Heating of a wall {constant wall heat flux, A very thick solid wall is initially at the temperature T₀. At time t = 0, a constant heat flux q₀ is applied to one surface of the wall (at y = 0), and this heat flux is maintained. Find the time-dependent temperature profiles T(y, t) for small times. Since the wall is very thick it can be safely assumed that the two wall surfaces are an infinite distance apart in obtaining the temperature profiles. 

(a) Follow the procedure used in going from Eq. 12.1-33 to Eq. 12.1-35, and then write the appropriate boundary and initial conditions. Show that the analytical solution of the problem is 

(b) Verify that the solution is correct by substituting it into the one-dimensional heat conduction equation for the temperature (see Eq. 12.1-33). Also show that the boundary and initial conditions are satisfied.

Transcribed Image Text:

4at 90 T(у, t) — Тә 2y exp (-y²/4at) exp(-и?) du y/V4at