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Special semidiscrete approximations, namely, basic, first, and second semidiscrete problems are proposed for a boundary value problem describing a stationary radiative–conductive heat transfer in a two-dimensional system of heat-conductive plates of width  ɛ  separated by vacuum interlayers. We prove the unique solvability for the first and second semidiscrete problems, establish a comparison theorem, and obtain estimates of their solutions. For the first semidiscrete problem we also obtain some results concerning stability and derive an error estimate of order  O ( ɛ ). Results of numerical experiments are presented.

Semidiscrete approximations for the stationary radiative–conductive heat transfer problem in a two-dimensional system of plates