for the past 10 years have really been focused in Europe. I think they have been the leaders, essentially the UK, maybe some of the Nordic countries. But a lot of other countries are taking note. They don't want to be left behind. So we're now seeing pending BIM mandates in places like Germany, Japan. We have the US taking a closer look at it as well. We're in Germany here. Is Germany moving too slow? If you read the newspapers here, there's every day a headline about airports, train stations, tunnels about infrastructure projects that failed. I don't think they're moving too slow. I think they're on the journey, which is good, the recognition that you need to actually begin to look at new processes and ways of transforming the way that you're working, and certainly so that you don't have some of those project failures. Yeah, so it's a journey. So I think you guys are right on track. Who needs to become active to push BIM? Is it the administration, the industry? I think the industry, more than anything, is probably the one that's going to make it happen. I mean, politicians can put things into law, but it really is going to be the industry that makes it successful. What are your innovations of Autodesk you're showing here at Intergeo? So some of the stuff that we're showing back at our booth have to do with some of the integrations that we've built with our strategic alliance partner, which is Esri, who are also here at Intergeo. We're doing a lot of stuff with scan to BIM, or the whole idea of reality capture and turning reality meshes into BIM models. So that's a lot of stuff we're showing up at the booth. But some of the stuff I talked about in the keynote had to do with even future-looking things, things related to robotics and how they're going to change the industry, things like generative design and letting the computing power of the cloud actually evaluate thousands of options so that you really only have to look at the five that are the most important. So those are some of the exciting things that are happening at Autodesk. Did you get some inspiration here at Intergeo the last days? I want the birdly thing where you fly in virtual reality. I think there's a lot of very interesting things that we're doing as an industry. So certainly just walking around the exhibition hall and seeing some of the stuff that people are doing, it's exciting. Karen Weiss, thanks for joining us here and thank you for watching. Bye.


Hello everyone my name is Jane Katten and I'm the CEO at Agewell. I want to welcome you to our show tonight called Aging Matters brought to you by our special sponsor MVP Healthcare. We'd like to thank them very much for their sponsorship. Before we jump into our show I'd like to tell you a little bit more about Agewell. Agewell is the largest area agency on aging in the state of Vermont and we serve clients in four counties in Franklin, Grand Isle, Chittenden and Addison. Last year we served over 15,500 clients and let me tell you a little bit more about the programs that we offer. You may have heard of Meals on Wheels or Home Delivered Meals. This is a tremendous program where we bring nutritious food, therapeutic diets to our clients straight to their homes. We have congregate meals. We also have wonderful events that include food, activities, music all around the state. The other wonderful part of our programming is the wellness portion of our programs and that includes evidence-based programs that are related to activity. So wellness, exercise, you may have heard of Tai Chi or Tai Chi for arthritis. So these are activities that our clients can take part in anytime. We also have a wonderful group of social workers who are out in the field and they are providing a little bit more wraparound support for clients who may need more help so that they can stay independent at home. All of our clients are over the age of 60 years or under the age of 60 with a disability on long-term care Medicaid. The last program that is so important to us is our volunteer program. It is over 1,100 people strong and our volunteers really are the backbone of our home-delivered meals program. But not only that, they offer friendly visitation. They might do some transportation to doctor's visits or any other thing that our client may need help with. So as we've learned a little bit about age well, our show Aging Matters will be sharing interesting topics that we think are important to help people age well. So every month I'll be hosting different guests and we'll be exploring topics of interest. And today I'm delighted to have a wonderful guest with us here today, Dr. Alan Ramsey. Welcome. And he's here to discuss two very interesting topics. The first one is called the social determinants of health. And the second is called food as medicine. So welcome, Dr. Ramsey. Again, nice to see you. Thank you. And before we jump in to some questions specifically about our topics, maybe you can tell us a little bit about your background and what interests you about what we're going to speak about tonight. I'd be happy to. And Jane, thank you for inviting me to participate in this first program on how important aging is to all of us, all of our Vermonters. So I've been a family doctor in Vermont for over 40 years. Most of that was spent at Colchester Family Practice in the Department of Family Medicine. And then in 2012, I was appointed to the Green Mountain Care Board for five years. And so I moved my practice to the People's Health and Wellness Clinic in Berry, Vermont, which is a free clinic. So as you might expect, when you practice this long, your patients age with you. And so aging becomes more how you age healthy in a healthy way becomes more and more important. So that's where my interest in the Age Well Board of Directors evolved. You know, I've been on the board now for five years. And I've found that being involved in a community organization that can make things better for my patients as they age is a really important service. And so that's what happened. Well, thank you. That's that is a tremendous background and we're very lucky to have you here this evening. So as I mentioned, Dr. Ramsey, our show today will focus on the social determinants of health and a concept called food is medicine. So let's jump right in. And I've got a few questions to start us off. Tell us what exactly are the social determinants of health? We've heard this term in health care and in the social services. What are they? Okay, well, let me start by saying healthier organizations, insurance companies divide social determinants of health into a set of domains.  So when I see a new patient at the People's Health and Wellness Clinic, I always ask them five or six important questions. The first question goes without saying, do they have access to the health care system? Typically no. That's why they're being seen in our free clinic. Number two, do they have housing? Number three, do they have transportation? Number four, what's their educational status or are they employed? In other words, what's the economic social determinant that they have to face? Are they lonely? Do they have family in the area? Do they have social contacts that prevent them from declining into a sense of loneliness? And lastly, and also very importantly, do they have food security? So in the real perspective of an office clinic, that's what happens. Now, I'm asking those questions, knowing that there's very little I can do in my clinic session to really reconcile some of those important issues. So what I have to do is to look for community agencies that can provide services that I can't provide in the office. Now, are they important? It has been studied and looked at over and over again that people who suffer for any one of these important social determinants of the health have poorer health outcomes. They cost more in the health care system. They generate more problems in the system. So addressing social determinants of health and not only identifying them in primary care, but seeking out organizations like Agewell that can really participate in lessening the environmental effect of those things. Dr. Ramsey, you touched on the concept of the five domains. And one of them I understand from my research is called social and community context. So