The effect of an external magnetic field on natural convection in an inclined rectangular enclosure

2007 ◽  
Vol 221 (12) ◽  
pp. 1609-1622 ◽  
Author(s):  
M C Ece ◽  
E Büyük
Keyword(s):  
Magnetic Field ◽  
Natural Convection ◽  
Differential Quadrature Method ◽  
Convection Flow ◽  
Rectangular Enclosure ◽  
Aspect Ratios ◽  
Inclination Angles ◽  
Side Walls ◽  
Vertical Walls ◽  
The Magnetic Field

Steady, laminar, natural-convection flow in the presence of a magnetic field of an arbitrary direction in an inclined rectangular enclosure with isothermal vertical walls and adiabatic horizontal walls was considered. The governing equations were solved numerically for the stream function, vorticity, and temperature ratio using the differential quadrature method for various Grashof and Hartman numbers and three different magnetic field directions, aspect ratios, and inclination angles. Counter-clockwise inclination of the enclosure enhances the convection whereas the clockwise inclination retards it. The magnetic field applied normal to the side walls are more effective for square and tall enclosures whereas the magnetic field applied parallel to the side walls is more effective for shallow enclosures.

An Unsteady Double-Diffusive Natural Convection in an Inclined Rectangular Enclosure with Different Angles of Magnetic Field

2016 ◽  
Vol 13 (04) ◽  
pp. 1641015 ◽  
Author(s):  
Sabyasachi Mondal ◽  
Precious Sibanda
Keyword(s):  
Magnetic Field ◽  
Natural Convection ◽  
Staggered Grid ◽  
Convection Flow ◽  
Rectangular Enclosure ◽  
Nusselt Numbers ◽  
Inclination Angles ◽  
The Magnetic Field ◽  
Buoyancy Ratio ◽  
Double Diffusive

An unsteady double-diffusive natural convection flow in an inclined rectangular enclosure subject to an applied magnetic field and heat generation parameter is studied. The enclosure is heated and concentrated from one side and cooled from the adjacent side. The other two sides are adiabatic. The governing equations are solved numerically using a staggered grid finite-difference method to determine the streamline, isotherm and iso-concentration contours. We have further obtained the average Nusselt numbers and average Sherwood numbers for various values of buoyancy ratio and different angles of the magnetic field by considering three different inclination angles of the enclosure while keeping the aspect ratio fixed. The results indicate that the flow pattern, temperature and concentration fields are significantly dependent on the buoyancy ratio and the magnetic field angles. It is found that different angles of the magnetic field suppress the convection flow and its direction influences the flow patterns. This leads to the appearance of inner loop and multiple eddies.

MIXED CONVECTION IN AN INCLINED AND LID-DRIVEN RECTANGULAR ENCLOSURE HEATED AND COOLED ON ADJACENT WALLS

2008 ◽  
Vol 32 (2) ◽  
pp. 213-226 ◽  
Author(s):  
Elif Büyük Öğüt
Keyword(s):  
Mixed Convection ◽  
Differential Quadrature Method ◽  
Side Wall ◽  
Temperature Fields ◽  
Convection Flow ◽  
Rectangular Enclosure ◽  
Aspect Ratios ◽  
Laminar Mixed Convection ◽  
Inclination Angles ◽  
Steady Laminar

Steady, laminar, mixed convection flow was considered in an inclined lid-driven rectangular enclosure heated from one side moving with a constant speed and cooled from the stationary adjacent side while the other sides are kept stationary and adiabatic. The governing equations were solved numerically for the stream function, vorticity, and temperature ratio using the differential quadrature method for various Reynolds, Grashof, and Richardson numbers as well as different aspect ratios and inclination angles for the enclosure. The results show that the motion of the side wall, the aspect ratio, and the inclination angle of the enclosure had significant effects on the flow and temperature fields.

Effect of a Magnetic Field on the Heat Transfer Rate on Free Convection in a Rectangular Cavity

2005 ◽  
Author(s):  
Gustavo Gutierrez ◽  
Ezequiel Medici
Keyword(s):  
Magnetic Field ◽  
Heat Transfer ◽  
Natural Convection ◽  
Heat Transfer Rate ◽  
Transfer Rate ◽  
Stokes Equations ◽  
Rectangular Cavity ◽  
Convection Flow ◽  
Interesting Phenomenon ◽  
The Magnetic Field

The interaction between magnetic fields and convection is an interesting phenomenon because of its many important engineering applications. Due to natural convection motion the electric conductive fluid in a magnetic field experiences a Lorenz force and its effect is usually to reduce the flow velocities. A magnetic field can be used to control the flow field and increase or reduce the heat transfer rate. In this paper, the effect of a magnetic field in a natural convection flow of an electrically conducting fluid in a rectangular cavity is studied numerically. The two side walls of the cavity are maintained at two different constant temperatures while the upper wall and the lower wall are completely insulated. The coupling of the Navier-Stokes equations with the Maxwell equations is discussed with the assumptions and main simplifications assumed in typical problems of magnetohydrodynamics. The nonlinear Lorenz force generates a rich variety of flow patterns depending on the values of the Grashof and Hartmann numbers. Numerical simulations are carried out for different Grashof and Hartmann numbers. The effect of the magnetic field on the Nusselt number is discussed as well as how convection can be suppressed for certain values of the Hartmann number under appropriate direction of the magnetic field.

