Interaction of Heat Transfer by Conduction, Convection, and Radiation in a Radiating Fluid

Consideration is given to the interaction of conduction, convection, and radiation in a fully developed laminar flow. The flat duct consists of two diffuse, nonblack, isothermal parallel surfaces a finite distance apart; the fluid between them emits and absorbs thermal radiation. The problem is formulated in terms of a nonlinear integro-differential equation, and the solution is obtained by a method employed by Barbier. Numerical examples show the influence of the system parameters such as the optical thicknesses, the ratio which determines the relative role of energy transport by conduction to that by radiation, the emissivity of the duct walls as well as the differences between heating and cooling on the temperature variations across the duct and on the heat-transfer characteristics. Two methods for obtaining approximate temperature distributions for optically transparent and opaque radiating media are outlined and the results discussed.