Eur. Phys. J. B 62, 77-86 (2008)
https://doi.org/10.1140/epjb/e2008-00115-0

Fluid friction in incompressible laminar convection: Reynolds' analogy revisited for variable fluid properties

¹ Department of Aerospace Engineering, Indian Institute of Technology, Bombay, Mumbai, 400076, India
² Institut fr Thermofluiddynamik, Technische Universität Hamburg-Harburg, 21073 Hamburg, Germany

Corresponding author: ^a spm@aero.iitb.ac.in

Received: 19 August 2007
Revised: 17 December 2007
Published online: 19 March 2008

Abstract

The Reynolds' analogy between the Stanton number (St) and the skin friction coefficient (c_f) is popularly believed to hold when St increases with increasing c_f, for simple situations. In this investigation, the validity of Reynolds' analogy between St and c_f for micro-convection of liquids with variations in fluid properties is re-examined. It is found that the Sieder-Tate's property-ratio method for obtaining Nusselt number corrections is theoretically based on the validity of Reynolds' analogy. The inverse dependence of Reynolds number and skin friction coefficient is the basis for validity of the Reynolds' analogy, in convective flows with fluid property variations. This leads to the unexpected outcome that Reynolds' analogy now results in St increasing with decreasing c_f. These results and their analyses indicate that the validity of Reynolds' analogy is based on deeper foundations, and the well-known validity criterion is a special case.