Transient conduction in a plate with counteracting convection and thermal radiation at the boundaries

During the flash dehydroxylation of powdered kaolinite it is desirable that a rapidly propagating thermal wave penetrates the cold powder particles in a way that raises the particle interior to the reaction temperature of 600°C without the particle exterior being heated beyond 1000°C. In a production unit this is achieved by performing the heat treatment in a device where particles are heated by convection from hot gas and are subject to heat loss by thermal radiation to cool walls. This paper concerns the fundamental heat transfer problem of the process, decoupled from the thermal effects of the dehydroxylation reaction. Using a plate as the approximation for the particle shape a semi-analytical solution for the plate temperature distribution is obtained as a function of the five dimensionless process parameters: Biot number, radiation number, wall/gas and particle/gas temperature ratios and mode of convection. Accuracy is demonstrated by comparison with an existing numerical solution for the limiting case of pure radiative heating of a plate initially at absolute zero.