On radiative and conductive heat transfer in spacecraft

The “radiative” boundary condition in a heat conduction problem relates the heat flux in a point of the wall to the temperatures in all the other points of the surface system.That is, this condition is of a “functional” type. This “functional” can be solved in discrete terms by using the conventional technique of dividing the body in small discrete elements or “nodes”. This paper instead presents an approach on a continuous scheme, by which the functional is solved in terms of “spacewise harmonics” of the temperature inside the body; the heat conduction problem is thus reduced to an ordinary form differential system whose unknowns are these “harmonics”. An interative linearized procedure to solve this system is also suggested, by which “exact” solutions are obtained. The merits of these solutions, with respect to practical discrete element computations, are in the better spacewise resolution and in the consequent more accurate treatment of both radiation and conduction. The application of the procedure is, however, limited to particular geometries. It is relevant to note that among these possible geometries many are included of practical interest, like hollow cylinders and polygons, cubic boxes etc. A numerical example completes the work.