Contents
- Index
Sphere_T_ND
Function sphere_T_ND(r_bar, Fo, Bi) returns the non-dimensional temperature within a sphere whose outer surface (r=r_o) is exposed to convection. The supplied values, r_bar, Fo, Bi represent the dimensionless position, Fourier number and Biot number respectively.
Inputs:
where r = radial position and r_o = outer radius
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 sphere_T_ND is called by the function sphere_T to determine the non-dimensional temperature, theta, as described in Section 3.5.2 of Nellis and Klein.
2. The solutions provided by EES are the 1st 20 terms of the infinite series solution
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:
r_bar=0.3
Fo=0.23
Bi=1.02
THETA=sphere_t_nd(r_bar, Fo, Bi)
{Solution:
THETA=0.6895}
Transient Conduction Index