A quasilinearization approach for the transient response of bodies with surface radiation

A technique for predicting the radiant heat transfer between a plate, cylinder or sphere and the surrounding medium is formulated using the quasilinearization method introduced by Bellman (1965). In particular, it is shown that solutions to the surface radiation problem may be calculated directly from analytical solutions of the corresponding convection problem, which are available in graphical form for a number of simple configurations. Short-term results for cooling and long-term results for heating problems are obtained; only a few iterations are needed to establish sufficiently accurate temperature values. Application of the technique to situations involving more general thermal boundary conditions and/or multidimensional cases is also mentioned.