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EFFECT OF CONFINEMENT ON THE STEADY FLOW OF BINGHAM PLASTIC FLUIDS PAST A HEATED SQUARE CYLINDER

P. Mishra
Department of Chemical Engineering, Indian Institute of Technology Kanpur, Kanpur, U.P, India

Rajenda P. Chhabra
Department of Chemical Engineering, Indian Institute of Technology Kanpur, Kanpur, U.P.208016, India

DOI: 10.1615/IHMTC-2017.500
pages 369-376

摘要

The Bingham plastic fluids are characterized by their dual nature, i.e., coexistence of yielded (fluid-like) and unyielded (solid-like) regions depending upon the existing stress levels vis-a-vis the fluid yield stress. This feature makes their homogenization and heating/cooling far more complicated than that for simple Newtonian fluids like air and water [1]. In this work, the heat transfer characteristics for the steady flow of Bingham plastic fluids over a square cylinder confined in a plane slit have been explored numerically in terms of the isotherm contours, local Nusselt number and average Nusselt number for the following ranges of conditions: Bingham number, 0.01 ≤ Bn ≤ 100, Reynolds number, 0.1 ≤ Re ≤ 40, Prandtl number, 10 ≤ Pr ≤ 100, and blockage ratio (ratio of side of cylinder to channel height), β(l/H) = 0.2, 0.3, 0.4. Furthermore, the influence of the two different thermal boundary conditions i.e. constant heat flux condition (CHF) and constant wall temperature (CWT) prescribed on the surface of the square cylinder has also been delineated. The emphasis is laid on elucidating the effect of blockage ratio on the overall heat transfer as blockage ratio influences the temperature gradients and due to the extra dissipation at the confining walls. In Bingham plastic fluids, heat transfer occurs by two competing mechanisms i.e., by convection in fluid-like and by conduction in solid unyielded regions. Thus the overall heat transfer is determined in a complex manner by these two competing mechanisms. Finally, a simple predictive correlation is presented which captures the effect of Re, Bn, Pr and β on the average Nusselt number (in terms of the Colburn j-factor) for both CHF and CWT conditions.

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