A solution of the Cauchy problem by finite element method.

Abstract

The paper presents the main results of the algorithm and the solution of the transient heat conduction finite element method. As the study area is considered homogeneous, isotropic body of rectangular cross-section. Within the body set point heat source located at an equal distance from each other. On the upper horizontal boundary of the negative effect of the convective temperature of the outside air. Required to determine the minimum power source of heat needed to create a positive temperature field in the body near the upper boundary of the study area. To determine the optimum capacity of internal heat source solved the Cauchy problem with the initial decision is made the temperature field established by solving the problem of stationary heat conduction. Results of the solution presented in the form of graphs of temperature on a horizontal slice in time and in the body of the isotherms for different time periods.