Radiation and Convection in Circular Pipe with Uniform Wall Heat Flux

Abstract

The interaction of thermal radiation with laminar forced convection in thermally developing circular pipe flow is analyzed theoretically. The analysis considers an absorbing and emitting gray fluid bounded by a heated black wall having a uniform heat flux subjected at a certain finite length of wall and insulated otherwise. The contribution of thermal radiation is obtained by solving the two-dimensional exact integral equations for the divergence of radiative heat flux with the use of finite element node approximation technique. The governing energy equation is solved numerically by the Crank-Nicolson finite difference method with an iterative procedure. Effects of various radiation and convection parameters such as optical radius, Peclet number, and inlet fluid temperature on wall radiative heat flux are presented. The effects of the parameters on the development of fluid bulk temperature and wall temperature are also analyzed.