Criteria for Predicting Transitions in Free Convection Heat Transfer From Isothermal Convex Bodies in Fluids With Any Prandtl Number: A New Analytical Model

ABSTRACT

This article presents criteria for predicting transitions in free convection from isothermal convex bodies in fluids with any Prandtl number (conduction–laminar and laminar–turbulent transitions). Laminar–turbulent transition results for vertical plates happening in the vicinity of Grashof number 10⁹ in fluids with any Prandtl number and other geometries show that this criterion based on Grashof number is a better choice compared to that of the Rayleigh number, as the Prandtl number yields a large change in the transition Rayleigh number. Besides, for convex geometries other than vertical plates, the laminar–turbulent transition occurs at values slightly less than Grashof number 10⁹ owing to longitudinal vortices bringing about separation over their surface and helping laminar–turbulent transition to arise sooner. On the other side, the results of the conduction–laminar transition criterion for different convex bodies disclose that the Rayleigh number is superior to the Grashof number. Likewise, the present results for five different geometries over a wide range of Prandtl numbers are compared with the available experimental data, and excellent agreement is found. This reveals that the proposed criteria is powerful enough to predict the two transition phenomena in free convection heat transfer from isothermal convex bodies for a wide range of convex geometries in fluids with any Prandtl number.

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Notes on contributors

Pouria Arabi

Pouria Arabi is a Ph.D. student in mechanical engineering at Shiraz University, Shiraz, Iran. He worked on analytical and numerical modeling of free convection heat transfer for his master's thesis and received his M.Sc. at Shiraz University in September 2013. His research interests have encompassed conduction and convection heat transfer, numerical as well as experimental modeling of heat and fluid flow, turbulent flow modeling, and energy and environment, in addition to biomechanics.

Khosrow Jafarpur

Khosrow Jafarpur is a professor of mechanical engineering at Shiraz University, Shiraz, Iran. He received his Ph.D. at the University of Waterloo, Canada, in 1992 and joined Shiraz University in the same year. His research includes convection and conduction heat transfer, solar energy measurement, and solar stills, as well as heat transfer (and optimization) in welding, porous media, and nanosystems. He is the author or co-author of about 145 papers on these topics.