Heat transfer in a homogeneous suspension including radiation and history effects

An analytical formulation of the thermal response of particles subjected to time-dependent temperature perturbations in the surrounding medium is presented. The suspension of particles is considered homogeneous and dilute. The continuous medium containing the dispersion of particles is assumed to be weakly participating, having a small but nonzero absorption coefficient. The particles in suspension are small, so that the mechanisms of heat transfer between the particles and the continuous phase are conduction and radiation only. The general solution for the temperature response of the particles to time-dependent perturbations in the continuous phase is derived for the limit of small Biot and infinitesimal Peclet numbers. The method used to derive the general solution consists of including the linearized radiation effects in the integro-differential equation that describes the temperature history of the particles. A fractional-differential operator that contains a Riemann-Liouville-Weyl half-derivative term is then applied to the radiation-diffusion equation to render the governing equation analytically tractable. The resulting equation is solved exactly by the method of variation of parameters. Linear and harmonic perturbations are analyzed and discussed, and the radiative and history term contributions to the temperature response of the particles are studied.