as we think about the five domains, you talked also about social isolation, loneliness. Is one of the domains more important than the other to focus on? Are they all an issue together? What do we do about these? Well, that's a great question. In some people, typically not as we age in younger people employment, the economic issues. I think as we age and have fewer social interactions with, through work and family, loneliness can be a very critical issue around these social determinants. Loneliness means it contributes to depression, contributes to cognitive decline, contributes to worsening self care, contributes to acceleration of chronic disease processes. All of those things happen when a person becomes lonely and isolated and don't have the contacts that they need. Thank you. Those are, those are so impressive. I don't think we realize how impactful some of these social determinants are on people's lives. So let's take a moment, you know, and especially as you're talking about isolation and loneliness, that let's talk a moment about the pandemic and as we're emerging out of the pandemic. In your practice, did you see the effects of the pandemic or the isolation that your patients or even some of our clients may have felt during that time? How do we, how do we address that? Are there still effects going on from, from emerging out of the pandemic with regard to isolation or social involvement, social activities? I think there's still going to be a recovery period. I think we don't know what the oncoming winter brings us in terms of flu and COVID and now we worry about RSV. So I think there's going to be a slow, slower transition out of some of the consequences of the pandemic. And those consequences for me were more difficulty discussing other behaviors with my patients, talking about smoking cessation, talking about immunizations, you know, talking about substance alcohol use. All of those things became more difficult as people were more isolated. So we had, so the idea is to think about how to engage that person with agencies outside of the clinic that can deal with loneliness, can deal with some of these issues. And it's another reason I got involved in age well. So, but there's more than age well, you know, and I do make certain recommendations to my patients who I feel are getting more and more isolated, asking them to reach out a little more aggressively to their family and to their other social interactions, reach out to their church or synagogue or mosque or exercise classes. There are things that people can do as well as utilize services in the community. There's nothing probably more important than that. So staying healthy is another big part of avoiding loneliness.  Wonderful. Well, thank you for those thoughts and those those strategies. I think they're very, very important to remind everybody. So as a community based agency, one of age well's main roles is to tackle food insecurity, among other things that you heard about earlier. So the idea of nutrition being a big part of managing the social determinants of health, is this also important? Yeah, you know, people realize that that if you really think about it, we almost have in this country and around the world, an epidemic of diet related chronic disease. Diet, we think diet related chronic disease. In the United States, it's manifest by obesity and rising significantly rising rates of diabetes. But there are many other things that are involved in that. I call it epidemic of dietary related chronic disease. And as a physician, I got very little training in nutrition. And so and I don't think that's changed much in the last 25 or 30 years of medical education. There's just so many complex issues that take take the place of learning about nutrition, learning about food as medicine. So let's let's shift gears a little bit then and talk more about the idea of food as medicine. We're hearing more about this term everywhere we go now. What does that mean? What is it food as medicine? Well, to different people, it means different things. And you know, in an office setting, it might mean nutritional education. Okay. In a community setting, it might be therapeutic design meals, or Trent trying to get people to transition to more fruits and vegetables, you know, so it can mean a lot of different things to different people. But remember, what we eat is the one thing that we can control that can have an at an advantageous effect on how we age and how we stay healthy, how we eat. That's a behavior. So and it may be more important than any medicine that I prescribe, you know, and there have been studies about this studies about the impact about transitioning to fruits and vegetables and the control of hypertension, the reduction of cardiovascular risk. There have been studies. I think they stopped doing studies because they were also positive. So we have a lot of information to support the fact that food is good medicine.  But I think in our program, and I know I hope you'll be able to talk a little bit about the therapeutically designed meal program. Definitely. Just just to take this a little bit further, it's interesting that the concept of good food and nourishment is being promoted more and more as good medicine. But hasn't this always been the case? I think you were alluding to this. We remember the old adage, an apple a day keeps the doctor away. We've all heard that when we were growing up, certainly. So what's changed to make this concept new? Well, I think the prevalence of chronic disease, you know, change. But you remind me about some of the history here. And the best quote that I found was from a little over 2,000 years ago. A man named Hippocrates said, let food be thy medicine and medicine be thy food. That is a very famous quote that turns up in the American Society of Nutrition uses that to really say that we've talked about this for 2,000 years. And the issues that we get into is that changing how we eat and changing our nutrition is something that is going to help us down the line. It's not going to help us tomorrow. And we seem to want quick fixes on everything. Now, how does that apply to the aging Vermonter? Okay, the aging Vermonter is going to benefit over a shorter period of time by having the right nutrition to assist in the control of chronic conditions as they evolve. Okay. So an 18 year old or a 20 year old or a 25 year old over 20 or 30 years changing them is going to have a big deal. A 60 or 65 or even 70 year old person who changes who makes that transition to more plant based nutrition is going to have a benefit fairly quickly. Okay, they're going to feel better. They're going to have better exercise tolerance. They have better energy. They're going to sleep better. Those things have all been studied and proven so wonderful. Thank you. So it sounds like there's many things each of us can do to manage our own health, which is the point you're making, definitely, like focusing on simple steps to eat healthy foods. I know that H well offers therapeutic meals. You mentioned this just a moment ago through our meals on wheels program. And from your perspective as a family physician, can these tailored meals talk a little bit more about how the tailored meals can help if a person's challenged to plan meals. They might have a chronic disease, diabetes, or even get the right kind of groceries from what you know about therapeutic meals. Well, again, take looking at the evidence. There have been some very specific studies that have shown, you know, short term and long term benefit, a proto prescription program. Some insurance companies, some payers are saying that we will provide fruits and vegetables through a prescription program. And have shown that that does things that reduces the blood sugars, reduces the weight. So what we what our therapeutic meals are designed to do is to take away some of that complicated decision making around changing from eating one way to changing to eating a new way when you get a meal delivered that's therapeutic, you don't have to worry anymore about Oh, you know, is this what's best for me. So I think that's an important aspect of a third of our program. We don't provide, you know, pharmaceutical orders or prescriptions for vegetables and fruits like something that we