Analysis of nonlinear heat conduction based on determining the front of temperature perturbation

An analytical solution of nonlinear problem of heat conduction is derived using an integral method of heat balance. In order to improve the accuracy of solution, the temperature function is approximated by polynomials of higher degrees. The polynomial coefficients are determined using additional boundary conditions which are found from the basic differential equation and preassigned boundary conditions including the conditions on the front of temperature perturbation. It is demonstrated that the introduction of additional boundary conditions even in a second approximation results in a significant increase in the accuracy of solution of the problem.