Numerical prediction of turbulent heat transfer in gas pipe flows subject to combined convection and radiation

Abstract

An analysis is made of the interactive heat transfer problem involving turbulent forced convection and radiation in the thermal development region of a gas pipe flow. A source of distortion of temperature and heat transfer rates is usually attributed to the presence of thermal radiation in high-temperature gas flows. In particular, this paper is concerned with a situation wherein an absorbing-emitting gas having a fully developed turbulent velocity enters an isothermal pipe with black walls. The turbulent model adopted for the velocity profile involves the solution of one differential equation for the kinetic energy of turbulence. Under the idealization of gray gas, the radiation contribution is modeled by a differential method, the so-called method of moments, that circumvents the partial integrodifferential equation typical of this kind of problem. Accordingly, the new formulation governing the combined heat exchange process accounts for a coupled system consisting of a partial differential equation for temperature and an ordinary differential equation for the irradiation. The former is solved by a hybrid methodology using the method of lines in conjunction with a control volume discretization in the radial direction only. Similarly, the latter is discretized by control volumes too. Solutions of the resulting initial value problem were obtained numerically by a Runge-Kutta-Fehlberg scheme, which deals successively with the associated system of algebraic equations. Remarkably rapid convergence was achieved by adopting a coordinate transformation that clusters grid points near the wall. Results based on 10 lines are presented for the axial distributions of bulk temperature and total Nusselt numbers as a function of the controlling parameters of the combined heat exchange process. The numerical predictions have been compared with the available results, and the agreement was satisfactory for all cases tested.