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Planewall_T_ND
The function planewall_T_ND(x_bar, Fo, Bi) returns the non-dimensional temperature within a bounded plane wall with one edge exposed to convection (x=L) and the other adiabatic (x=0). The supplied values, x_bar, Fo, Bi represent the dimensionless position, Fourier number and Biot number respectively.
Inputs:
where x = position and L = thickness of wall
where alpha = thermal diffusivity and time = time (relative to step change)
Output:
where T = temperature, T_i = initial temperature, and T_f = bulk fluid temperature
Notes:
1. Function planewall_T_ND is called by the function planewall_T to determine the non-dimensional temperature, theta.
2. The solutions provided by EES are the 1st 20 terms of the infinite series solution, as explained in section 3.5.2 of Nellis and Klein.
3. The result for Fo<0.001 is determined by interpolation of the solution at Fo=0.001 and the known value (the initial condition) at Fo = 0.
Example:
x_bar=0.7
Fo=0.6
Bi=1.5
THETA=planewall_t_nd(x_bar, Fo, Bi)
{Solution:
THETA=0.4946}
Transient Conduction Index