Combined Radiation and Convection in Absorbing, Emitting, Nongray Gas-Particulate Tube Flow

Abstract

The interaction of thermal radiation with conduction and convection in thermally developing absorbing, emitting, nongray gas–particulate turbulent suspension flow through a circular tube is investigated. The contribution of thermal radiation is obtained through evaluation of the total hemispherical emittance of the particulate cloud and through evaluation of single band absorptances for molecular gases, modified to account for the interaction with the particles. The governing differential equation is derived as a (nonlinear) energy equation, coupled with integral equations to find the thermal radiation contributions. The energy equation is solved numerically by an implicit finite difference method with an iterative procedure. Qualitative results for Nusselt numbers are shown for a variety and range of parameters, such as optical thickness of particulates and single molecular gas bands, relative gas band position and band width, and temperature ratios (heated as well as cooled suspension flows).