MATHEMATICAL MODEL OF OPTIMIZATION OF THE TRANSPARENT PARTITION THICKNESS IN THE TROMBЕ WALL HEAT EXCHANGE SYSTEM
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Abstract
The study is devoted to the issue of mathematical modeling of effective heat transfer in a blood clot wall, which is a structural element of passive solar heating of buildings. The problem of optimization the geometry of the transparent partition wall of the Thrombus, partially absorbing and transmitting solar energy, is considered in the work. The air temperature in the air layer is selected as the optimization objective function. A mathematical model for optimizing the wall thickness of a transparent partition, at which the maximum air temperature in the gap is reached, is built in the work. The model was constructed using the equations of thermal balance, the Bouguer-Lambert-Beer lawlaw, and the necessary and sufficient conditions for the extremum of the objective function. The determining ratios take into account the processes of convective and radiant heat transfer. The numerical calculation method is implemented using the implicit differentiation method and the Newton iterative method. The optimal values of the wall thickness of a transparent partition, at which the maximum value of the air temperature in the wall layer of the Thrombus is reached, as well as the corresponding temperatures of the partition and the surface of a massive wall coated with a phase transition material, are obtained based on the constructed mathematical model. The constructed graphical dependences of the air temperature in the gap on the wall thickness of the transparent partition clearly demonstrate the presence of a maximum of the objective function. The optimal values of the wall thickness of the transparent partition and the air temperature in the interlayer decrease with increasing absorption coefficient of the glass partition material according to the results of numerical experiments. The constructed mathematical model and numerical calculation method will make it possible to increase the efficiency of heat transfer in the Thrombus wall by reducing heat energy losses when choosing the optimal thickness of the glass partition.
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