Question:
Because of symmetry, the temperature gradient ∂T/∂x at the centerline of an infinite plate will be zero when both sides are subjected to the same boundary condition in a cooling process. This may be interpreted that a half plate will act like a plate with one side insulated (∂T/∂x = 0), and the Heisler charts may be employed for the solution of problems with this boundary condition. Suppose an aluminum plate having a thickness of 5 cm is placed on an insulating material and is initially at a uniform temperature of 200ºC. The exposed surface of the plate is suddenly subjected to a convection boundary with h = 5000 W/m2 · ºC and T∞ = 25ºC. How long will it take for the back surface of the plate to reach a temperature of 90ºC?