E.L. Kuznetsova, V.F. Formalev
An effect of the linearization of nonlinear radiant heat flow on the thermal field in the body due to the complex heat exchange on its outer boundary contacting with high temperature gas flow has been investigated. It’s shown that the explicit approximation of nonlinear heat flows on lower schema’s layer results significant errors of surface and body temperature numerical computation for convective, conductive and radiant heat exchange problems. These errors are proportional to third degree of surface’s temperature and to the first degree of the surface heating’s velocity. So, the high error level reduces to the instability of solution and temperature computation. Surface temperature’s oscillations are eliminated if the temperature goes down to ~1500 К, but the stable solution has the significant error.
A new numerical method combining implicit approximation on the time layer of the nonlinear radiant member with the linear operator of marching for algebraic equations with three-diagonal matrices has been proposed. This method uses the exact outer boundary temperature’s computation from the fourth-order algebraic equation’s quadrature. Exact surface temperature on the upper schema’s layer allows marching using, eliminates the instability due to explicit approximation of radiant heat flows and approximation errors.
The proposed method has been used for multi-dimensional boundaries in heat transfer problems with modification due to the radiant heat flow in each surface point, so that each equation of longitudinal marching has the fourth degree of the temperature.
This numerical approach can be effectively used for heat transfer problems with the surface temperatures upper than 600 K