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Future, you'd probably use this boundary problem and clear up for Fourier's 2nd Legislation to obtain The inner temperature distribution. Assuming no internal heat generation, the solution is ρ C p ( ∂ T ∂ t + v → ▽ T ) = k ▽ T displaystyle rho C_ p ( partial T about partial t + overrightarrow v bigtriangledown T)=kbigtriangledown T