ABSTRACT
This chapter explains the mathematical models for the heat conduction. The mathematical model for the heat conduction relates two fundamental values: the temperature distribution represented by a scalar function and the heat flux represented by a vector-function. The chapter considers non stationary processes in an isotropic conducting medium. One can see that the thermal diffusivity does not take part in the stationary heat conduction. The temperature distribution has to satisfy the Laplace equation in a domain D with prescribed boundary values on ∂D. The chapter outlines the constructive methods of the Fourier series to boundary value problems. Boundary value problems stated can be transformed into discrete problems following the principle of transition continuous to discrete. The chapter also outlines the finite-difference method effective in the numerical solution to the heat and other evolution equations. It addresses Rayleigh-Ritz method to the Dirichlet problem for the simple second order differential equation.
