Future, you should use this boundary issue and resolve for Fourier's 2nd Legislation to obtain the internal temperature distribution. Assuming no internal warmth generation, the solution is ρ C p ( ∂ T ∂ t + v → ▽ T ) = k ▽ T displaystyle rho C_ p ( partial T more than partial t + overrightarrow v bigtriangledown T)=kbigtriangledown T