Effect of thermal radiation on the laminar free convection from a heated vertical plate

Abstract

An analytical attempt is made to understand the non-equilibrium interaction between thermal radiation and laminar free convection in terms of a heated vertical plate in a stagnant radiating gas. The effect of radiation is taken into account in the integral formulation of the problem as a one-dimensional heat flux, evaluated by including the absorption in thin gas approximation and the wall effect in thick gas approximation. The local Nusselt numbers thus obtained help to interpret the gas domains from transparent to opaque and from cold to hot. The present thick gas model approximates the radiant flux as q R = − 16σ 3α 1− 1 − ϵ w 2 exp (− 3 2αy ) T 3 ∂T ∂y whose limit for large α and small but non-zero y is the Rosseland gas, q R Rs = − ( 16σ 3α ) T 3( ∂T ∂y ) , and that for y = 0 and large but finite α is q R w = − α w( 8σ 3α ) T 3 w( ∂T ∂y ) w .