Transport Phenomena Thermal Conductivity

Question :

Transient conduction in an iron slab. In this problem, we will investigate the evolution of the temperature distribution in a semi-infinite slab of iron (>99.99%) when one face is instantaneously elevated from 90 to 900K.

Prepare two solutions:

(1) the analytical solution assuming constant thermal conductivity (k at 90K).

(2) the numerical solution assuming the iron thermal conductivity varies with

temperature itself.

The data given in the following table are provided for your reference. We are particularly interested in the temperature profiles at t = 5 min and t = 50 min.

Temperature (K)

90

150

200 300

Thermal conductivity

(W/cm K)

1.46 1.04 0.94 0.803 0.694 0.547 0.433 0.38

400

600 800 900

Answer :