ISSN Online: 2377-424X
ISBN Print: 1-56032-797-9
International Heat Transfer Conference 11
HEAT CONDUCTION WITH NON-LINEAR BOUNDARY CONDITIONS VIA INTEGRAL TRANSFORMS AND SYMBOLIC COMPUTATION
Abstract
Transient heat conduction governed by non-linear boundary
conditions is solved through integral transforms. Two kinds of filters are developed using as a basis either a second or a third kind boundary condition. The developed filters are applied to solve two examples in a slab: conduction with time variable Biot number, and conduction conjugated at the boundary with convection and radiation. Both filters give results with good agreement between them. The two approaches presented in this paper extend the power of the generalized integral transform technique in efficiently solving diffusion problems with non-linearity in the boundary conditions. All details derivation of the formulae, implementation and computations are presented as Mathematica notebooks in a forthcoming
book, where we also consider the cylinder and sphere
geometries.