Optimal layout of the cooling systems in spacecrafts

A numerical solution of the temperature distribution in an airfoil with assigned internal cooling loops is given. The solution is obtained by a boundary element equation method with mixed boundary conditions (assigned constant temperatures of the cooling loops or a heat flux distributed along them). It is shown that with an assigned distribution of the heat flux on the surface and temperatures of the cooling loops within the airfoil, it is possible to state a correct problem relating to the temperature field within the airfoil. The problem is formalized in terms of boundary element equations for an arbitrary number of loops of arbitrary shape. Viewing the cooling system as a system of concentrated sources of an assigned layout, the problem of the optimal distribution of the heat density between them for ensuring a constant temperature along the external boundary is formulated.