provide tailored therapeutic medication or meals. So so your your conversations or your thoughts remind me of a story about a client who is actually on a therapeutic diet with age well for diabetes control. And he has reported that the portion sizes, the the types of foods he has on his diabetic diet, and just the the frequency that he's learning how to eat he's taking advantage of some dietary counseling. He is losing weight. His diabetes is coming under better control. And his family physician is singing his praises, because he's thought about his his diet to help manage his diabetes. So I think you've hit on exactly the right concepts. I think we all have stories like that. Where we juggle medications and do the best we can. And then finally, we realize that a change in eating habits that therapeutic meals is going to be medicine, it's going to be food is medicine. So let's think take that one more step. This is this is you talk about fruits and vegetables, prescription for health, think about eating healthy. What do you think is holding back our health care system of providing more support? Maybe I think the insurers are starting to catch on. Certainly health systems all over are starting to catch on. But but what is really holding us back from investing in this kind of concept of food as medicine? Well, it's complicated. Again, some of it is short term outcomes versus long term gain. Some of it is how we pay for health care. You know, and everybody on the age well board is knows having spent five years in health care policy on the Green Mountain Care Board. It became very clear that the way you're going to control how the growth in health care costs in Vermont is to invest more in primary care mental health and community based services. That is how we achieve the holy grail of controlling the growth and health care costs in Vermont. Now, has that happened? Not to the degree where we see health care costs being controlled.  But our investments in those three categories, primary care, mental health and community based services like age well, still lags behind the necessity that what in need where it needs to be. Well, let's hope that over time, more investment in population health will come our way. So I want to thank you, Dr. Ramsey for sharing some very interesting insights into the social determinants of health and food as medicine to wrap up some of our thoughts. If you could offer advice on what you think are the most important or maybe the most simple steps that older adults can take, especially if they're dealing with the challenges associated with the social determinants of health. What would that be? Well, stay connected to community based services to your primary care office. Make them aware of your needs. Let offices help coordinate services or refer you to an agency where we care management services like age well can be provided. The health care system, I think of it metaphorically as an ocean. And there are certain things like I think that the People's Health and Wellness Clinic is a safe haven in this ocean. It's like, you know, I think of age well is the same way. The health care system is complicated, difficult to navigate people, particularly as the age need all the help they can be, they can get. So I would ask I would suggest that I would suggest when things are getting worse emotionally, physically, think about ways to get into a counseling arrangement counseling situation, take advantage of volunteer programs, seek out community service programs that you can volunteer in that you're passionate about that you really believe in. So there are things that can be done. And it's just a matter of accepting the help that's out there. That's wonderful. Thank you for those thoughts. Dr. Ramsey, I'd like to thank you for taking the time today to join us on Aging Matters. And to all our viewers, I hope you enjoyed our show today. And please tune in next time as we dive into some new topics that will help us all to age well. And remember, as Dr. Ramsey so wisely suggested, if you or anyone you know needs help or assistance or any kinds of support to help you stay at home to remain independent, please think about age well, our helpline staff are available five days a week. And we have a helpline number that I'm going to share with you. Please call 1-800-642-5119. We're here to help. Take care. And thank you for joining us. I hope to see you next time.


Earlier we used to have a full fridge to convection course long back like this 40 hours, then we compressed it into advanced heat and mass transfer course. Some of you have taken that course and now this has been made into an elective, so that more of convective topics can be covered basically. In that what Dr. Arvind has done so far is given you the for almost 30 hours laminar heat transfer, convective heat transfer study is incomplete without turbulent without the study of turbulent heat transfer, but turbulent heat transfer cannot be done without the knowledge of turbulent boundary layers which cannot be done without the knowledge of turbulence per say. So, this is a very unique and complex kind of a convective heat transfer compared to the laminar convective heat transfer which you have done so far. In your course on incompressible compressible flow you have done incompressible, so boundary layer theory must have been done there, turbulence was done turbulent boundary layers was it one classes we will try to do something about it although the time is a little limited, but we will try to do this. But before I go into turbulent heat transfer and free convection Dr. Arvind I can do the quiet flow you said quiet flow can be done. I would like to tackle one other particular problem in convective heat transfer which is called the quiet flow. It is a very simple geometry it is not a boundary layer flow, but it gives us tremendous amount of experience actually exercise experience in simplifying the total overall complete Navier-Stokes equations to a very very simple set of equations. And then you are able to solve it by hand in the class without necessity of any other complex solution methodologies like series solutions or transformations numerical methods especially you can get with certain assumptions which are very reasonable you can get solutions for heat transfer in a very direct complete fashion without resort to computers or any other complex mathematical techniques. Number one number two what is so great about it why should we do that we have we have very nice codes available today you know you put in all these things into your code whether a finite difference technique finite volume or finite elements you will get the answer that is true. But the beauty of this particular problem as I see it and it is really exciting that very important concepts in convective heat transfer at least couple of them three of them come out of this very simple solution. So basically there are three reasons why this particular flow situation that I am going to do is important one it is considered in literature as one exact solution of the complete Navier-Stokes equations if you please make a difference between the complete set of Navier-Stokes equations and the Prandtl's boundary layer equations what is the difference between these two by the way I will be asking some questions please respond I do not write too much on the board I want you to write down what is the difference between the Navier-Stokes equations and the Prandtl's as the name suggests boundary layer equations what is the boundary layer yeah what is the boundary layer what is defined a boundary layer do not say all that you be a little bit more firm yeah you are right so where the viscosity effects therefore what particular force does viscosity affect no you have to answer me what force does this property of viscosity of fluid affect control share no you should not take so much time to answer this question you know so viscosity property of the fluid there is a force share force these together along rather along with the velocity actually give you the shear stress fine so there is a layer as you said very close to the surface where when you say viscosity is important it is not viscosity that is important actually it has an effect it is a shear force shear stress that is