Magneto-convection and its effect on partially active thermal zones in a porous square domain A.K. Nayak ⇑ , S. Malik, K. Venkateshwarlu, P.K. Jena Department of Mathematics, IIT Roorkee, Roorkee, Uttarakhand, India article info Article history: Received 19 October 2015 Received in revised form 10 December 2015 Accepted 18 December 2015 Keywords: Magnetic convection Porous mixture Upwind scheme Amplitude Oscillatory frequency abstract A numerical study of hydromagnetic mixed convective flow inside a cubical enclosure filled with a porous mixture is presented. The flow enhancement is observed due to a sinusoidal time dependent discrete temperature gradient along the boundaries. A two dimensional computational visualization technique is used to study the detailed physical insights of the thermally activated porous flows subjected to the magnetic field effects. The time history analysis is made for flow and thermal stratification for a series of fluid parameters such as Grashof number, Hartmann number and Darcy number, porosity and oscilla- tory frequency. The total heat transfer effects are computed for both high convection (due to magnetic field) and diffusive forces (due to temperature). The local Nusselt number is increasing along the side walls for increase of Hartmann number. Bulk average temperature is found to be maximum due to the variation of Grashof number and oscillatory frequency. Ó 2015 Elsevier Ltd. All rights reserved. 1. Introduction Magneto-hydrodynamics (MHD) flow of an electrically- conducting fluid coupled with heat transfer has large scale applica- tions in engineering problems such as magneto-hydrodynamics generators, nuclear reactors for nuclear waste repository, electrical equipment cooling, plasma physics, the migration of moisture in fibrous insulation, the spreading of chemical pollutants in satu- rated soil, geothermal energy extraction and the boundary layer control theory in the field of aerodynamics [1,2]. Bejan and Khair [1] studied the natural convection flow effects in a fluid saturated medium with combined heat and mass transfer. They have ana- lyzed the convection near a vertical surface in a porous medium for various possible regimes based on the various values of buoy- ancy ratio and Lewis number. Lai and Kulacki [2] extended the problem of Bejan and Khair [1] to include wall fluid injection effects, since it has the application in the migration of moisture in fibrous insulation, where it may exist an interfacial velocity at the wall due to injection. Among the engineering activities, natural convection heat transfer in the porous layer has been applied to sensible heat stor- age using porous media, porous insulation materials, the oil sepa- ration technique of oil and sand by using steam [3]. Natural convective heat and mass transfer in an inclined porous layer was also studied experimentally by Inaba et al. [3]. Therein, two opposing walls of the tall rectangular cavity were thermally insu- lated, while the other walls are kept at different temperatures. In their studies, they tried to obtain fundamental information related to the natural convection heat transfer rate through the inclined porous layer in wide ranges of parameters, such as, inclination angles, modified Rayleigh numbers, geometrical dimensions etc. Chamkha and Khaled [4] considered magnetic field and wall mass transfer effects on coupled heat and mass transfer by natural convection from a vertical semi-infinite plate maintained at a con- stant heat flux. They have extended their problem to include a por- ous saturated medium which embeds the permeable surface in Chamkha and Khaled [5], where the parametric study involved the skin-friction parameter, Nusselt number, and the Sherwood number. Coupling of heat and mass transfer can find a great importance in natural phenomena such as currents in ocean driven by differen- tially heating and acting as a freight trains for salt as mentioned by Bejan [6] and also the role of factory waste gas diffusion in a differ- entially heated circulated air [4]. A significant number of studies has been done for the fluid flow and heat transfer in different geometries considering both porous and non-porous medium [8–11]. Most of these study includes the Brinkman-extended Darcy equation of motion and flow governing parameters like Grashof number, Richardson number, Darcy number etc. MHD convection in an electrically conducting-fluid-saturated porous medium with temperature modulation of the boundaries http://dx.doi.org/10.1016/j.ijheatmasstransfer.2015.12.037 0017-9310/Ó 2015 Elsevier Ltd. All rights reserved. ⇑ Corresponding author. E-mail address: ameeyakumar@gmail.com (A.K. Nayak). International Journal of Heat and Mass Transfer 95 (2016) 913–926 Contents lists available at ScienceDirect International Journal of Heat and Mass Transfer journal homepage: www.elsevier.com/locate/ijhmt