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A model is proposed for the heat transfer between viscous gas-dynamic flows and cooled rocket-engine components based on composite permeable shells. The mathematical model includes the equations of dynamic and thermal boundary layers, a three-dimensional nonsteady heat-conduction equation for the cooled components, and an equation for the complex hydraulic flow. An absolutely stable and economical method is proposed for the solution of three-dimensional nonsteady heat-conduction problems in multiply connected regions. Cooling by means of composite permeable shells with injection is shown to be more effective than traditional convective cooling.