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 I0(0)/αk(Tb − T0). In the case of bidirectional radiation to a finite solid, the relatively homogeneous heating can be accomplished at the optical thickness αL ≅ 100. 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 ≳ 101, but the heating is limited to a region near the wall, which results in an inhomogeneous temperature profile. At αL ≳ 102, the temperature profiles become identical with that obtained for αL → ∞. © 2005 American Institute of Chemical Engineers AIChE J, 2006