Heat Transfer Analysis of Small Particles in a Homogenous Suspension
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 non-zero absorption coefficient. The particles in suspension are small, so that the mechanisms of heat transfer between the particles and the continuous phase are of diffusive and radiative nature 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 Péclet 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 then applied to the radiation-diffusion equation in order to render the governing equation analytically tractable. The resulting equation is solved exactly by the method of variation of parameters for the temperature potential between the particles and the medium. Linear and harmonic perturbations are analyzed and discussed, and the radiative and history term contributions to the temperature response of the particles are studied.
C.F.M. Coimbra, D.K. Edwards and R.H. Rangel (1998). "Heat Transfer in a Homogeneous Suspension Including Radiation and History Effects" - AIAA Journal of Thermophysics and Heat Transfer Vol. 12 No. 3 pp. 304-311 .
C.F.M. Coimbra, D.K. Edwards and R.H. Rangel (1997). "Particle Temperature Response to Transient Thermal Perturbations in a Dilute Suspension Including Radiation Heat Transfer" - ASME / IMECE Symposium on Dispersed Flows in Combustion, Incineration and Propulsion Systems - Dallas - USA.