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Research Papers: Flows in Complex Systems

# A Differential Quadrature Solution of MHD Natural Convection in an Inclined Enclosure With a Partition

[+] Author and Article Information
Kamil Kahveci

Mechanical Engineering Department, Trakya University, 22030 Edirne, Turkeykamilk@trakya.edu.tr

Semiha Öztuna

Mechanical Engineering Department, Trakya University, 22030 Edirne, Turkeysemihae@trakya.edu.tr

J. Fluids Eng 130(2), 021102 (Jan 24, 2008) (14 pages) doi:10.1115/1.2829567 History: Received January 12, 2007; Revised July 16, 2007; Published January 24, 2008

## Abstract

Magnetohydrodynamics natural convection in an inclined enclosure with a partition is studied numerically using a differential quadrature method. Governing equations for the fluid flow and heat transfer are solved for the Rayleigh number varying from $104$ to $106$, the Prandtl numbers (0.1, 1, and 10), four different Hartmann numbers (0, 25, 50, and 100), the inclination angle ranging from $0degto90deg$, and the magnetic field with the $x$ and $y$ directions. The results show that the convective flow weakens considerably with increasing magnetic field strength, and the $x$-directional magnetic field is more effective in reducing the convection intensity. As the inclination angle increases, multicellular flows begin to develop on both sides of the enclosure for higher values of the Hartmann number if the enclosure is under the $x$-directional magnetic field. The vorticity generation intensity increases with increase of Rayleigh number. On the other hand, increasing Hartmann number has a negative effect on vorticity generation. With an increase in the inclination angle, the intensity of vorticity generation is observed to shift to top left corners and bottom right corners. Vorticity generation loops in each region of enclosure form due to multicelluar flow for an $x$-directional magnetic field when the inclination angle is increased further. In addition, depending on the boundary layer developed, the vorticity value on the hot wall increases first sharply with increasing $y$ and then begins to decrease gradually. For the high Rayleigh numbers, the average Nusselt number shows an increasing trend as the inclination angle increases and a peak value is detected. Beyond the peak point, the foregoing trend reverses to decrease with the further increase of the inclination angle. The results also show that the Prandtl number has only a marginal effect on the flow and heat transfer.

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## Figures

Figure 1

Geometry and coordinate system

Figure 2

Distributions of the velocities along the lines y=0,0.5,0.75 for Pr=1 and Ha=0

Figure 3

Streamlines and isotherms for Ra=106, Pr=1, and φ=0deg

Figure 4

Streamlines and isotherms for Ra=106, Pr=1, and φ=30deg

Figure 5

Streamlines and isotherms for Ra=106, Pr=1, and φ=60deg

Figure 6

Streamlines and isotherms for Ra=106, Pr=1, and φ=90deg

Figure 7

Vorticity contours for Ra=106, Pr=1, and φ=0deg

Figure 8

Vorticity contours for Ra=106, Pr=1, and φ=30deg

Figure 9

Vorticity contours for Ra=106, Pr=1, and φ=60deg

Figure 10

Vorticity contours for Ra=106, Pr=1, and φ=90deg

Figure 11

Variation of the vorticity along the hot wall with the Rayleigh number for Pr=1 and Ha=50

Figure 12

Variation of the vorticity along the hot wall with the Hartmann number for Pr=1 and Ra=106

Figure 13

Variation of location of maximum values of vorticity along the hot wall for φ=0

Figure 14

Variation of the local Nusselt number with the Rayleigh number for Pr=1 and Ha=50

Figure 15

Variation of the local Nusselt number with the Prandtl number for Ra=106 and Ha=50

Figure 16

Variation of the local Nusselt number with the Hartmann number for Ra=106 and Pr=1

Figure 17

Variation of the average Nusselt number with the Rayleigh number

Figure 18

Variation of the average Nusselt number with the inclination angle

Figure 19

A comparison for the average Nusselt number

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