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The thermal diffusivity a in this equation is defined as
where
X = thermal conductivity
cp = specific heat at constant pressure
p = density
(3.32)
The numerical solution of Equation 3.31 is given in Section 4.3.4. For commonly
occurring geometrical shapes, analytical expressions for transient conduction are given
in the following sections.
3.2.1 Temperature Distribution in One-Dimensional Solids
The expression for the heating or cooling of an infinite plate [2] follows from Equation
3.31 (Figure 3.8):
The Fourier number F0 is defined by
where
Tw= constant surface temperature of the plate
Ta = initial temperature
Tb = average temperature of the plate at time tT
tk = heating or cooling time
X = half thickness of the plate [X = -]
2 2
a, =(n/2)
a = thermal diffusivity, Equation 3.32
Figure 3.8 Non-steady-state conduction in an infinite plate
(3.33)
(3.34)