Lie group analysis of stagnation-point flow of a nanofluid
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RESEARCH PAPER
Lie group analysis of stagnation-point flow of a nanofluid Kalidas Das
Received: 14 November 2012 / Accepted: 20 January 2013 Ó Springer-Verlag Berlin Heidelberg 2013
Abstract This article concerns with a steady twodimensional boundary layer flow of an electrically conducting incompressible nanofluid over a stretching sheet in a porous medium with internal heat generation/absorption. The transport model includes the effect of Brownian motion with thermophoresis in the presence of chemical reaction and magnetic field. Lie group analysis is applied to the governing equations. The transformed self similar nonlinear ordinary differential equations along with the boundary conditions are solved numerically. The influences of various relevant parameters on the flow field, temperature and nanoparticle volume fraction as well as wall heat flux and wall mass flux are elucidated through graphs and tables. Keywords Nanofluid Lie group analysis Chemical reaction Magnetic field
1 Introduction In the last few years, convective heat transfer in nanofluids is a topic of major contemporary interest both in sciences and engineering. An innovative way of improving the thermal conductivities of heat transfer fluids is to suspend small solid particles in the fluids. To achieve this, nanofluids have been used. Nanofluids are nanometer-sized particles (diameter less than 50 nm) dispersed in a base fluid such as water, ethylene glycol, toluene and oil. Addition of high thermal conductivity metallic nanoparticles (e.g., K. Das (&) Department of Mathematics, Kalyani Government Engineering College, Kalyani, Nadia, West Bengal 741235, India e-mail: [email protected]
aluminum, copper, silicon, silver and titanium or their oxides) increases the thermal conductivity of such mixtures, thus enhancing their overall energy transport capability. Nanoparticles are of great scientific interest as they are effectively a bridge between bulk materials and atomic or molecular structures. The enhanced thermal conductivity of nanofluid together with the thermal conductivity of the base liquid and turbulence induced by their motion contributes to a remarkable improvement in the convective heat transfer coefficient. Various benefits of the application of nanofluids include improved heat transfer, heat transfer system size reduction, minimal clogging, micro-channel cooling and miniaturization of the system. Therefore, research is underway to apply nanofluids in environments, where higher heat flux is encountered and the convectional fluid is not capable of achieving the desired heat transfer rate. Convective flow in porous media has been widely studied in the recent years due to its wide applications in engineering as post-accidental heat removal in nuclear reactors, solar collectors, drying processes, heat exchangers, geothermal and oil recovery, building construction, etc. They are also used in other electronic applications, such as microelectronic devices with smaller features and faster (multi-gigahertz) operating speeds. It sh
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