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Research Papers: Natural and Mixed Convection

# Numerical Analysis of Interaction Between Inertial and Thermosolutal Buoyancy Forces on Convective Heat Transfer in a Lid-Driven Cavity

[+] Author and Article Information
D. Senthil kumar, Akhilesh Gupta

Department of Mechanical and Industrial Engineering, Indian Institute of Technology Roorkee, Roorkee 247 667, India

K. Murugesan1

Department of Mechanical and Industrial Engineering, Indian Institute of Technology Roorkee, Roorkee 247 667, Indiakrimufme@iitr.ernet.in

1

Corresponding author.

J. Heat Transfer 132(11), 112501 (Aug 13, 2010) (11 pages) doi:10.1115/1.4002029 History: Received August 19, 2009; Revised May 03, 2010; Published August 13, 2010; Online August 13, 2010

## Abstract

In this paper, results on double diffusive mixed convection in a lid-driven cavity are discussed in detail with a focus on the effect of interaction between fluid inertial force and thermosolutal buoyancy forces on convective heat and mass transfer. The governing equations for the mathematical model of the problem consist of vorticity transport equation, velocity Poisson equations, energy equation and solutal concentration equation. Numerical solution for the field variables are obtained by solving the governing equations using Galerkin’s weighted residual finite element method. The interaction effects on convective heat and mass transfer are analyzed by simultaneously varying the characteristic parameters, $0.1, $100, and buoyancy ratio (N), $−10. In the presence of strong thermosolutal buoyancy forces, the increase in fluid inertial force does not make significant change in convective heat and mass transfer when the thermal buoyancy force is smaller than the fluid inertial force. The fluid inertial force enhances the heat and mass transfer only when the thermal buoyancy force is either of the same magnitude or greater than that of the fluid inertial force. The presence of aiding solutal buoyancy force enhances convective heat transfer only when Ri becomes greater than unity but at higher buoyancy ratios, the rate of increase in heat transfer decreases for $Re=400$ and increases for $Re=800$. No significant change in heat transfer is observed due to aiding solutal buoyancy force for $Ri≤1$ irrespective of the Reynolds number.

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## Figures

Figure 1

Schematic diagram of the problem

Figure 2

Validation results

Figure 3

Streamline patterns for the effect of buoyancy forces for different Ri at Re=100 and Le=1

Figure 4

Streamline patterns for the effect of Ri for different Re at Le=N=1

Figure 5

Temperature and concentration contours for the effect of buoyancy forces for different Ri at Re=100 and Le=1

Figure 6

Temperature and concentration contours for the effect of Ri for different Re at Le=N=1

Figure 7

Effect of buoyancy force and Reynolds number on average Nusselt number for Ri=0.1 and Le=1

Figure 8

Effect of buoyancy forces on hot wall average Nusselt number for Reynolds number variation

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