MHD convection and entropy generation of nanofluid in a porous enclosure with sinusoidal heating Sumit Malik, A.K. Nayak ⇑ Department of Mathematics, Indian Institute Technology of Roorkee, Roorkee 247667, India article info Article history: Received 7 November 2016 Received in revised form 6 March 2017 Accepted 31 March 2017 Keywords: Cu-water nanofluid Porous mixture Magnetic convection Energy flux vector Entropy generation Bejan number abstract A numerical study of heat transfer and entropy generation of a magneto-hydrodynamic (MHD) nanofluid flow inside an enclosure filled with a fluid saturated porous medium is presented. The flow is influenced by time periodic discrete heat sources along the short side walls. A detailed physical insights of time dependent flow and heat transfer is presented based on various flow governing parameters such as Grashof number (10 4 —10 6 ), Hartmann number (1–50), Darcy number (0.001–1.0) and nanoparticle vol- ume fraction (0.0–0.20) with a fixed Prandtl number (6.2). The resulting energy flux vectors are simulated to analyze the convection generated heat transfer ratio. Entropy generation and Bejan number are used to study the performance of the system. Ó 2017 Elsevier Ltd. All rights reserved. 1. Introduction Large scale applications such as magneto-hydrodynamic gener- ators, electrical equipment cooling, plasma physics, geothermal energy extraction, the chemical pollutants spreading in saturate soil and boundary layer control theory in the field of mechanics requires a better understanding of Magneto-hydrodynamic flow of an electrically-conducting fluid coupled with heat transfer [1]. Many engineering applications deal with the heat transfer by nat- ural convection in enclosures such as cooling of electronic devices, solar energy, heat exchanger design, continuous strips or filaments [2,3]. In practical applications, the process of heating and cooling of fluid is very sensitive and sometimes requires very quick response of heating as well as cooling. Clear fluid like water and ethylene glycol fails this quick response property to heating and cooling due to which the nanoparticles with relatively high thermal con- ductivity such as Cu, Al 2 O 3 , and TiO 2 are required to be suspended into the base fluid. Now a days, the MHD flow inside a porous med- ium has drawn the interest of several researchers because of its importance in many industrial applications such as MHD power generator designing, control of chemical waste and pollutants dis- semination, optimization of solidification processes of metals and alloys. The relative problem also appear in the operation of micro- electronic devices and electronic packages [4]. The effect of MHD convection in an electrically conducting fluid inside a differentially heated rectangular enclosure is investigated by Rudraiah et al. [5]. They found that the convective heat transfer decreases with increasing Hartmann number. Oztop et al. [6] stud- ied a square cavity with two semicircular heaters placed at the lower wall considering adiabatic horizontal walls and isothermal boundary conditions on vertical walls in presence of magnetic field. They concluded that the flow strength as well as convective heat transfer decreases with increasing magnetic field effect. Siva- sankaran et al. [7] used finite volume method to study the effect of sinusoidal boundary temperatures at the vertical walls in a lid dri- ven square cavity having adiabatic horizontal walls. They con- cluded that the amplitude ratio increases the heat transfer rate. The work is further extended in the presence of magnetic field and found that increment in Hartmann number decreases the total heat transfer rate in Buoyancy-driven convection [8]. Subse- quently, Sivasankaran and Pan [9] used saturated porous medium with same boundary conditions to investigate the effect of ampli- tude ratio on the heat transfer rate. The temperature difference is found to be increasing with increase of amplitude ratio, Darcy number and porosity. Mostly, nanofluids are used to obtain higher heat transfer rate in industry compared to low conductivity clear fluid. The term ‘nanofluid’ was coined by Choi and Eastman [10] and a number of experimental as well as numerical studies have been conducted by considering the thermal conductivity of nanofluids till date. Experimentally, Eastman et al. [11] used 0.3% volume fraction of http://dx.doi.org/10.1016/j.ijheatmasstransfer.2017.03.123 0017-9310/Ó 2017 Elsevier Ltd. All rights reserved. ⇑ Corresponding author. E-mail address: ameeyakumar@gmail.com (A.K. Nayak). International Journal of Heat and Mass Transfer 111 (2017) 329–345 Contents lists available at ScienceDirect International Journal of Heat and Mass Transfer journal homepage: www.elsevier.com/locate/ijhmt