important and these shear forces are of a magnitude much higher than what it could be outside the boundary therefore they are important the property of the fluid which comes into picture is the viscosity for you to have a shear shear force shear stress it is not simply viscosity that is enough there should be a velocity there should be a relative velocity if you look at what is the fundamental expression for shear for viscosity defining viscosity or the shear stress equation give me the complete thing say it loudly if we make mistakes it is ok no problem so you must have the viscosity there should be a gradient it is not simply the velocity the gradient so tau equal to mu du by dy du by del y is the what is this law called Newton's law of viscosity so it is actually a definition for viscosity in one way so what does the Prandtl's boundary layer equation how does it now differ from the Navier-Stokes equations if you want I will go back a little bit before Navier-Stokes equations what kind of equations were present were used for fluid flow what is that Euler's equation so Euler's equations now can you tell me what is the difference between Euler's equations and the Navier-Stokes equation that they look very very similar almost identical except for something what is the difference between Euler's or Euler's equations and the Navier-Stokes equations viscous term is coming into picture in the name that is a very big achievement find out when the Navier why is it called Navier-Stokes equation please find out if you have not when was it actually proposed please find out I want all of you I guess I am interested all of you to be interested in the history of these things history of science per se history tells you a lot today when I am talking about this Dr. Irwin this talking about it is as if we know about it forever it has been as a given thing for us to come to this stage lot of work lot of thinking lot of research has been expended in the last 200 years and what we are giving today is as if it has been there forever you should really look at how the history of fluid mechanics has developed history of heat transfer has developed who have contributed to all this and what were they doing today the moment I talk about heat transfer you will get an expression what were they doing when they did not have the equation who developed this equation for example you know I want you to please think look at history today everything is available at your fingertips so Navier-Stokes equation fundamentally was a great jump in knowledge as well as utility compared to the Euler equation this was in the 19th century 19th century was the time when tremendous advances were made in both in fluid mechanics to an extent in heat transfer but the real advances in heat transfer have been in the 20th century real 1900 to 2000 has been a great period for advance advances in heat transfer per se but as per at least we are concerned convective heat transfer the real foundation for that was in the 19th century starting from the Euler's equations in the Navier-Stokes equations what was what is the fundamental heat transfer equation which was developed in the 19th century which you use it all the time in convection also use it four years of heat conduction find out go to the original paper if you have a chance go to the paper Fourier James Fourier the French mathematician he gave this heat conduction law Navier's Euler's equations were there without discuss terms in Navier-Stokes Navier and so these two are different people by the way find out why there are two names there Navier is different Stokes is different you might have heard of the Stokes hypothesis you have not heard of the Navier's hypothesis so find out why this was called so so Navier Stokes equations finally in the late 19th century really gave a push to the science of fluid mechanics from one particular point of view that is consideration of the shear stresses and only then really the aeronautics industry developed aeronautics industry loved once this point was understood that even for air which has a very low viscosity shear stresses could be important under certain conditions tau equal to mu du by dy so you can neglect the shear stress in a flow either when du by dy is 0 or vanishing or nu is vanishing air has a very low viscosity but even though air has low viscosity and many engineering several engineering fluids including water low viscosity in their flow shear stresses become important when velocity gradients become important that's the point you should look at otherwise viscosity was known they did not know how to bring this into mathematical form what is the D'ambert's principle or D'ambert's paradox if everything is considered as ideal you know in machines ideal fluids so a solid body can move through it forever without being retarded but experimentally everybody would see everybody could see it was retarded and that was what was given tremendous retardation tremendous slowing down of any vehicle which moves in the air including the automobiles for example so there was tremendous research that was going on at that time and the credit for bringing in shear stress into our engineering consideration and mathematical possibilities is given to Navier-Stokes and the Fourier's law of heat conduction from the heat transfer point of view but in 1904 something extremely important also happened 1904 so Navier-Stokes equations were available 1904 something else happened what is that Prandtl let with Prandtl please find out about his life you have a book by him in the library green bound book please go on study that let with Prandtl proposed after studying Navier-Stokes equation after lot of experimentation he was the first one to propose the shear stresses are very important it's all very fine but these are important only adjacent in a very thin layer adjacent clear solid surface on which the fluid is flowing this was a it would now appear to be as a as a what is it as given but for him to come out with that physical idea concept and then take care of the complex normally a Navier-Stokes equation that was a huge achievement of those times now you are coming to that so from Euler you graduated to Navier-Stokes from Navier- Stokes I would say you graduated upwards to Prandtl's boundary layer equations because he simplified them tremendously he said all these complete Navier-Stokes equations need not be considered in their completeness in the layer very close to the surface it is enough if I take certain terms certain assumptions I can make and then a mathematical equation I can derive a mathematical model the solution of which will give me the shear stress what is the major major mathematical impediment I was in difficulty with Navier-Stokes equations the complete Navier-Stokes equations look at the left hand side u del u by del x v del u by del x nonlinearity and nonlinearity and this is the problem with Navier-Stokes equation mathematical point of view for engineers while pure science is important pure mathematics is important but for engineers certain assumptions are okay certain overall picture is okay as long as we get engineering wise applicable solutions without bothering too much about how they originated a scientist need not know engineering but an engineer should know the science behind boundary layers science will fluid mechanics then you will be able to appreciate it better but more than that you will be able to correct yours and later also so let me Prandtl simplified the Navier-Stokes equations into what now we call as Prandtl's bound they are referred to as Prandtl's boundary layer equations meaning they are fully applicable in that boundary layer which is a very thin layer next to the surface this he made it only for the shear stress not for the heat transfer actually although we then expanded up extended upon it is one part I'll come back to this what now we'll come to the heat transfer side what is the fundamental objective of convective heat transfer h why do we want it why give me a complete answer yeah that's the result number is then you know simply a non-dimensional what is that equation give me give me the equation I know you know all of it not that you don't know I'm trying to I'm the my my first my first class I'm the developing region I