Temperature in a slab with heat production, the slab of thermal conductivity k in Example 12.1-2 is initially at a temperature T₀. For time t > 0 there is a uniform volume production of heat S₀ within the slab. 

(a) Obtain an expression for the dimensionless temperature k(T – T₀)/S₀b² as a function of the dimensionless coordinate η = y/b and the dimensionless time by looking up the solution in the book by Cars law and Jaeger. 

(b) What is the maximum temperature reached at the center of the slab? 

(c) How much time elapses before 90% of the temperature rise occurs?

Transcribed Image Text:

2y exp(-u) du