Chapter 3 - Fins and differential heat balances

A thin flat plate of length L, thickness t, and width w (which is much larger than l) is thermally joined to two large heat sinks that are maintained at a temperature To. The bottom of the plate is well insulated, while the net heat flux to the top surface of the plate is known to have a uniform value of q''.

a) Derive the differential equation that determines the steady-state temperature distribution T(x) in the plate.
b) Solve the foregoing equation for the temperature distribution, and obtain an expression for the rate of heat transfer from the plate to the heat sinks.