scholarly journals Homotopy Analysis Solution of Hydromagnetic Mixed Convection Flow Past an Exponentially Stretching Sheet with Hall Current

2012 ◽  
Vol 2012 ◽  
pp. 1-26 ◽  
Author(s):  
Mohamed Abd El-Aziz ◽  
Tamer Nabil
Keyword(s):  
Magnetic Field ◽  
Mixed Convection ◽  
Convection Flow ◽  
Mixed Convection Flow ◽  
Electrically Conducting ◽  
Hall Parameter ◽  
Homotopy Analysis ◽  
Continuous Sheet ◽  
Exponentially Stretching ◽  
The Magnetic Field

The effect of thermal radiation on steady hydromagnetic heat transfer by mixed convection flow of a viscous incompressible and electrically conducting fluid past an exponentially stretching continuous sheet is examined. Wall temperature and stretching velocity are assumed to vary according to specific exponential forms. An external strong uniform magnetic field is applied perpendicular to the sheet and the Hall effect is taken into consideration. The resulting governing equations are transformed into a system of nonlinear ordinary differential equations using appropriate transformations and then solved analytically by the homotopy analysis method (HAM). The solution is found to be dependent on six governing parameters including the magnetic field parameterM, Hall parameterm, the buoyancy parameterξ, the radiation parameterR, the parameter of temperature distributiona, and Prandtl number Pr. A systematic study is carried out to illustrate the effects of these major parameters on the velocity and temperature distributions in the boundary layer, the skin-friction coefficients, and the local Nusselt number.

Visualization and Prediction of Natural Convection of Water Near Its Density Maximum in a Tall Rectangular Enclosure at High Rayleigh Numbers

2000 ◽  
Vol 123 (1) ◽  
pp. 84-95 ◽  
Author(s):  
C. J. Ho ◽  
F. J. Tu
Keyword(s):  
Natural Convection ◽  
Vertical Wall ◽  
Three Dimensional ◽  
Temperature Fields ◽  
Convection Flow ◽  
Oscillatory Convection ◽  
Uniform Temperature ◽  
Density Maximum ◽  
Rectangular Enclosure ◽  
Rayleigh Numbers

An experimental and numerical investigation is presented concerning the natural convection of water near its maximum-density in a differentially heated rectangular enclosure at high Rayleigh numbers, in which an oscillatory convection regime may arise. The water in a tall enclosure of Ay=8 is initially at rest and at a uniform temperature below 4°C and then the temperature of the hot vertical wall is suddenly raised and kept at a uniform temperature above 4°C. The cold vertical wall is maintained at a constant uniform temperature equal to that of the initial temperature of the water. The top and bottom walls are insulated. Using thermally sensitive liquid crystal particles as tracers, flow and temperature fields of a temporally oscillatory convection was documented experimentally for RaW=3.454×105 with the density inversion parameter θm=0.5. The oscillatory convection features a cyclic sequence of onset at the lower quarter-height region, growth, and decay of the upward-drifting secondary vortices within counter-rotating bicellular flows in the enclosure. Two and three-dimensional numerical simulations corresponding to the visualization experiments are undertaken. Comparison of experimental with numerical results reveals that two-dimensional numerical simulation captures the main features of the observed convection flow.

The Effect of the Top Wall Temperature on the Laminar Natural Convection in Rectangular Cavities With Different Aspect Ratios

2009 ◽  
Vol 131 (5) ◽  
Author(s):  
Wenjiang Wu ◽  
Chan Y. Ching
Keyword(s):  
Natural Convection ◽  
Aspect Ratio ◽  
Wall Temperature ◽  
Vertical Wall ◽  
Flow Region ◽  
Temperature Profiles ◽  
Aspect Ratios ◽  
Vertical Walls ◽  
C And N ◽  
Laminar Natural Convection

The effect of the top wall temperature on the laminar natural convection in air-filled rectangular cavities driven by a temperature difference across the vertical walls was investigated for three different aspect ratios of 0.5, 1.0, and 2.0. The temperature distributions along the heated vertical wall were measured, and the flow patterns in the cavities were visualized. The experiments were performed for a global Grashof number of approximately 1.8×108 and nondimensional top wall temperatures from 0.52 (insulated) to 1.42. As the top wall was heated, the flow separated from the top wall with an undulating flow region in the corner of the cavity, which resulted in a nonuniformity in the temperature profiles in this region. The location and extent of the undulation in the flow are primarily determined by the top wall temperature and nearly independent of the aspect ratio of the cavity. The local Nusselt number was correlated with the local Rayleigh number for all three cavities in the form of Nu=C⋅Ran, but the values of the constants C and n changed with the aspect ratio.

Influence of a horizontal magnetic field on the natural convection of paramagnetic fluid in a cube heated and cooled from two vertical side walls

2008 ◽  
Vol 47 (6) ◽  
pp. 668-679 ◽  
Author(s):  
Tomasz Bednarz ◽  
Elzbieta Fornalik ◽  
Hiroyuki Ozoe ◽  
Janusz S. Szmyd ◽  
John C. Patterson ◽  
...  
Keyword(s):  
Magnetic Field ◽  
Natural Convection ◽  
Horizontal Magnetic Field ◽  
Vertical Side ◽  
Side Walls
Sign in / Sign up

Export Citation Format

Share Document