Heat and mass transfer in MHD viscoelastic fluid flow over a vertical cone and flat plate with variable viscosity B. Rushi Kumar ⇑ , R. Sivaraj Fluid Dynamics Division, School of Advanced Sciences, VIT University, Vellore 632014, India article info Article history: Received 24 April 2012 Received in revised form 27 July 2012 Accepted 1 September 2012 Available online 27 October 2012 Keywords: MHD Viscoelastic fluid Variable viscosity Variable thermal conductivity Chemical reaction abstract The present paper is concerned with the study of flow, heat and mass transfer characteristics in the unsteady free convective flow of an incompressible viscoelastic fluid over a moving vertical cone and a flat plate in the presence of magnetic field and higher order chemical reaction. The fluid viscosity and thermal conductivity are assumed to vary as a linear function of temperature. The governing partial dif- ferential equations are solved numerically using the implicit finite difference method of Crank–Nicolson type. The features of the fluid flow, heat and mass transfer characteristics are analyzed by plotting graphs and the physical aspects are discussed in detail. The results obtained show that the impact of magnetic field, buoyancy ratio parameter, viscosity variation parameter, Ecart number and chemical reaction parameter plays an important role in the viscoelastic fluid flow through porous medium. The mass trans- fer of the reactive species strongly depends on the chemical reaction parameter as well as the order of chemical reaction. Ó 2012 Elsevier Ltd. All rights reserved. 1. Introduction The convective heat transfer over a cone is important for the thermal design of various types of industrial equipments such as heat exchangers, canisters for nuclear waste disposal, nuclear reac- tor cooling systems and geothermal reservoirs [1]. The theory of laminar boundary layer flows on a moving surface occur in several engineering applications. Aerodynamic extrusion of a plastic sheet, the cooling of an infinite metallic plate in a cooling bath and fila- ment extruded continuously from a dye are examples of practical applications. Continuously moving surface through an otherwise quiescent medium has many applications in manufacturing pro- cesses. Such processes are hot rolling, wire drawing, spinning of fil- aments, metal extrusion, crystal growing, continuous casting, glass fiber production and paper production [2–4]. The use of non-New- tonian fluids has grown considerably because of more applications in chemical process industries, food preservation techniques, petroleum production and power engineering. These include the rheology of liquid crystal precursors employed in the manufacture of carbon super-fibers, thermocapillary bubble dynamics in weakly elastic fluids, mayonnaise elastic–viscous flows and polygalacturo- nase-based food stuff. The Walters-B viscoelastic fluid model was developed by Walters [5] to simulate the viscous fluids possessing short memory elastic effects and can simulate accurately many complex polymeric, biotechnological and tribological fluids. Some theoretical studies [6–8] had analyzed the flow, heat and mass transfer characteristics of Walters Liquid Model-B. In the last few decades, heat and mass transfer analysis of chemically reacting fluid flow through porous medium with the influence of magnetic field have attracted a considerable attention of researchers because such process exist in many branches of science and technology [9–12]. In most cases of chemical reactions, the reaction rate de- pends on the concentration of the specie. A reaction is said to be first order, if the rate of the reaction is directly proportional to the concentration species itself. A reaction is said to be of order l, if the reaction rate is proportional to the lth power of the concen- tration [13–15]. In most of the studies, the effects of both the viscous dissipation and Joule heating are neglected since they are of the same order as well as negligibly small. However, it is more realistic to include the effects of viscous dissipation and Joule heating to explore the im- pact of the magnetic field on the thermal transport in the boundary layer. The effect which bears a great importance on heat transfer is viscous dissipation. When the viscosity of the fluid is high, the dis- sipation term becomes important. For many cases, such as polymer processing which is operated at a very high temperature, viscous dissipation cannot be neglected. The main advantage of Joule heat- ing is the rapid and relatively uniform heating achieved together with the lower capital cost compared to other electro heating methods such as microwave and radio frequency heating. The applications of Joule heating technique in industries include the blanching, evaporation, dehydration and pasteurization of food 0017-9310/$ - see front matter Ó 2012 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.ijheatmasstransfer.2012.09.001 ⇑ Corresponding author. Tel.: +91 9566927966. E-mail addresses: rushikumar@vit.ac.in (B. Rushi Kumar), sivaraj.kpm@gmail.com (R. Sivaraj). International Journal of Heat and Mass Transfer 56 (2013) 370–379 Contents lists available at SciVerse ScienceDirect International Journal of Heat and Mass Transfer journal homepage: www.elsevier.com/locate/ijhmt