A perturbation method for nonlinear, onedimensional conduction with heat generation
Abstract
The Fourier conduction equation is nonlinear when the thermal conductivity and bulk heat generation rate are temperaturedependent. For the particular case involving Joulean heating with constant voltage gradient, the latter is inversely proportional to the temperature. This paper describes a simplified, closed form solution for the onedimensional slab insulated on one wall with a fixed temperature on the other. The Kirchoff transformation is used to eliminate the nonlinearity due to temperaturedependent thermal conductivity and the transformed temperature is then asymptotically expanded in the thermal coefficient of electrical resistivity. The resulting equation through the first order terms is examined and the requirements to obtain 0.1 percent accuracy determined.
 Publication:

Heat Transfer 1982, Volume 2
 Pub Date:
 1982
 Bibcode:
 1982hetr....2....9J
 Keywords:

 Conductive Heat Transfer;
 Heat Sources;
 Perturbation Theory;
 Thermal Conductivity;
 Electrical Resistivity;
 Nonlinear Equations;
 Slabs;
 Stainless Steels;
 Fluid Mechanics and Heat Transfer