E5.21 Wall of Finite Thickness Heated on both Sides

Example 5.21: A long steel slab having thickness of 8 in is initially at 200 °F. Determine the temperature at the centerline 10 minutes after its surface temperature has suddenly been changed to 900 °F. Use thermal diffusivity, α = 0.41 ft²/h.

Solution: This is a situation of a wall of finite thickness heated on both sides.

Time lapsed, θ = 0.167 h. Thickness of the slab, L = 8 in = 0.667 ft. The value of the argument, χ, can be

found to be

The dimensionless temperature, Y can be found using Gurney Lurie Charts (Fig. 18.9) as 0.279.

Using the values of surface temperature, T_s = 900 °F, and initial temperature, T_o = 200 °F, the temperature of the body at the center of the slab can be found to be