Reconsider Prob. 5–107. Using EES (or other) software, investigate the effect of the cooling time on the temperatures of the left and right sides of the plate. Let the time vary from 5 min to 60 min. Plot the temperatures at the left and right surfaces as a function of time, and discuss the results.

Data from problem 107

Consider a large uranium plate of thickness L = 9 cm, thermal conductivity k = 28 W/m · K, and thermal diffusivity α = 12.5 × 10^-6 m²/s that is initially at a uniform temperature of 100°C. Heat is generated uniformly in the plate at a constant rate of ė = 10⁶ W/m³. At time t = 0, the left side of the plate is insulated while the other side is subjected to convection with an environment at T_∞ = 20°C with a heat transfer coefficient of h = 35 W/m² · K. Using the explicit finite difference approach with a uniform nodal spacing of Δx = 1.5 cm, determine

(a) The temperature distribution in the plate after 5 min

(b) How long it will take for steady conditions to be reached in the plate.