A metal rod is in contact with a constant temperature source at each end. At steady state the heat conducted towards the center is balanced by the heat loss by radiation. This leads to a symmetrical temperature profile in the rod. The model is based on the steady state energy balance combined with Fourier's law which gives
d2T/dx2 = alpha* T^4
BC
T=2000K at x =0
dT/dx = 0 at x = L/2
Knowledge of the derivative at the center of the rod requires a solution involving repeated estimates of the temperature gradient at the rod end.This is taken care of by the cost block. Integration is done from one of the ends to the center of the rod.
Assumptions
Steady state approach is used.
References: J. Ingham, I.J. Dunn, E. Heinzle & J.E. Prenosil, Chemical Engineering Dynamics : Modelling with PC Simulation, VCH Publishers Inc., New York (USA).
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