# The CONSERVATIVE DIFFERENCE SCHEMES FOR OPTIMAL PLACEMENT OF HEAT SOURCES IN A PARALLELEPIPED

## CONSERVATIVE DIFFERENCE SCHEMES FOR OPTIMAL PLACEMENT OF HEAT SOURCES IN A PARALLELEPIPED

## Keywords:

optimal placement; heat sources; integro-interpolation method; conservative schemes; Big M method.## Abstract

In this paper, a method and algorithm for solving the non-stationary problem of optimal placement of heat sources of minimum power in the space have been developed. As a result, the temperature in the space is within the specified limits and the value of the functional is minimized. The mathematical model of the process is described by the heat conduction equation with a variable coefficient. The numerical model of the problem is constructed using implicit conservative difference schemes. To solve the problem of thermal conductivity control, a linear programming problem was used. Software for numerical modeling has been developed. The results of a computational experiment are presented.

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## How to Cite

*Acta of Turin Polytechnic University in Tashkent*,

*12*(1), 14–18. Retrieved from https://acta.polito.uz/index.php/journal/article/view/121