The Bombay Technologist

Free Convection in Non-Newtonian Fluids from Heated Objects

Raj Chhabra

Department of Chemical Engineering, Indian Institute of Technology, Kanpur

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Abstract

This paper presents an overview of our research activity in the field of free convection in non- Newtonian fluids from variously shaped heated objects. In particular, consideration is given to two broad classes of fluids, namely, power-law fluids (shear-thinning and shear-thickening type) and Bingham plastic fluids. We have sought numerical solutions to the coupled momentum and energy equations within the framework of Boussinesq approximation to capture the temperature dependence of the liquid density; all other thermo-physical properties are, however, assumed to be independent of temperature within the narrow range of temperature differences imposed in the system. The present results span wide ranges of Grash of number, Prandtl number and power- law index for a range of shapes including a sphere, a horizontal cylinder, elliptic cylinders of various cross-sections, a semi-circular cylinder and a square bar maintained at a constant temperature which is greater than that of the surrounding liquid. Extensive results on isotherm contours and streamline patterns and on Nusselt number are presented to delineate its scaling with Grash of number, Prandtl number and power- law index. Finally the present results are shown to be in good agreement with the scant experimental results available in this field. The paper is concluded by elucidating the role of shape and orientation of the heated object on free convection. The universal appeal of a composite parameter, akin to the Rayleigh number, in correlating the Nusselt number results for a wide variety of 2-D axisymmetric shapes is demonstrated. Finally, additional challenges posed by the Bingham plastic fluids are briefly discussed by way of free convection from a heated cylinder submerged in quiescent Bingham plastic fluids.