Heat transfer analysis of a particle-containing channel flow

This paper describes an analytical model of heat transfer in a two-dimensional, steady, nonreacting particle-containing channel flow. An idealized gas flow of specified uniform velocity between insulated parallel plates is assumed and the nonvaporizing particles are conceptualized as contained within an thin sheet injected at the symmetry plane. Two dimensionless parameters that affect the solution are described. These are the effective gas diffusivityK and the dimensionless particle number densityP. The linear, coupled differential equations governing the energy exchange between the gas and liquid phases are solved by means of the Green's function technique. This procedure yields a Volterra integral-series equation as the solution of the gas-phase energy equation. A series solution of this integral equation is obtained by the method of successive substitutions and terms up to second order are calculated.