want to develop by tomorrow day after into my fully developed flow conditions q is equal to and what is it called is it really a law that's the point now I wanted to ask can you okay now just go back and what are the modes fundamental modes are mechanisms of heat transfer so there is these are the leftists these are the rightists here they don't want they say only conduction radiation they say conduction conversion radiation yeah actually convection if you see is a modified form of conduction basically the ultimate mode of heat transfer right at the interface at that first micro layer is conduction how do you know this mathematically what do you do how do you know this no sleep okay no I'm looking at that so how do you connect conduction to convection with this concept let me put it the other way how do you conduct connect conduction to your heat transfer coefficient conduction at the wall at the interface to the heat transfer coefficient what is it so h delta t is equal to minus k dt by dy equal to 0 now on both sides what is the difference in the in the coefficients in terms of the future the characteristics of the coefficients h delta t you have k dt by dy no unit twice okay but anything more than that okay one on the right hand side dt by dy is a gradient and on the left side it's not a gradient okay number that's very clearly seen but I want you to tell me the difference between the other two factors the other factor on the right hand side on the left hand side what is property now you come k is a property of the fluid h is not h is a function of what then you give me the variables that's the flow condition yeah geometry and the properties therefore it is not a property it is a characteristic now therefore now I'm coming to this point q is equal to h delta t or h a delta t we should not be strictly calling it a law now come to conduction write down the expression for conduction for your slug you know that if you want to q is equal to minus k dt by dy write down for radiation q is equal to sigma epsilon t14 minus 324 write down for convection h delta t now look at these three expressions for conduction you have k is a thermal conductivity which is a property on the right hand side for the radiation you have epsilon property coming into picture and in both of these cases of course there is no flow in the convection case you have q is equal to h delta t where there is no property alone properties incorporated in h while you call correctly four years law of heat conduction six siphon words one's law of radiation it is not strictly right to call these newton's expression as newton's law of cooling because it depends upon geometry flow and the property you might say what is so great about it I want you to understand the difference you don't have to accept everything as it is said you know you have to understand that convection is not a in a way not a fundamental mode of heat transfer it is a modified form of conduction it doesn't matter in your calculations but you should understand as scientists engineers similarly newton's law of cooling so then if it is not a law what is it it is simply a relationship it is simply a definition of h no like tau is equal to mu du by dy newton's law of cooling it is a law of cooling it is a law because mu comes into picture it is a property q is equal to h a delta t or h delta t flux h is a characteristic it is a definition of h this was a very fundamental thing find out how this came out of you called it newton's law anyway already so although heat transfer developed tremendously in the 18th and 19th 19th and 20th centuries newton himself has contributed certain things especially newton's second law of motion you are going to use newton's law of viscosity you are going to use and the so-called newton's law of cooling so called i am saying so some of these concepts came from the time of newton that is at the in the 18th century 17th 18th century there there is not much of work then four years law of heat conduction came into picture Euler's equations came into picture graduated to navier stokes equation then came this seminar year of 1904 when prancer said i do not have to solve the entire navier stokes equations because these the engineering at that time the engineering objective of the study was sheer stress as far as the aeronautics is concerned that was the the drag coefficient that they wanted that was the purpose drag coefficient cannot come from your Euler's equation is just does not exist there the complete navier stokes equation has discussed some so it has to be solved then prantle said no you do not have to solve this let me try to simplify order of magnitude analysis scale analysis finally he gave those even though they are non-linear still they are much less formidable than the navier stokes equations u del u by the x plus v del u by del y equal to new del square by del y square minus 1 by rho dp by dx so many terms mathematical terms he cancelled out with certain argument assumptions some very right some approximately right but his intent was can i handle the navier stokes equation in much simpler simpler way for me to get my skin friction coefficient that was only from the fluid mechanics part of you then came of course much later the energy equation the same concept of boundary layer for viscosity and shear stress was extended to the energy equation to then term a thermal boundary layer they simply surmise as viscosity is important in a very thin layer maybe k is important only in a very thin layer although these two may not be equal but they just like a hydrodynamic hydrodynamic is not a nice but hydro is water actually so it is a aerodynamic boundary layer fluid better would be a fluid mechanical boundary fluid dynamic boundary layer like that there is a thermal boundary layer these two concepts which came only in the 20th century 1904 prantles he he presented it in an international conference nobody bothered about nobody bothered till 1934 in one of the international conferences there were six papers on boundary layers 1945 there were 280 papers and by 2000 there is no year in which there is less than 1000 papers on boundary theory that is the import the significance the importance i would even say greatness of this particular concept which we today talk as if i i i came up with this concept i tell you this exists i have never seen it we have done experiments that is a different matter so 1904 it is already 110 years old along with him at the his contemporary was nusselt nusselt now you know he he is remembered with his he died only in 1950s a nusselt number i am now going one step ahead that he transfer coefficient which is a whose definition is given by the newton's law of cooling was given a non-dimensional form by nusselt in 1925 he said he came through non-dimensional he didn't know about the biking ampy theorem at that time he simply made a scale analysis he found this group hx by k was non-dimensional and then he said i i should be able to relate it by that time Reynolds number was already when did the Reynolds number when was it proposed Reynolds number i know the Osborne Reynolds 1883 at another major experiment by Reynolds experiment please look into Reynolds experiment where he injected a colored die into a pipe flow under extremely low velocity conditions and he could see a very nice as now we call a laminar filament of a layer and then when he increased the flow he started saying fluctuations he said what is happening the velocity at every point is changing with time and space that's how the idea of turbulence was actually visualized and then that particular parameter or a period of time it was given the name Reynolds number what does Reynolds number signify what does it physically signify inertia by viscous forces so as you increase inertia is your u del u by del x actually you please make it out Reynolds number is inertia by viscous so rho u du by dx divided by mu d square du by dx square if you do that you will just get rho vd by mu that is vd by nu v being a characteristic velocity Frankel did another thing I mean he he he didn't do it per se but when he non-dimensionalized I mean he made a scale analysis he got this term nu by alpha actually mu Cp by k that is called the Frankel number today now you see over a