Combined heat conduction and heat radiation in one‐dimensional solid

The transient changes in the temperature of a solid material heated by radiation were obtained by numerical calculations using an unsteady one‐dimensional (1‐D) energy equation. The radiative loss of heat from the surface of a heated solid increases with an increase in the radiation flux. Therefore, the net blackbody radiation into a semi‐infinite solid keeps a higher proportion of the initial flux at a lower dimensionless initial flux I 0 (0)/αk(T b − T 0 ). In the case of bidirectional radiation to a finite solid, the relatively homogeneous heating can be accomplished at the optical thickness αL ≅ 10 0 . The heating rate is very low at αL ≲ 10 −1 resulting from the absorption of a small part of the radiation energy. On the other hand, the heating rate is high at αL ≳ 10 1 , but the heating is limited to a region near the wall, which results in an inhomogeneous temperature profile. At αL ≳ 10 2 , the temperature profiles become identical with that obtained for αL → ∞. © 2005 American Institute of Chemical Engineers AIChE J, 2006