Function

x - distance from adiabatic surface [m] or [ft]

time - time relative to beginning of convection [sec]

T_i - initial temperature of plane wall [C], [K], [F], or [R]

T_f - bulk fluid temperature [C], [K], [F], or [R]

alpha - thermal diffusivity [m^2/s] or [ft^2/hr]

k - thermal conductivity of plane wall [W/m-K] or [Btu/hr-ft-R]

h - heat transfer coefficient [W/m^2-K] or [Btu/hr-ft^2-R]

L - thickness of plane wall [m] or [ft]

Function planewall_T determines the non-dimensional length, Biot and Fourier numbers and calls the function planewall_ND, which determines theta. Theta is then resolved by planewall_T into the temperature. A separation of variables technique is used to solve for the temperature, as explained in section 3.5.2 of Nellis and Klein.

$UnitSystem SI K Pa J

x=0.2 [m]

time=5000 [sec]

T_i=303 [K]

T_f=363 [K]

alpha=8.608e-5 [m^2/s]

k= 233 [W/m-K]

h= 50 [W/m^2-K]

L= 0.5 [m]

T=planewall_T(x, time, T_i, T_f, alpha, k, h, L)

{Solution: T=312.4 [K]}