period of time from the fluid mechanics point of view 1883 Reynolds turbulent laminar turbulent transition came into picture and a number Reynolds number came into existence then Frankel gave the Baudelaire theory in 1904 Frankel talked about Musselt were around 1925 Frankel by the way Frankel did another thing in 1925 we have not had gone to turbulent Baudelaire but I'll tell you now he developed the first what we call the zero order model for turbulent flow called the Prandtl's mixing length theory please note down we will talk about it later so Musselt then gave us the non-dimensional form of x there is nothing more to it we can talk about convection by conduction we can then improve give physical significance they have physical significance so over a period of time you finally got convective heat transfer to be represented by Musselt as a function of Reynolds and Prandtl Musselt is a non-dimensional form of the heat transfer coefficient which came from Newton's so called of Coulomb Reynolds number from Reynolds because of the laminar that that number differentiates between laminar and turbulent flows and then Prandtl number what does Prandtl number signify when I give you a Prandtl number what would you what information will you get fluid properties yeah take off yeah it identifies the fluid that is the thing yeah it's fluid properties therefore it identifies the fluid there is nothing you can't miss anything if you say Prandtl number is equal to 0.72 it is air and most of the gases somebody need not tell you find out whether it is a oil or a liquid metal or water no it is gas end of the matter on the other hand if I said this Prandtl number of this fluid is 0.01 not 0.01 you know it is a liquid metal mu C p by k k is extremely high on the other hand if I say the Prandtl number is some thousand to fifty thousand mu C p by k where k and mu are varying with temperature and that has to be oils so you have oils light oils heavy oils so the moment that is the beauty of this particular number Reynolds number gives you the type of flow non-dimension missile number gives you the non-dimensional heat transfer coefficient which is hd hd by k no you can write it as h over k by d so it is a convective heat transfer coefficient divided by the conduction part it is a relation between these two and then Prandtl number signifies the fluid this is extremely important so if you look at this general expression Nusselt as a function of Reynolds Prandtl you have everything coming into picture here left hand side is what we want that is the objective of convective heat transfer study getting you said Nusselt number in the beginning getting the heat transfer coefficient in the form of a non-dimensional number but it this is a function of the flow the geometry and the properties flow on the geometry property come through the Reynolds number it will tell you a lambda or a turbulent and the Prandtl number says this is the fluid you cannot therefore use this is what I tell a lot of students so do not think the equations are available in the some tables so why should I attend my class I can simply take any equation you will get all equations in force convection and Nusselt as a function of Reynolds and Prandtl but you should know what is the background of this what is the significance of all this how do how does H which is our major goal in convection how does it vary with flow that is the velocity the geometry and the properties of the fluid so the engineering objectives are two in convection heat transfer actually it is not one we should say it is two because you have to get the skin friction also that is a purely fluid mechanical thing but when you are talking about convective heat transfer skin friction coefficient determination is important and heat transfer coefficient determination is important when do you think viscosity or do you think viscosity will affect the heat transfer or not viscosity is a purely fluid property heat transfer coefficient is a function of the property these two are the objectives do they inter relate do they affect each other that affects the whole process do they affect each other how does heat transfer affect fluid flow now if mu is a function of temperature not so much of pressure rho is a function of pressure and temperature so heat transfer is very important therefore we talk about low temperature heat transfer high temperature heat transfer and the effect of properties which are a function of president properties are a function of pressure and temperature so we should look at the president temperature how do they affect the properties whether they will affect my skin friction on the other hand how about friction viscosity affecting heat transfer coefficient what is it resisting that is a new term maybe we mean the same but I am not able to get the yeah viscosity affects the flow okay yeah this is like in all our the same thing we look at different angle so you should give me different angles to this viscosity causes friction I want I was looking at from the friction generates heat sometimes it is negligible most of the time we want it to be negligible but not all the time when frictional heat is not negligible it affects your temperature profiles this effect is called the effect of viscous dissipation so actually you should it is mathematically already there in your energy equation do you remember u del u by del x plus v del u rather u del t by del x plus v del t by del y is equal to alpha del square t by del y square simplest of the boundary equations plus q triple prime by rho cp if you have the heat generation and the last term is what mu mu phi phi the dissipation most of the time we neglected we say you are causing a lot of problems so we will let me not bother you but imagine if that is important your whole energy equation is affected by that again it is not simply the viscosity that viscosity along with the velocity gradients that phi is nothing but all velocity gradients as you will see so they are all mutually affecting each other so it is possible in certain conditions we consider sometimes we do not then as scientists we should say when do you consider viscous dissipation when we do not that is from viscous dissipation point of view now if you come to the flow itself you know laminar turbulent we talk about this but there is a in between zone the transitions actually laminar what is the turbulent what is the critical Reynolds number for flat plate for flat plate 5 into for pipe when you say 5 into 10 where you got it from Bhagavad Gita is it where did you get it from one beautiful value actually if you go a little bit detail there is a transition zone so there is a initial Reynolds critical Reynolds number and a complete critical number it depends upon so many things including the surface type of surface obviously so it is not that suddenly the flow which has been very nice well behaved it jumps to turbulent flow it happens over a Reynolds number range so initial Reynolds number in our general handling of convection we may not bother much about it but you should know that there is a range and it can be controlled in fact a whole lot of things can be controlled by controlling the flow that is possibly in some ways it is under in your control and especially also controlling turbulence itself and the transition to turbulence so if you know some of these fundamentals you would like instead of simply accepting whatever there is shear stress or heat transfer coefficient you may say can I control this can I control the flow for whatever reason can I control the heat exchanging process within certain limits you can do it that is why we should you should try to go as deep into the fundamentals as possible as an engineer finally an actual technical person may not bother about these things but he knows if you go to a person who is handling heat exchanger and he knows how to increase the heat transfer rate how to decrease he may not know the basis of that sometimes he increases the flow he is actually increasing the Reynolds number basically there are many ways of controlling heat transfer and if you know that Reynolds number of the flow from the flow point of the controls heat transfer in a unit exchanger you can do something with the velocity you can some do something