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Elevated Temperature Region with Linear Distribution for Semi-Infinite Body Adjacent to the Adiabatic Surface

Function SemiInf14(T_i, alpha, a, DELTAT, x, time) returns the temperature within a semi-infinite body that has an initial temperature that is non-uniform.  The region immediately adjacent to the adiabatic surface (0 < x < a) is at an elevated temperature: T = T_i+DELTAT*(1-x/a) while the remainder of the material (x>a) is at T_i.

The calling protocol is:

T = SemiInf14(T_i, alpha, a, DELTAT, x, time)

Inputs:
T_i = temperature far from the surface [C] or [K]
alpha = thermal diffusivity [m^2/s]
a = extent of the elevated temperature region [m]
DELTAT = temperature elevation at x=0 [C] or [K]
x = position relative to surface [m]
time = time relative to beginning of heat flux cycle [s]

This function can be used with English units set in EES.  In this case, T_i is in [F] or [R], alpha is in [ft^2/hr], a is in [ft], DELTAK is in [F] or [R], x is in [ft], and time is in [s].

Outputs:
T is the temperature in [C] or [K] (or [F] or [R] in English units)

Carslaw, H.S. and J.C. Jaeger, Conduction of Heat in Solids, 2nd Edition, Oxford, (1959).

Example
\$UnitSystem SI Mass J K Pa Radian
\$VarInfo T units=K
T_i=300 [K]
alpha=1e-3 [m^2/s]
x=0.002 [m]
time=0.1 [s]
a=0.005 [m]
DELTAT=100 [K]
T=semiinf14(T_i, alpha, a, DELTAT, x, time)

{Solution:
T=313.8 [K]
}

Transient Conduction Index