Buoyancy driven convection of nanofluids in an infinitely long channel under the effect of a magnetic field Sandip Sarkar a , Suvankar Ganguly a , G. Biswas b,c,⇑ a TATA Global R&D Division, Tata Steel, Jamshedpur 831007, India b Department of Mechanical Engineering, Indian Institute of Technology Guwahati, Guwahati 781039, India c Department of Mechanical Engineering, Indian Institute of Technology Kanpur, Kanpur 208016, India article info Article history: Received 16 August 2013 Received in revised form 17 November 2013 Accepted 12 December 2013 Available online 9 January 2014 Keywords: Nanofluids Magnetic field Thermal buoyancy Electrical conductivity Bejan number abstract In this paper, we have proposed a theoretical analysis to investigate buoyancy driven convection of nano- fluids in an infinitely long channel under superimposed magnetic field. We derive closed form analytical solutions for the magnetohydrodynamic flow and temperature field under two distinctive wall boundary conditions. Proceeding further ahead, we also present an analysis for the total entropy generation due to magnetohydrodynamic fluid friction and heat transfer irreversibilities. Utilizing water based Al 2 O 3 nanofluids, results are shown for the following range of conditions as 0 6 Ha 6 50, 0 6 / 6 4% and 10 3 6 Gr 6 10 5 . It is revealed that magnetohydrodynamic effect reduces flow strength. Likewise the case of the velocity profiles, magnetic effect reduces the magnitude of temperature distribution. Total entropy generation shows decreasing trend when the volume fraction of the nanofluids is increased. Increasing nanoparticle size results in increasing total entropy generation and the Bejan number. Ó 2013 Elsevier Ltd. All rights reserved. 1. Introduction The need of a fluid for industrial purposes with higher heat dissipation properties has been in place for a long time. Though water offers advantages over other fluids due to easy availability and properties, use of water is limited by its lower thermal conduc- tivity in comparison to other materials. A new class of heat transfer fluids offering significant improvement in heat transfer perfor- mance is nanofluids [1]. Nanofluids is a mixture of a carrier fluid and suspended metallic nanoparticles and is characterised by higher thermal conductivities and high heat transfer coefficients compared to the base fluids. The presence of nanoparticles changes the transport properties of the fluid, which ultimately enhances the heat transfer rate of nanofluids. The possible application area of nanofluids is in advanced cooling systems, micro/nano-electrome- chanical devices as well as in large scale thermal management systems, viz. heat exchangers, evaporators and industrial cooling applications. Serious attention has been paid over the last few years [2–6] to study the thermal properties and heat transfer characteristics of nanofluids primarily because of the immensely significant technological implications of the use of nanofluids. Several exper- imental and theoretical studies on the subject have been reported in open literature. Eastman et al. [2] measured the thermal conduc- tivity of nanofluids containing alumina (Al 2 O 3 ), Copper oxide (CuO) and copper (Cu) nanoparticles in different base fluids and observed a significant improvement (60%) in thermal conductivity as com- pared to the corresponding base fluids for only 5 vol.% of nanopar- ticles. Xuan and Li [3] indicated that the suspension of Cu-nanoparticles (2–5% by volume) in transformer oil with the use of oleic acid as dispersant had superior characteristics of con- ductivity compared to the suspension of Cu particles in water. They concluded that the thermal conductivity of nanofluids is also dependent on the properties of base fluids and the nanoparticles. Xie et al. [4] investigated the effects of the specific surface area (SSA) of the dispersed nanoparticles, pH value of the suspension, and thermal conductivity of the base fluid on the thermal conduc- tivity of the Al 2 O 3 nanofluids. In another study, Das et al. [5] have demonstrated the effect of particle size on the enhancement of thermal conductivity. The effect of volume fraction has been found to be prominent with the lower volumetric fraction of the nanofl- uids providing better heat transfer. Ding et al. [6] investigated the heat transfer performance of aqueous suspensions of carbon nano- tubes (CNT nanofluids) and observed a significant enhancement of heat transfer coefficient of the nanofluids. In recent years, studies on convective heat transfer characteris- tics of nanofluids have been conducted and reported in literature 0017-9310/$ - see front matter Ó 2013 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.ijheatmasstransfer.2013.12.033 ⇑ Corresponding author at: Department of Mechanical Engineering, Indian Institute of Technology Kanpur, Kanpur 208016, India. Tel.: +91 361 2690401; fax: +91 361 2692321. E-mail addresses: gtm@iitk.ac.in, gtm@iitg.ernet.in (G. Biswas). International Journal of Heat and Mass Transfer 71 (2014) 328–340 Contents lists available at ScienceDirect International Journal of Heat and Mass Transfer journal homepage: www.elsevier.com/locate/ijhmt Downloaded from http://www.elearnica.ir