When Fourier's equation is applied: Q ˙ ˙ = − − k A r d T d r = − − 2 k π π r ℓ ℓ d T d r and rearranged: Q ˙ ˙ ∫ ∫ r 1 r 2 1 r d r = − − 2 k π π ℓ ℓ ∫ ∫ T 1 T 2 d T then the rate of heat transfer is: Q ˙ ˙ = 2 k π π ℓ ℓ T 1 − − T 2 ln ⁡ ⁡ ( r 2 / r 1 ) the thermal resistance is: R c = Δ Δ T Q ˙ ˙ = ln ⁡ ⁡ ( r 2 / r 1 ) 2 π π k ℓ ℓ and Q ˙ ˙ = 2 π π k ℓ ℓ r m T 1 − − T 2 r 2 − − r 1 , where r m = r 2 − − r 1 ln ⁡ ⁡ ( r 2 / r 1 ) . It is important to note that this is the log-mean radius.