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 =...
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I cant seem to use this graph correctly in order to get answers that seem correct.

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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.

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