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The paper presents a physico-mathematical model for determining the heat transfer parameters between viscous gasdynamic flotations and cooled gas turbine blades made using the technology of composite permeable membranes (CPM). The mathematical model includes equations of dynamic and thermal boundary layers taking into account injection, three-dimensional transient heat conduction in CPM cooled frames, complex hydraulic flow and cooling inside the channels of a cooled blade with air taken from the power plant compressor. A complex problem was solved to determine the thermal state of microrocket engines, where a method was proposed for immersing a multiply-connected domain in a region of the simplest form. A new economical, absolutely stable method is proposed for numerically solving of spatial nonstationary heat transfer problems in multiply-connected domains. The results obtained showed greater cooling efficiency at lower cooling medium costs. [ABSTRACT FROM AUTHOR]

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