# MAGNETOHYDRODYNAMIC MIXED CONVECTION IN A LID-DRIVEN RECTANGULAR ENCLOSURE PARTIALLY HEATED AT THE BOTTOM AND COOLED AT THE TOP

## Main Article Content

## Abstract

In the present study, numerical simulation of magnetohydrodynamic (MHD) mixed convection heat transfer and fluid flow has been analyzed in a lid-driven enclosure provided with a constant flux heater. Governing equations were solved via differential quadrature (DQ) method. Moving wall of the enclosure has constant temperature and speed. The calculations were performed for different Richardson number ranging from 0.1 to 10, constant heat flux heater length from 0.2 to 0.8, location of heater center from 0.1 to 0.9, Hartmann number from 0 to 100 and aspect ratio from 0.5 to 2. Two different magnetic field directions were tested as vertical and horizontal. It was found that results of DQ method show good agreement with the results of literature. The magnetic field was more effective when it applied horizontally than that of vertical way. In both direction of magnetic field, it reduced the flow strength and heat transfer. Thus, it can be used as an important control parameter for heat and fluid flow.

## Article Details

**Thermal Science**, [S.l.], mar. 2017. ISSN 2334-7163. Available at: <http://thermal-science.tech/journal/index.php/thsci/article/view/2100>. Date accessed: 24 june 2017. doi: https://doi.org/10.2298/TSCI141121053O.

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Accepted 2017-03-13

Published 2017-03-13

## References

[2] Guo, G., Sharif, M.A.R., Mixed Convection in Rectangular Cavities at Various Aspect Ratios with Moving Isothermal Sidewalls and Constant Flux Heat Source on the Bottom Wall, International Journal of Thermal Sciences, 43 (2004), 5,pp.465-475

[3] Oztop, H.F., Combined Convection Heat Transfer in a Porous Lid-Driven Enclosure due to Heater with Finite Length, Int. Comm. Heat Mass Transfer, 33 (2006),6,pp.772–779

[4] Ogut, E.B., Mixed Convection in an Inclined Lid-Driven Enclosure with a Constant Flux Heater using Differential Quadrature (DQ) Method, International Journal of the Physical Sciences, 5 (2010),15,pp. 2287-2303

[5] Kahveci, K., Ogut, E.B., Mixed Convection of Water-Based Nanofluids in a Lid-Driven Square Enclosure with a Heat Source, Heat Transfer Research, 42 (2011),8, pp. 711-735

[6] Oreper, G.M., Szekely, J., The Effect of an Externally Imposed Magnetic Field on Buoyancy Driven Flow in a Rectangular Cavity, Journal of Crystal Growth, 64 (1983),3,pp.505-515

[7] Ozoe, H., Maruo, M., Magnetic and Gravitational Natural Convection of Melted Silicon-Two Dimensional Numerical Computations for the Rate of Heat Transfer, JSME, 30 (1987), 263, pp. 774- 784

[8] Ece, M.C., Buyuk, E. Natural Convection Flow under a Magnetic Field in an Inclined Rectangular Enclosure Heated and Cooled on Adjacent Walls, Fluid Dyn. Res., 38 (2006),8,pp.564–590

[9] Oztop, H.F., et al., Numerical Simulation of Magnetohydrodynamic Buoyancy-Induced Flow in a Non-Isothermally Heated Square Enclosure, Comm Nonlinear Science Numerical Simulation, 14(2009),3,pp.770-778

[10] Ogut, E.B., Magnetohydrodynamic Natural Convection Flow in an Enclosure with a Finite Length Heater Using the Differential Quadrature (DQ) Method, Numerical Heat transfer Part A-Applications, 58 (2010),11, 900-921

[11] Hossain, M.A., et al., Buoyancy and Thermocapillary Driven Convection Flow of an Electrically Conducting Fluid in an Enclosure with Heat Generation, Int J Thermal Sci, 44 (2005), 7,pp.676-684

[12] Chamkha, A., Hydromagnetic Combined Convection Flow in a Vertical Lid-Driven Cavity with Internal Heat Generation or Absorption, Numerical Heat Transfer, Part A, 41 (2002),5,pp.529-546

[13] Chatterjee, D., Gupta, S.K., Hydromagnetic Mixed Convective Transport in a Nonisothermally Heated Lid-Driven Square Enclosure Including a Heat-Conducting Circular Cylinder, Industrial & Engineering Chemistry Research, 53 (2014),51, pp. 19775−19787

[14] Selimefendigil F., Öztop, H.F., Numerical study of MHD Mixed Convection in a Nanofluid Filled Lid Driven Square Enclosure with a Rotating Cylinder, International Journal of Heat and Mass Transfer 78 (2014), pp.741–754

[15] Ganji, D.D., Malvandi, A., Natural Convection of Nanofluids inside a Vertical Enclosure in the Presence of a Uniform Magnetic Field, Powder Technology, 263 (2014), pp. 50–57

[16] Aminossadati, S.M. et.al , Computational Analysis of Magnetohydrodynamic Natural Convection in a Square Cavity with a Thin Fin, European Journal of Mechanics B/Fluids, 46 (2014), pp. 154–163

[17] Sutton, G.W., Sherman, A., Engineering Magnetohydrodynamics, McGraw-Hill, New York, 1965

[18] Bellman, R.E., Casti, J., Differential Quadrature and Long Term Integration, J. Math. Anal. Appl, 34 (1971),2,pp. 235-238

[19] Shu, C., Richards, B.E., Application of Generalized Differential Quadrature to Solve Two-Dimension Incompressible Navier-Stokes Equations, Int J Numer Methods Fluids, 15 (1992),7,pp. 791-798

[20] Shu, C., Richards, B.E., Parallel Simulation of Incompressible Viscous Flows by Generalized Differential Quadrature, Comput System Eng, 3 (1992), 1-4, pp. 271-281

[21] Kahveci, K, Oztuna S., MHD Natural Convection Flow and Heat Transfer in a Laterally Heated Partitioned Enclosure, European Journal of Mechanics B/Fluids, 28 (2009), pp.744–752

[22] Ece, M. C. ve E. Büyük, Natural Convection Flow Under a Magnetic Field in an Inclined Rectangular Enclosure Heated and Cooled on Adjacent Walls, Fluid Dynamics Research, 38 (2006), 564-590

[23] Ece, M. C. ve E. Büyük, The Effect of an External Magnetic Field on Natural Convection in an Inclined Rectangular Enclosure, Proceedings of the Institution of Mechanical Engineers, Part C, Journal of Mechanical Engineering Science, 221, (2007),pp.1609-1622

[24] Rudraiah, N., et al., Effect of a Magnetic Field on Free Convection in a Rectangular Enclosure, Int. J. Engng. Sci., 33 (1995),8,pp. 1075-1084

[25] Torrance, K., et al., Cavity Flows Driven by Buoyancy and Shear, J Fluid Mec., 2 (1972),51,pp.221- 231