Evaluation of candidate approaches in the study of conjugate convection from a fin array

An array of vertical fins standing on the top of a rectangular channel with a fluid flowing inside the channel and natural convection on the outside is an ubiquitous arrangement frequently encountered in heat transfer. The quantity of primary interest for this geometry is the heat duty (or heat transfer per unit mass). Several candidate approaches to solve this problem are available, and these range from a simple back of the envelope calculations to sophisticated conjugate heat transfer analysis using CFD techniques. This paper looks at four such approaches to this problem, and the results confirm that for a large portion of the range of parameters considered, solving the fluid flow and energy balance equations may become necessary to get meaningful numbers.