انتقال حرارت تابشی و همرفتی در جریان اشعه گاز در یک لوله گرم یا سرد با دیوار خاکستری Radiant and convective heat transfer for flow of a radiation gas in a heated cooled tube with a grey wall

Abstract-An analytical investigation is presented of the influence of radiative heat transfer on the complex heat exchange problem involving How of an optically active (radiating) gas inside a tube of diffuse grey properties. The method used is based on Hottel’s formulation of zone division, and involves the transformation-zone approach, where radiation gas emission is replaced with an equivalent surface emission. Separable-kernel and surface transformation techniques give a set of non-linear differential equations treated by the Runge-Kutta method with Hamming modification. The solutions are governed by several independent parameters such as the wall and radiation gas emissivities, inlet and exit gas temperatures, length diameter ratio of the tube, uniform and non-uniform heat flux and variableconvective heat transfer coefficient at the inner surface. The results apply both to heating and cooling situations. INTRODUCTION THE THERMAL design and analysis of energy conversion systems and devices such as furnaces, combustion chambers, combustors, fluidized beds, and open cycle coal- and natural-gas-fires MHD must often take account of the effects of thermal radiation. Radiation is also a significant mode of heat transfer in many high temperature technological areas such as heating and annealing furnaces, thermal control of spacecraft, nuclear reactor safety and fire spread. In some instances, the radiation will impose an additional heat load on a part which is to be kept cool, and hence this exchange must be estimated when the cooling requirements are computed. In other cases, the radiation will cause a region operating at a high temperature to have it reduced. Heat transfer by forced convection to a gas flowing in a tube has received detailed study in the literature, but little consideration has been given to the added effects caused when thermal radiation (in participating media) is also present. The situation considered here is the heat exchange in a circular tube with a uniform or non-uniform heat flux supplied along the wall, and there is a constant or variable convective heat transfer coefficient at the inner surface. The purpose of this paper is to examine the interaction of radiative and convective transfers for flow of a radiation gas in a circular tube. The present paper also provides the additional analysis necessary to extend refs. [l-3] to include a radiative contribution of a radiation gas. The proposed method which includes the influence of gas emission is based on the zone division approach first formulated by Hottel [4, 51 and developed by Siegel and Perlmutter [l, 2, 61. In this, the non-isothermal gas and surface are divided into infinitely small isothermal elements. Also, it involves the transformation-zone technique. where the emission of the gas body is replaced with an equivalent surfdce emission [I, 7-l 01. Previously, the analysis presented here has been applied to heated tubes only, [8, 91, whereas, in fact, it is equally valid for cooled tubes. This is made explicit in the final derived equation where the upper and lower signs refer to heated and cooled conditions, respectively. Also, the analysis is a development of that presented by Siegel and Perlmutter [2] and Perlmutter and Siegel [I]. We have deliberately used the same notation and derivation to enable the reader to appreciate the additional features of this work. ANALYSIS The system to be analysed is shown schematically in Fig. I (the tube system treated here is similar to that studied by Siegel and Perlmutter [I, 21). A radiative gas at a specified inlet temperature T,., flows into the tube and is heated to an average exit temperature Tg,,. A uniform or non-uniform heat flux q(X) is supplied to the tube wall by external means, and the outside surface of the tube is assumed to be insulated. Each end of the tube is exposed to an outside environment or reservoir at specified temperatures, T,,, and r,,, at the inlet and exit of the tubes respectively. The inside of the tube wall is a diffuse grey surface with an emissivity E. The Planck mean volume absorption coefficient x is constant and the optical thickness K << I. It is assumed that there is no axial conduction in the tube wall or in the radiation gas and that the convection heat transfer coefficient h(X) is nonuniform throughout the tube.