Analytical Study of Stationary Temperature Field in Transpirational–Cooled Porous Wall

Kurzfassung

A one-dimensional heat conduction problem in porous wall with cooling fluid was considered theoretically. The case related to the porous injector head of rocket engine, where heat transfers toward coolant flow, was studied. The equations for the temperatures of permeable media and coolant were solved analytically. To reduce the order and to simplify equations several reasonable assumptions were used. 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 of the temperature gradient near the hot side of porous wall especially in case of thin wall. The thickness of wall, at which the temperature of the hot wall is not high, was found. The expressions for temperatures of wall and coolant at hot side are given.