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Say you have an incompressible thermal conducting fluid contained between two infinite horizontal plates separated by a distance $H$. Initially both the plates and the fluid are at rest at temperature $T_{0}$. At time $t=0$, the upper plate is raised to temperature $T_{1}>T_{0}$ and moved horizontally at speed $U$. Assuming laminar flow, why is temperature $T$ a function of $y$ and $t$ only?

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  • $\begingroup$ plane symmetry? $\endgroup$ – Hydro Guy Sep 5 '15 at 14:42
  • $\begingroup$ Thanks for the edit! Hopefully next time I can get at least the title correct... $\endgroup$ – jackwo Sep 5 '15 at 14:43
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Why not? You expect heat to transfer differently at another point on the plate. Any point on plate one has a plate two at the same temperature, the same distance apart, and the same fluid in between.

The movement of the plate does not introduce a difference as the fluid in between still has the same history.

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