METHOD OF ADDITIONAL REQUIRED FUNCTIONS IN TASKS OF HEAT CONDUCTION WITH VARIABLE PHYSICAL PROPERTIES OF THE ENVIRONMENT

Abstract

Using additional required functions and additional boundary conditions in an integral method of a heat balance, high-precision approximate analytical solutions of the task of heat conduction for the infinite plate with variable physical properties of the environment in case of the symmetric boundary conditions of the first kind are received. For finding of the decision into areas 0,05 ≤ < ∞ the additional required function characterizing change of temperature in center of a plate which in view of the infinite speed of distribution of the warmth put in the parabolic equation of heat conduction begins to change right after application of a boundary condition of the first kind is entered. Therefore, the range of its change includes all range of time of nonstationary process and all range of change of temperature. For obtaining the decision in case of small and midget values of time the model with a final speed of distribution of warmth based on determination of the front of temperature perturbation and additional boundary conditions is used. The combination of these two models (with the infinite and a final speed warmth distribution) allowed to gain rather simple look approximate analytical solutions of the complex non-linear challenge (with nonlinearity of the second kind) in all range of time of nonstationary process, practically with the given accuracy rating. Reviewing in both models of additional required functions allows to consolidate the solution of partial equations to integration of ordinary differential equations.