An exact methodology for solving nonlinear diffusion equations based on integral transforms
Abstract
This paper develops a new methodology for the solution of nonlinear diffusion equations. The solution technique is based on integral transforms and leads to exact numerical results. The formal methodology is applied to the problem of onedimensional transient heat conduction. A new form of the heat equation is developed using a generalized expression for temperaturedependent thermal conductivity, based on a powerseries expansion, for the three standard orthogonal coordinate systems. The resulting form of the heat equation suggests that the finite integral transform technique may reduce the dimensionality of the heat equation prior to the initiation of any numerical procedure. An example in a slab with linearly varying thermal conductivity is shown to produce exact results for the temperature distribution.
 Publication:

Applied Numerical Mathematics
 Pub Date:
 November 1987
 Bibcode:
 1987ApNM....3..467F
 Keywords:

 Conductive Heat Transfer;
 Diffusion Theory;
 Integral Transformations;
 Nonlinear Equations;
 Slabs;
 Temperature Dependence;
 Temperature Distribution;
 Thermal Conductivity;
 Fluid Mechanics and Heat Transfer