## THERMAL SCIENCE

International Scientific Journal

### EFFECT OF THERMALLY ACTIVE ZONES AND DIRECTION OF MAGNETIC FIELD ON HYDROMAGNETIC CONVECTION IN AN ENCLOSURE

**ABSTRACT**

The aim of the present numerical study is to investigate the effect of thermally active zones and direction of the external magnetic field on hydromagnetic convection in an enclosure. Nine different relative positions of the thermally active zones are considered. Top and bottom of the enclosure are adiabatic. The governing equations are solved by the finite volume method. The results are obtained for different directions of the external magnetic field, thermally active locations, Hartmann numbers, Grashof numbers and aspect ratios. It is observed that the heat transfer is enhanced for heating location is either at middle or at bottom of the hot wall while the cooling location is either at top or at middle of the cold wall. The flow field is altered when changing the direction of the magnetic field in the presence of strong magnetic field. The average Nusselt number decreases with an increase of the Hartmann number and increases with increase of the Grashof number and aspect ratio.

**KEYWORDS**

PAPER SUBMITTED: 2010-02-10

PAPER REVISED: 2011-02-01

PAPER ACCEPTED: 2011-10-06

**THERMAL SCIENCE** YEAR

**2011**, VOLUME

**15**, ISSUE

**Supplement 2**, PAGES [S367 - S382]

- Kuhn, D., Oosthuizen, P.H., Unsteady natural convection in a partially hearted rectangular enclosure, Journal of Heat Transfer, 109 (1987), pp. 798 - 801
- Tanda, G., Natural convection in partially heated vertical channels, Heat and Mass Transfer, 23 (1988), pp. 307-312
- Valencia, A., Frederick, R. L., Heat transfer in square cavities with partially active vertical walls, International Journal of Heat and Mass Transfer, 32 (1989), pp. 1567-1574
- Ho, C. J., Chang, J. Y., A study of natural convection heat transfer in a vertical rectangular enclosure with two-dimensional discrete heating: Effect of aspect ratio, International Journal of Heat and Mass Transfer, 37 (1994), 6, pp. 917 - 925
- Yucel, N., Turkoglu, H., Natural convection in rectangular enclosures with partial heating and cooling, Heat and Mass Transfer, 29 (1994), pp. 471 - 478
- El-Refaee, M.M., Elsayed, M.M., Al-Najem, N.M., Noor, A.A., Natural convection in partially cooled tilted cavities, International Journal of Numerical Methods in Fluids, 28 (1998), pp. 477 - 499
- Nithyadevi, N., Kandaswamy, P., Sivasankaran, S., Natural Convection on a Square Cavity with Partially Active Vertical Walls: Time Periodic Boundary Condition, Mathematical Problems in Engineering, 2006 (2006), pp. 1 - 16
- Kandaswamy, P., Sivasankaran, S., Nithyadevi, N., Buoyancy-driven convection of water near its density maximum with partially active vertical walls, International Journal of Heat and Mass Transfer, 50 (2007), pp. 942 - 948
- Chen, T.H., Chen, L.Y., Study of buoyancy-induced flows subjected to partially heated sources on the left and bottom walls in a square enclosure, International Journal of Thermal Sciences, 46 (2007), pp. 1219-1231
- Oztop, H.F., Abu-Nada, E., Numerical study of natural convection in partially heated rectangular enclosures filled with nanofluids, International Journal of Heat and Fluid Flow, 29 (2008) pp. 1326-1336
- Arici, M.E., Sahin, B., Natural convection heat transfer in a partially divided trapezoidal enclosure, Thermal Science, 13(4) (2009), pp. 213 - 220
- Sivakumar, V., Sivasankaran, S ., Prakash, P., Lee, J., Effect of heating location and size on mixed convection in lid-driven cavity, Computers & Mathematics with Applications, 59 (2010), pp. 3053-3065.
- Aich, W., Hajri, I., Omri, A., Numerical analysis of natural convection in a prismatic enclosure, Thermal Science, 15(2) (2011), pp. 437-446
