7.5 The transient temperature change T in a plane wall of thickness L is given by the differential equation

Where α is the thermal diffusivity with units of L2t−1. Determine the nondimensional groups that characterize the situation for a plane wall with a fixed temperature at TL at x = L and a periodic surface temperature variation at x = 0 given by (T − TL) = (T0 − TL) cos ωt where ω is the frequency of the oscillation and T0 is a temperature higher than TL.
Nondimensional temperature parameters use a temperature difference rather than temperature alone. The reference value of time comes from nondimensionalizing the boundary condition.

Transcribed Image Text:

x 1 OT