The heat diffusion equation for transient conduction in a one-dimensional slab is:

a at

Suppose the heat flux is q, =0 at x=0 and the surface at x = L is exposed to a

convection environment with fluid temperature T. and convection coefficienth . The

boundary conditions are:

of =0 at x=0 and -k = h(T-T.) at x = L

ax

Suppose the slab is initially at uniform temperature T(x, 0) = T; . The dimensionless

form of this equation, its initial condition, and its boundary conditions are:

Fo

where O =

T - T. = = *, and Fo =

T- T.

O =1 for Fo = 0,

30 =0 at 5 =0, and

do = -Bio at 5 =1 where Bi = hL

25

k

Figure 5.7 in the 5th Edition of A Heat Transfer Textbook (the latest PDF version of the

text) has a temperature response chart for the solution to this problem. Use this chart

to solve the following problem:

A large 100-mm thick steel plate is initially at uniform temperature T, = 180 C at

time t =0. Both sides of the plate are exposed to 30C oil with convection coefficient

h = 1500 W/m? . K. The thermal conductivity, heat capacity, and density of the steel are

k = 38 W/m . K, c, = 485 J/kg . K, and p = 7800 kg/m3.

a) Find the temperature at the center of the slab when t = 125 s.

b) Find the temperature at the surface of the slab when t= 125 s.