Effective Methods for Calculation of Heat Losses in Plate

The approximation of some nonlinear heat transport problem in a plate is based on the finite volume method [1]. Corresponding integrals are approximated using different quadrature formulae. This procedure allows one to reduce a 2-D boundary value problem described by a partial differential equation to an initial-value problem for a system of ordinary differential equations of the order depending on the approximation formulae used. Solution of the corresponding problem is obtained using Maple and Mathematica routines. 1. The Mathematical Model We consider the dimensionless initial-boundary problem for the temperature T(t,x) distribution in the plate in the following form: 0),,0(),() ( 22>∈+∂∂=∂ ∂ tlxTFxTftT (1.1)), ( 111 TfxT =∂ ∂ (1.2