Question

Q. Unsteady conduction

A large steel plate 0.02 m thick leaves a heat treating furnace at 425 oC. And the plate is

plunged into water (at 25 oC) and cooled from both sides. How long does it take for the

maximum temperature to reach 65 oC?

For steel plate: thermal conductivity, k=30 W/m·K, density ?=7600 kg/m3, heat capacity

cp=700 J/kg·K. Heat transfer coefficients: h=6000 W/m2·K in water.

Please use two methods to calculate this question:

(1) Directly apply the exact analytical solution (one term approximation, verify whether this

approximation is valid) given in Lecture note. You need use Appendix to find the values

for different functions.

(2) Use the diagram below to solve the problem. Water temperature is T1. Initial temperature

is T0. Center of the plate at y=0, surface of the plate at y=L.

Compare your results obtained from different methods, which one is more accurate?

Answer 1