Summary
The effect of a magnetic field on the buoyancy-driven flow of water inside a square cavity with differentially heated side walls is studied numerically. A finite difference scheme consisting of ADI (Alternating Direction Implicit) and SOR (Successive Over Relaxation) methods are used to solve the coupled nonlinear equations. The flow pattern and the heat transfer characteristics inside the cavity are presented for Hartmann number Ha varying over 0 to 100, while the vertical walls are maintained at uniform but different temperatures withθ c = 0°C (cold wall) and 4°C≤θ h ≤12°C (hot wall), while the horizontal walls are thermally insulated. The magnetic fieed dampens the flow field and the heat transfer. As the Hartmann number Ha increases, the temperature field resembles that of conduction type. The average Nusselt number\(\overline {Nu} \), the heat transfer coefficient, decreases with the increase of the Hartmann number Ha. The temperature distribution and flow fields are depicted in the form of streamlines, isotherms and mid-height velocity profiles in the graphs attached for 0≤Ha≤100, varying the hot wall temperatures from 0°C to 12°C.
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Abbreviations
- A :
-
aspect ratio
- (g, g):
-
(scalar, vector) acceleration due to gravity
- Gri's:
-
Grashof numbers
- H :
-
height
- L :
-
length
- B 0 :
-
magnetic field strength
- Ha:
-
Hartmann number
- \(\bar H\) :
-
magnetic field strength
- Nu:
-
local Nusselt number
- \(\overline {Nu} \) :
-
average Nusselt number
- Pr:
-
Prandtl number
- p:
-
pressure
- T :
-
dimensionless temperature
- t :
-
dimensional time
- u, v :
-
dimensional velocity components
- U, V :
-
dimensionless velocity components
- x, y :
-
dimensional coordinates
- X, Y :
-
dimensionless coordinates
- α:
-
thermal diffusivity
- β:
-
volumetric coefficient of thermal expansion
- μ:
-
dynamic viscosity
- ν:
-
kinematic viscosity
- ω:
-
dimensional vorticity
- σ e :
-
electrical conductivity of the medium
- ψ:
-
dimensional stream function
- Ψ:
-
dimensionless stream function
- p :
-
density
- τ:
-
dimensionless time
- θ:
-
dimensional temperature
- ζ:
-
dimensionless vorticity
- c :
-
cold wall
- h :
-
hot wall
- 0:
-
reference state
References
Watson, A.: The effect of inversion temperature on the convection of water in an enclosed rectangular cavity. Q. J. Mech. Appl. Math.25, 425–446 (1972).
Inaba, H., Fakuda, T.: An experimental study of natural convection in an inclined rectangular cavity filled with water at its density extremum. J. Heat Transfer106, 109–115 (1984).
Zebib, A., Homsy, G. M., Meiburg, E.: High Marangoni convection in a square cavity. Phys. Fluids28, 3467–3476 (1985).
Nansteel, M. W., Medjani, K., Lin, D. S.: Natural convection of water near its density maximum in a rectangular enclosure: Low Reynolds number calculations. Phys. Fluids30, 312–317 (1987).
Wilkes, J. O., Churchill, S. W.: The finite differenc computation of natural convection in a rectangular enclosure. AIChE J.12, 161–166 (1966).
Sundaravadivelu, K., Kandaswamy, P.: Buoyancy-driven non-linear convection in a square cavity. Int. J. Heat Mass Transfer (in press).
Rudraiah, N., Barron, R. M., Venkatachalappa, M., Subbaraya, C. K.: Effect of magnetic field on free convection in a rectangular enclosure. Int. J. Eng. Sci.33, 1075–1084 (1995).
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Kandaswamy, P., Kumar, K. Buoyancy-driven nonlinear convection in a square cavity in the presence of a magnetic field. Acta Mechanica 136, 29–39 (1999). https://doi.org/10.1007/BF01292296
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DOI: https://doi.org/10.1007/BF01292296