Combined effects of fluid yield stress and geometrical arrangement on natural convection in a square duct from two differentially heated horizontal cylinders

[+] Author and Article Information
Lubhani Mishra

Department of Chemical Engineering Pandit Deendayal Petroleum University Gandhinagar, Gujarat 382007 India lubhanimishra11@gmail.com

R. P. Chhabra

Kanpur Kanpur, 208016 India chhabra@iitk.ac.in

1Corresponding author.

Contributed by the Heat Transfer Division of ASME for publication in the Journal of Thermal Science and Engineering Applications. Manuscript received May 23, 2019; final manuscript received July 22, 2019; published online xx xx, xxxx. Assoc. Editor: Sandip Mazumder.

ASME doi:10.1115/1.4044429 History: Received May 23, 2019; Accepted July 22, 2019


Laminar natural convection in Bingham plastic fluids has been investigated from two differentially heated cylinders in vertical or diagonal alignments in a square enclosure. The momentum and energy equations have been solved to elucidate the effect of Rayleigh number (104 to 106), Prandtl number (10 to 100), Bingham number (0.01 to Bnmax), and geometric parameters (0 to -0.25 for vertical alignment) and (0.15 to 0.35 for diagonal alignment) on the detailed structure of the flow field and the overall heat transfer characteristics of the system. New extensive results are visualized in terms of streamlines, isotherm contours and plots of the local and average Nusselt number. Additional insights are developed by examining the shear-rate contours and the yield surfaces. At high values of the Bingham number, the average Nusselt number reaches its asymptotic value corresponding to the conduction limit. The increasing Rayleigh number promotes fluid-like behavior which influence the heat transfer in a complex manner. The augmentation in heat transfer depends on the volume of fluid participating in buoyancy flow. Finally, predictive correlations have been developed for the average Nusselt number and the limiting Bingham number.

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