Thermodynamics of natural convection in enclosures with viscous dissipation

Abstract

Consideration of the viscous dissipation effects in natural and mixed convection heat transfer must be taken carefully, both in what concerns the thermodynamics of the problem and the relevance of the dissipation term. This applies equally to external or internal natural and mixed convection, and to spaces filled with a single fluid or to spaces filled with fluid-saturated porous media. The main question is related to the fact that, in natural convection, the work done by the pressure forces must equal the energy dissipated by viscous effects, which is the unique situation compatible with the First Law of Thermodynamics, the net energy generation in the overall domain being zero. If only the (positive) viscous dissipation term is considered in the energy conservation equation, the domain behaves like a heat multiplier, the heat output being higher than the heat input. If this is not taken into consideration, erroneous conclusions about flow and temperature fields and heat transfer results are obtained. In mixed convection problems, part of the viscous dissipation term is equally due to the work of pressure forces. Attention is given mainly to the natural convection problem in a square enclosure, the main conclusions applying for general natural or mixed convection heat transfer problems.