One Method of Heat Transfer Process Mathematical Modeling in Solids

Based on the introduction of a new desired function and additional boundary conditions (characteristics), a solution to the heat conduction problem for an infinite plate is obtained under boundary conditions of the first kind. It is shown that the introduction of a new unknown function - the heat flux density on the plate surface - allows us to reduce the solution of the initial boundary-value problem to the solution of an ordinary differential equation with respect to this function. It is noted that the proposed method can be used to solve partial differential equations that do not allow separation of variables. The accuracy of the solutions obtained according to the method under consideration depends on the degree of the approximating polynomial, to determine the unknown coefficients of which additional boundary conditions (characteristics) are used.