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Upcoming, you'd probably implement this boundary condition and clear up for Fourier's 2nd Regulation to get The interior temperature distribution. Assuming no inside warmth technology, the answer is ρ C p ( ∂ T ∂ t + v → ▽ T ) = k ▽ T displaystyle rho C_ p ( partial T over partial t + overrightarrow v bigtriangledown T)=kbigtriangledown