Combined effects of blockage and yield stress on drag and heat transfer from an in-line array of three spheres

Abstract

This work reports results on the drag and heat transfer from an in-line array of three isothermal spheres falling in a cylindrical confinement filled with Bingham plastic fluids. The effects of dimensionless parameters, such as the Reynolds number (1 ≤ Re ≤ 100), Prandtl number (1 ≤ Pr ≤ 100), Bingham number (0 ≤ Bn ≤ 100), blockage ratio (2 ≤ β ≤ 4) and sphere-to-sphere distance (1.5 ≤ t ≤ 6) have been elucidated. The flow and heat transfer characteristics were analysed in terms of yielded/unyielded regions, streamline and isotherm contours, drag coefficient, pressure coefficient, and local and average Nusselt number. Broadly, the drag coefficient shows a positive dependence on Bn and sphere-to-sphere distance (t) while it exhibits an inverse dependence on Re and β. On the other hand, the Nusselt number shows a positive dependence on Re, Pr, Bn and β; and a complex dependence on t for each sphere. Simple predictive expressions for the average Nusselt number for each sphere are formulated, thereby enabling its prediction in a new application.

GRAPHICAL ABSTRACT

Keywords:

• Array of spheres
• Bingham fluid
• drag
• heat transfer
• wall effects

Acknowledgments

RPC would like to thank the Department of Science and Technology, Government of India for the award of a J.C. Bose fellowship for the period 2015-2020.