- Delavar, M.A., Farhadi, M., Sedighi, K., Effect of discrete heater at the vertical wall of the cavity over the heat transfer and entropy generation using lattice Boltzmann method, Thermal Science, 15(2) (2011), pp. 423-435
- Sivasankaran, S., Do, Y., Sankar, M., Effect of Discrete Heating on Natural Convection in a Rectangular Porous Enclosure, Transport in Porous Media, 86 (2011), 291-311
- Sankar, M., Bhuvaneswari, M., Sivasankaran, S., Do, Y., Buoyancy Induced Convection in a Porous Enclosure with Partially Active Thermal Walls, International Journal of Heat and Mass Transfer, 54 (2011) pp. 5173-5182
- Terekhov, V.I., Chichindaev, A.V., Ekaid, A.l., Buoyancy heat transfer in staggered dividing square enclosure, Thermal Science, 15(2) (2011), pp. 409 - 422
- Bhuvaneswari, M., Sivasankaran S., Kim, Y.J., Effect of aspect ratio on convection in a porous enclosure with partially active thermal walls, Computers & Mathematics with Applications, (2011), in press (doi:10.1016/j.camwa.2011.09.033)
- Rudraiah, N., Barron, R.M., Venkatachalappa, M., Subbaraya, C.K., Effect of a magnetic field on free convection in a rectangular enclosure, International Journal of Engineering Science, 33 (1995), 8, pp. 1075-1084
- Khanafer, K.M., Chamkha, A.J., Hydromagnetic natural convection from an inclined porous square enclosure with heat generation, Numerical Heat transfer A, 33 (1998), pp. 891 - 910
- Qi, J., Wakayama, N.I., Yabe, A., Attenuation of natural convection by magnetic force in electro-nonconducting fluids, Journal of Crystal Growth, 204 (1999), pp. 408 - 412
- Hossain, M.A, Hafiz, M.Z., Rees, D.A.S., Buoyancy and thermocapillary driven convection flow of an electrically conducting fluid in an enclosure with heat generation, International Journal of Thermal Sciences, 44, (2005), pp. 676 - 684
- Sarris, I.E., Kakarantzas, S.C., Grecos, A.P., Vlachos, N.S., MHD natural convection in a laterally and volumetrically heated square cavity, International Journal of Heat and Mass Transfer, 48 (2005), pp. 3443 - 3453
- Sivasankaran, S., Ho, C.J., Effect of temperature dependent properties on MHD convection of water near its density maximum in a square cavity, International Journal of Thermal Sciences, 47 (2008), pp. 1184-1194
- Younsi, R., Computational analysis of MHD flow, heat and mass transfer in trapezoidal porous cavity, Thermal Science, 13(1) (2009), pp. 13-22
- Kolsi, L., Abidi, A., Borjini, M.N., Aïssia, H.B., The effect of an external magnetic field on the entropy generation in three-dimensional natural convection, Thermal Science, 14(2) (2010), pp. 341-352
- Bhuvaneswari, M., Sivasankaran S., Kim, Y.J., Magneto-convection in an Enclosure with Sinusoidal Temperature Distributions on Both Side Walls, Numerical Heat Transfer A, 59 (2011), pp. 167-184
- Sivasankaran, S., Malleswaran, A., Lee, J., Sundar P., Hydro-magnetic combined convection in a lid-driven cavity with sinusoidal boundary conditions on both sidewalls, International Journal of Heat and Mass Transfer, 54 (2011), pp. 512-525
- Sivasankaran, S., Bhuvaneswari, M., Kim, Y.J., Ho, C.J., Pan, K.L., Magneto-convection of cold water near its density maximum in an open cavity with variable fluid properties, International Journal of Heat and Fluid Flow, 32 (2011), pp. 932-942
- Sivasankaran, S., Bhuvaneswari, M., Lee, J., Effect of the partition on hydro-magnetic convection in a partitioned enclosure, Arabian Journal of Science & Engineering, (2011), in press (doi:10.1007/s13369-011-0110-4)
- Patankar, S. V., Numerical heat transfer and fluid flow. Hemisphere, McGraw-Hill, Washington, DC., 1980
- Davis, G.D.V., Natural convection of air in a square cavity: A bench mark numerical solution, International Journal of Numerical Methods for Fluids, 3 (1983), pp. 249 - 264
- Emery, A.F., Lee, J.W., The effects of property variations on natural convection in a square enclosure, Journal of Heat Transfer, 121 (1999), pp. 57 - 62