Abstract

Two-dimensional steady-state buoyancy driven flows of thermo-dependent shear-thinning power-law fluid confined in a square cavity, submitted to cross uniform heat fluxes, has been conducted numerically using a finite difference technique. The parameters governing the problem are the thermo-dependence number m (0≤m≤10) and the ratio between the heat flux imposed on the vertical walls and that imposed on the horizontal ones represented by a (0≤a≤1), while the flow behavior index n is fixed at (n=1.4) and the Rayleigh number at (R_a=5000). The effects of these parameters on the flow structure and heat transfer characteristics have been analyzed.

Highlights

  • Thermal buoyancy convection is a flow resulting from density variations within a non-isothermal fluid under the gravity effect

  • The numerical results from the code have been validated using the benchmark data of de Vahl Davis [16], Turki [8] and Ouertatani [17] for natural convection of Newtonian and non-Newtonian fluids in square enclosures with differentially heated vertical walls and an excellent agreement was obtained

  • As was reported in the past by [15], the convection is rather insensitive to Pr variations, provided that this parameter is large enough as it is the case for the non-Newtonian fluids and for a large category of fluids having a Newtonian behavior

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Summary

Introduction

Thermal buoyancy convection is a flow resulting from density variations within a non-isothermal fluid under the gravity effect. Such a phenomenon is of importance in various domains, which attracted many worldwide researchers, through the decades, to investigate it in many geometrical configurations and under various boundary conditions. Viscous non-Newtonian fluids can be divided into two categories: shear-thinning or pseudo-plastic fluids and shear-thickening or dilatant fluids. For the formers (shear-thinning fluids), the viscosity is a decreasing function of the rate of shear This property is specific to some complex solutions like ketchup, whipped cream, blood, paint, and nail polish. The viscous force causes it to go from being thick like honey to flowing like water For the latter (shear-thickening fluids), the viscosity increases with the rate of shear. The dilatant effect can readily be seen with a mixture of cornstarch and water, which acts in a counterintuitive way when thrown against a surface

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