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Research Papers

Magnetic Field Effect on Mixed Convection in Lid-Driven Trapezoidal Cavities Filled With a Cu–Water Nanofluid With an Aiding or Opposing Side Wall

[+] Author and Article Information
Ali J. Chamkha

Mechanical Engineering Department,
Prince Sultan Endowment for Energy
and Environment,
Prince Mohammad Bin Fahd University,
Al-Khobar 31952, Kingdom of Saudi Arabia
e-mail: achamkha@pmu.edu.sa

Muneer A. Ismael

Mechanical Engineering Department,
Engineering College,
University of Basrah,
Basrah 61004, Iraq
e-mail: muneerismael@yahoo.com

1Corresponding author.

Contributed by the Heat Transfer Division of ASME for publication in the JOURNAL OF THERMAL SCIENCE AND ENGINEERING APPLICATIONS. Manuscript received June 4, 2015; final manuscript received March 9, 2016; published online April 26, 2016. Assoc. Editor: Bengt Sunden.

J. Thermal Sci. Eng. Appl 8(3), 031009 (Apr 26, 2016) (12 pages) Paper No: TSEA-15-1159; doi: 10.1115/1.4033211 History: Received June 04, 2015; Revised March 09, 2016

The present study investigates mixed convection inside a Cu–water nanofluid filled trapezoidal cavity under the effect of a constant magnetic field. The mixed convection is achieved by the action of lid-driving of the right hot inclined side wall in the aiding or the opposing direction. The left inclined side wall is fixed and kept isothermal at a cold temperature. The horizontal top and bottom walls are fixed and thermally insulated. The magnetic field is imposed horizontally. The problem is formulated using the stream function-vorticity procedure and solved numerically using an efficient upwind finite-difference method. The studied parameters are: the Richardson number Ri = (0.01–10), the Hartman number Ha = (0–100), the volume fraction of Cu nanoparticles φ = (0–0.05), and the inclination angle of side walls Φ = (66 deg, 70 deg, 80 deg). The results have shown that the suppression effect of the magnetic field for the aiding case is greater than that for the opposing case. Meanwhile, the enhancement of the Nusselt number due to the presence of the Cu nanoparticles is greater for opposing lid-driven case.

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Figures

Grahic Jump Location
Fig. 1

Schematic illustration of the geometry

Grahic Jump Location
Fig. 3

Effect of Ha and Ri on streamlines (upper row) and isotherms (lower row) for aiding lid-driven case and Φ = 73 deg, solid lines φ = 0, and dashed lines φ = 0.03: (a) Ri = 0.1, (b) Ri = 1, and (c) Ri = 10

Grahic Jump Location
Fig. 4

Effect of Ha and side wall inclination on streamlines (upper row) and isotherms (lower row) for aiding lid-driven, Ri = 1.0, solid lines φ = 0, and dashed lines φ = 0.03: (a) Φ = 66 deg and (b) Φ = 80 deg

Grahic Jump Location
Fig. 5

Effect of Ha and Ri on streamlines (upper row) and isotherms (lower row) for opposing lid-driven and Φ = 73 deg, solid lines φ = 0, and dashed lines φ = 0.03: (a) Ri = 0.1, (b) Ri = 1, and (c) Ri = 10

Grahic Jump Location
Fig. 2

Numerical finite difference method grid

Grahic Jump Location
Fig. 6

Effect of Ha and side wall inclination on streamlines (upper row) and isotherms (lower row) for opposing lid-driven case, Ri = 1.0, solid lines φ = 0 and dashed lines φ = 0.03: (a) Φ = 66 deg and (b) Φ = 80 deg

Grahic Jump Location
Fig. 7

Distributions of local Nusselt number along the inclined right side wall NuR for Φ = 73 deg, φ = 0.03, and Ri = 1.0

Grahic Jump Location
Fig. 8

Distributions of local Nusselt number along the inclined right side wall NuR for Φ = 73 deg, φ = 0.03, and Ha = 0

Grahic Jump Location
Fig. 9

Distributions of local Nusselt number along the inclined right side wall NuR for Φ = 73 deg, Ha = 50, and Ri = 1.0

Grahic Jump Location
Fig. 10

Variation of average Nusselt number along the inclined right side wall Nuav for Φ = 73 deg, Ri = 1.0

Grahic Jump Location
Fig. 11

Variation of average Nusselt number along the inclined right side wall Nuav for Φ = 73 deg, Ha = 10

Grahic Jump Location
Fig. 12

Variation of average Nusselt number along the inclined right side wall Nuav for Ha = 10, Ri = 1.0

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