Analytical Study of Stationary Temperature Field in Transpiration Cooled Porous Wall

Abstract

A one-dimensional heat conduction problem in a porous wall with a cooling fluid was considered theoretically. The case related to the porous injector head of rocket engine, where the heat flux is directed toward a coolant flow, was studied. The equations for the temperatures of permeable media and coolant were solved analytically. Using reasonable assumptions the equation system was simplified and the order of equations as reduced. The margins, where the used assumptions are valid, were defined. The solution is expressed in hyperbolic functions and shows that the flow of coolant leads to the increase in the temperature gradient near the hot side of porous wall. The expressions for the temperatures of wall and coolant at hot-gas-side wall are given. The thickness of wall, at which the temperature of the hot wall is independent on the wall thickness, was found.