ABSTRACT
The plate is heated to an initial temperature distribution, T(x,O), at which time the heat source is turned off. The initial temperature distribution in the plate is specified by
T(x, 0.0) = 200.0x T(x, 0.0) = 200.0( 1.0 - x)
0.0:::: x:::: 0.5 0.5 :::: x :::: 1.0
(10.2a) (lO.2b)
where T is measured in degrees Celcius (C). This initial temperature distribution is illustrated by the top curve in Figure 10.2. The temperatures on the two faces of the plate are held at 0.0 C for all time. Thus,
T(O.O, t) = T( 1.0, t) = 0.0 (lO.2c)
The temperature distribution within the plate, T(x, t), is required. The exact solution to this problem is obtained by assuming a product solution of the
form T(x, t) = X(x)Tct), substituting this functional form into the PDE and separating variables, integrating the two resulting ordinary differential equations for X(x) and T(t), applying the boundary conditions at x = 0 and x = L, and superimposing an infinite
