A general non-circular duct convective heat-transfer problem for liquids and gases

Abstract

The present paper is a theoretical study of the heat transfer by steady laminar forced convection in non-circular ducts. The region of cross-section of the duct under consideration is simply connected and bounded by an arbitrary non-circular closed curve. An arbitrary additional heat source distribution is assumed to be present within the fluid medium. The thermal boundary condition used is that the wall temperature varies linearly in the axial direction. Including viscous dissipation and work of compression in the thermal energy balance, the most general solution has been given in terms of integral formulas both for gases and liquids by using the technique of conformal mapping. General power series solution has been given for the case of gases only. For demonstration, the case of Cardioid duct with additional heat source distribution of constant intensity has been investigated numerically. Out of the mathematical work, only final results have been presented, and the description of methods have been deleted. To investigate the qualitative as well as the quantitative effects of viscous dissipation in the case of liquids, and those of viscous dissipation jointly with work of compression in the case of gases on heat transfer due to constant axial temperature gradient, is the principal object of the present study, and the emphasis also has been mainly given to this. It is found that the said effects are qualitatively remarkable, and usually significant quantitatively also under the condition of constant physical properties; which is a common simplification in a large number of heat-transfer studies. It is also concluded that if viscous dissipation and work of compression are significant in the heat-transfer problem of the present paper then the free convection effects thereby are insignificant.