with the type of the surface that is the reason why I would like you to Dr. Arvind has done lot of thing on a flat plate and pipe I am just adding to that if he has not done that please read about the history and try to get a picture of where we are today why we want to study convective what has been the background that will give a little bit more I would think excitement understanding of the whole process otherwise it will become a little dry I will again talk about similar things I want you to draw start draw writing down drawing a convection chart a convection chart you must be able to do it on your own I will just guide you on that I like this particular thing I always emphasize for us to get a full picture especially for beginners I know you have already done quite a bit of convection but still I want to do this on the right is a chart chart or a sequence of events let me say on the right hand extreme you write the purpose of convective study determine and I want you to write what is it determination of I want you to write this no I want to write purpose of convection study is what determine h write down that and go one step ahead put an arrow there how do you get this edge in our in our scientific approach what do you need to get that edge model wise or experiment wise temperature difference no I have done all this I am actually trying asking you to put whatever you are done in a this chart fashion or a table fashion how do you get h actually from your analysis what is it that you use what expression for you to get h from all the analysis laminar itself what all you have done yeah what tell me what 4 years law at the surface no this is what I wanted at the surface you apply the 4 years law write down so 4 years law comes into picture minus k dT by dy at y equal to 0 equal to isn't it that is how you are going to get it that is the second what box in my chart where do you get the dT by dy at y equal to 0 you should always say dT by dy at y equal to 0 it is at the wall we are looking at convection heat transfer between a solid surface and a flowing fluid for me 3 conditions are to be satisfied in convection can you tell me what we are talking about a solid surface and a fluid okay I want 3 conditions for me to say this is convective heat transfer conditions is a very big word situation but I would like to use the word condition there is a solid surface there is a fluid when do we talk about convective heat transfer maybe I have not motion relative motion that is very important but before that something else correct relative motion is one of the conditions for me temperature gradient a temperature difference to the third one I am saying purposely convection is very simple you will say oh sir we know about it but that doesn't matter can convection occur if the surface is here and the fluid is flowing here they should be a contact this is what we are talking about so convective heat transfer is that type of heat transfer which occurs when a fluid and a solid surface are in contact with each of the number one there is a relative velocity and there is a temperature difference all the three must be why I am saying this if a solid surface and a flow of different temperatures are not in contact with each other also there is heat transfer occurring but what is that heat transfer will be radiation and if the fluid is in contact with the surface there is a temperature difference but there is no fluid motion even then heat transfer occurs what is that heat transfer huh so conduction can occur radiation can occur between a solid surface and a fluid depending upon whether in contact no motion no contact no motion but convection is contact and motion motion is created by the temperature difference motion is created by nature nature where we are talking about the G effect actually but it's better sometimes to call it free convection but you are perfectly correct what you can talk about is in forced convection there is a imposed flow a flow is forced by some means in free convection that flow is created inherently within the fluid itself because of the existing temperature difference so it's a good point that means I mean we know that for heat transfer first of all temperature difference must be there of course there is if there if these two are in thermal equilibrium there is no heat transfer so that is a but I am your point is well taken I am will emphasize that so convection is that mode of heat transfer between a solid surface and a fluid when they are in contact when there there is a relative motion and when there is a why I emphasize this is a following let us say there is a contact between the solid surface and the and the fluid there is a temperature difference but if they are moving together at the same velocity there is heat transfer but that's my conduction only there's no relative motion there's no boundary layer there so conduction can occur in a fluid I mean between a solid surface and a fluid when they are static both of them or both of them are moving at the same velocity that's why I have to bring in the term relative motion must be there even if there is a point one centimeters per second difference we say there is a relative motion but then you can also see the convert the heat transfer due to the fluid motion is very mild it's not that much in terms of Reynolds so that is my as you students at take on convection is it convection only between solid surface and a fluid under these conditions do you have to stress on solid surface it could be heat transfer it could be my sense and the point here is that it's not necessary that we always talk about a solid surface you know now there is a big water shortage in the city and we are going to feel it you know why one of the water short reasons for water shortage of course there is no rain but if you go to any of our reservoirs they are all open surfaces of water you think there is nothing happening there at the surface there is a wind blowing in fact at all o'clock the wind sets in the the sea breeze sets in and there is a wind flow over these surfaces what is happening at that time vaporation there is a mass transfer so when there is a concentration different there is a mass transfer that we call it as a convective mass transfer so there is a concentration boundary layer and similarly if there is a temperature difference between these two heat transfer will occur and sometimes you can have isolated cases of I am sorry isolated heat transfer mass transfer but there are cases where both of these are possible heat transfer mass transfer simultaneously but in convection fundamental to heat transfer and mass transfer is the fluid motion fluid motion plus conduction Fourier's heat law of conduction is your convective heat transfer fluid motion plus fixed law that is your mass transfer convective mass transfer so I would also therefore like to say convection is not necessarily between a solid surface although we focus on that between two fluids as long as there is contact temperature difference fluid motion relative velocity is another point about it now if this flow is from an external engine that is force convection free convection there are mixed convection cases also to get a handle on quantitative handle handle on heat transfer coefficients and skin friction we do two things either we follow a science model or a engineering model heat transfer as a as a subject has two aspects science and engineering engineering means you do actually experiments you get the heat transfer coefficient or whatever you want measure temperatures everything but even basis for those experiments is your actually theory part of it so when you talk of getting the heat transfer coefficient theoretically you develop a theoretical model I want you to from this come to that point that chart so heat transfer coefficient you get by equating minus k dt by dy at y equal to 0 y equal to 0 is very important y equal to 0 is the interface is equal to h delta t tw minus t infinity now go to the next verse next box what do you have to get in this equation what is it that you have to get temperature no first you should say I want you to say you want the temperature gradient at the wall you do not really care about the rest of the thing I want dt by dy at y equal to 0 