DEVELOPMENT OF METHODS AND ALGORITHMS FOR ESTIMATING THE TEMPERATURE DISTRIBUTION IN THE BODY OF A RECTANGULAR PARALLELEPIPED SHAPE UNDER THE INFLUENCE OF HEAT FLOW AND THE PRESENCE OF HEAT EXCHANGE

Abstract

The article describes methods and computational algorithms for estimating the temperaturedistribution law in the body of a rectangular parallelepiped shape under the influence of heat flowand the presence of heat exchange. It is believed that one of the faces is amenable to heat flow, andthe other faces are insulated or are under the influence of the environment. To use the variationalapproach, the total energy functional is calculated, taking into account the boundary conditions.Minimizing the functional and equating it to zero, we obtain a system of linear equations, thesolution of which gives the temperature of a rectangular parallelepiped at the nodal points. Further,substituting these nodal temperature values into the approximating function, we obtain the law oftemperature distribution in the body in the form of a rectangular parallelepiped. The temperaturedistribution law is obtained by dividing a rectangular parallelepiped into one, two and threeelements. To speed up the process of calculating the temperature distribution law, an algorithm hasbeen developed that allows you to create a program code that increases the calculation efficiency byan order of magnitude. This is achieved by the fact that the created code contains only a systemof linear equations, unlike the main program, which forms a general functional of full energies,calculates derivatives of this functional and obtains a system of equations.