Why is temperature a function of $y$ and $t$ only?

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?

• plane symmetry? – Hydro Guy Sep 5 '15 at 14:42
• Thanks for the edit! Hopefully next time I can get at least the title correct... – jackwo Sep 5 '15 at 14:43

1 Answer

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.