this is very important for me dt by dy is there from y equal to 0 to y equal to delta but I do not bother dt by dy y equal to 0 wall gradient now you go to the next how do you get the wall gradient at y equal to 0 only this is what is making all your convection a big issue to use a very mild wall all you need it dt by dy y equal to 0 therefore when you do experiments ladies and gentlemen you do not have to measure the entire temperature profile for you to get the heat transfer coefficient just close to the surface is enough actually you do not have to do go for the entire boundary thickness so for but mathematical that is from a theoretical point of view for you to get dt by dy equal to 0 you have to get t as a function of y that means now you have written the temperature profile now how do you get the temperature profile now we are talking about the boundary how do you get the temperature profile go to the next box what is the next point how do you get the solving you cannot simply say energy equation energy equation is not enough by itself for you to solve the energy equation you also have to solve the y what is there in the energy equation which makes you so yeah you have you that is the difference between your conduction equation which is the energy equation and this equation fluid flow affects your energy equation so u del t by del x v del t by del y for you to get this you have to solve the momentum equations and momentum equation you cannot solve it on their own you have to solve the continuity equation so when you solve the continuity and the momentum equations you will get the velocity profiles when you take those velocity profiles and put it into the energy equation you get the temperature profile when you get the entire temperature profile you just take the dt by dy at y equal to 0 multiplied by k equity to h del t then you will get get h now from where do you get that profile which equations now you have to get the profile so from where do you get the equation you have to solve the plant I want I want answers that I want plant it's boundary layer equations you have to solve not the not in a never stokes equation that's what I am coming to at this point you have to solve the plant it's boundary layer equations at the entire thing momentum equation energy equation of continuity it's it is understood that you have to do that so these are already simplified where do you get how do you get the plant boundary layer equations from where from so write down never stokes so simplification of never stokes use is it all this you have done I am just putting it in a certain form which I like where do you get the never stokes equations what is the basis of the never stokes equation Newton's second law I want I want start from the beginning I say first equation first continuity equation law of conservation of mass then next three equations yeah okay I will leave it at that three equations and then the last one law of from where does love conservation energy come which law first law of course if you are looking at mass time so you also at this space is a question will present on what physics do these equations depend on I am trying to get you related this edge that you want to engineering wise require to nature basically now look at this loss you are talking about first law of thermodynamics second law also issues a second law is important minus k dT by device for second law of thermodynamics expression actually and then all the velocities come from the momentum so law of conservation of mass now look at the how who developed this when were these developed what is the proof of this law of conservation of mass you write down you know immediately a mass cannot be destroyed created you say Newton Newton has done tremendous Newton was a really great scientist he has done in work in optics heat transfer fluid mechanics actually he was a philosopher who was looking at the celestial bodies he started developing equations for the motion of celestial bodies although he was just a banker he was in charge of the treasury of England actually at that time so he came out with these equations which happened for us to be applicable to fluids also on the earth and then Prandtl made it to the border layer and thermodynamics now where is the proof of the first law of thermodynamics I am talking about a theoretical proof where is the theoretical proof the second law of thermodynamics now you see in science we always say any model any law must have experimental validation now these are all called natural laws because nature itself is a proof for this on the other way we say in nature we have not found anything against this people have tried to prove the second law of thermodynamics actually theoretically but they got stuck what is the purpose of this for me this collects I want to connect the engineering aspect and nature finally we are dependent upon these nature in terms of the loss of nature it is not that one man came up with this loss whereas you have a four years law of heat conduction you have so-called Newton's law of cooling Newton's law of viscosity stiffen Boltzmann's but here you don't get why any one name so-and-so first law of thermodynamics he evolved over years from the 17th century and really find out when the first law of thermodynamics was given a mathematical representation try to find out on your own now in most of the classes what we do without you know telling you this we start let us look at the law of conservation mass and then derive I am trying to tell you the reverse of it you want h and you want also tau w by the way shear stress so the same thing you can relate tau equal to mu del u by del y but you want the shear stress at the wall tau w equal to mu del u by del y at y equal to 0 never forget that at y equal to 0 point for convection that du by dy I get from the velocity profile now you see velocity profile you have to get from your momentum and the continuity equation for shear stress that is the end of the matter as per speed mechanics is concerned but if you think heat transfer can be obtained without records to this it is not possible because your energy equation contains u and v so a natural law by the way this first law second law Newton's law these are called general laws physical laws general laws universal laws they will never be disputed anyway but your four years law Stephen Boltzmann's and Newton's law of viscosity these three are not general laws why tell me just look at the equation and you can make out tau w equal to mu del u by del y q is equal to minus k d by dy a q is equal to sigma epsilon 1 to 4 what is common in all these three equations common in terms of the nature of the equation there is a property the moment you say property there is a medium coming into picture so these are medium oriented medium based medium controlled equations though they are called particular laws so we have particular laws general universal natural or physical laws from a combination of these laws now combination of these laws lead you to the equations which we would refer to with all along with the boundary conditions the mathematical model so from the physical model where you take a control volume that is exactly what you are doing it control volume or a system apply these general laws you come down to very broad equations they are not enough for you to get heat transfer they will you give you only the profiles for you to get the heat transfer coefficient you have to come out with a particular law which is minus k d by dy for you to get the mass transfer you should have a fixed law for you to have the shear stress you must have Newton's law of viscosity so a combination of general laws based on nature and particular laws based on peoples they have developed it please read Fourier's law of heat conduction very nice paper it is in French some English translations are available how what now you and I take it to be so simple q is equal to minus k d by dy what is there please look at that particular 18 1829 or so it gives you tremendous information on what was his thinking at that time when you put all of these things together ladies and gentlemen we can then say we are ready to find out rather determine engineering wise heat transfer coefficient and the shear stress I will end now