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The Effects of Induced Magnetic Field and Radiation on MHD Mixed Convective Flow Over a Porous Vertical Plate in the Presence of Viscous and Magnetic Dissipation

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The Effects of Induced Magnetic Field and Radiation on MHD Mixed Convective Flow Over a Porous Vertical Plate in the Presence of Viscous and Magnetic Dissipation International Conference on Advances in Marine, Industrial and Mechanical Engineering (ICAMIME'2014) April 15-16, 2014 Johannesburg (South Africa) The Effects of Induced Magnetic Field and Radiation on MHD Mixed Convective Flow over a Porous Vertical Plate in the Presence of Viscous and Magnetic Dissipation J. Prakash1, A. G. Vijaya Kumar2, B. Rushi Kumar2 and S. V. K. Varma3 transfer have enormous applications. Radiative flows are Abstract—The objective of this investigation is to study the encountered in many industrial and environment processes effects of induced magnetic field and radiation on MHD heat and e.g. heating and cooling chambers, fossil fuel combustion mass transfer flow of a steady, viscous, incompressible, electrically energy processes, evaporation from large open water conducting, Newtonian fluid over a porous vertical plate in the reservoirs, astrophysical flows, solar power technology and presence of viscous and magnetic dissipation taking into account the space vehicle re-entry. Soundalgekar [1] investigated the induced magnetic field with a magnetic Prandtl number. The similarity solutions of the transformed dimensionless governing effects of magnetic field on hydromagnetic flow of a viscous equations are obtained by using perturbation technique. The incompressible fluid caused by uniformly accelerated motion influence of magnetic parameter (M), radiation parameter (R), near an infinite flat plate. The effects of transversely applied chemical reaction parameter (k), Magnetic Prandtl number (Prm), magnetic field, on the flow of an electrically conducting fluid Schmidt number (Sc), thermal Grashof number (Gr) and mass past an impulsively started infinite isothermal vertical plate Grashof number(Gm) on Non-dimensional velocity, temperature, studied by Soundalgekar et al. [2]. MHD effects on concentration and induced magnetic field have been shown impulsively started vertical plate with variable temperature in graphically. It is found that the effect of magnetic parameter and the presence of transverse magnetic field were considered by magnetic Prandtl number is to increase the velocity and temperature Soundalgekar et al. [3]. The dimensionless governing fields while the induced magnetic field is negatively increasing with equations were solved using Laplace-transform technique. them. Kumari and Nath [4] studied the development of the asymmetric flow of a viscous electrically conducting fluid in Keywords—Chemical reaction, MHD, Magnetic Prandtl the forward stagnation point region of a two-dimensional number, Heat and Mass transfer, , Magnetic Dissipation body and over a stretching surface were set into impulsive motion from the rest. The governing equations were solved I. INTRODUCTION using finite difference scheme. Transient MHD heat and mass HE study of Magneto hydrodynamics with heat and mass transfer flow with thermal diffusion in a rotating system was Ttransfer in the presence of radiation and diffusion has studied by Alam and Sattar [5]. Muthucumaraswamy and attracted the attention of a large of number of scholars due to Janakiraman [6] studied MHD and radiation effects on diverse applications. In astrophysics and geophysics, it is moving isothermal vertical plate with variable mass diffusion. applied to study the stellar and solar structures, radio Rajesh and Varma [7] studied thermal diffusion and radiation propagation through the ionosphere etc. In engineering, we effects on MHD flow past a vertical plate with variable find its applications like in MHD pumps, MHD bearings etc. temperature. Very recently, Kumar and Varma [8] The phenomenon of mass transfer is also very common in investigated thermal radiation and mass transfer effects on theory of stellar structure and observable effects are detectable MHD flow past an impulsively started exponentially on the solar surface. In free convection flow, the study of accelerated vertical plate with variable temperature and mass effects of magnetic field plays a major role in liquid metals, diffusion. electrolytes and ionized gases. In power engineering, the Diffusion rates can be altered tremendously with chemical thermal physics of hydro magnetic problems with mass reactions. The chemical reaction effects depend on whether the reaction is homogeneous or heterogeneous. This depends J. Prakash1 Department of Mathematics, University of Botswana, Private Bag on whether they occur at an interface or as a single phase 0022, Gaborone, Botswana: phone (0267) 355 2949; fax: (0267)318 5097; e- volume reaction. In well-mixed systems, the reaction is mail: [email protected]). A. G. Vijaya Kumar2, B. Rushi Kumar2 Fluid Dynamics Division, School of heterogeneous, if it takes place at an interface and Advanced Sciences, VIT University, Vellore-632 014, TN, India (e-mails: homogeneous, if it takes place in solution. In most cases, a [email protected]; [email protected]). chemical reaction depends on the concentration of the species S. V. K. Varma3 Department of Mathematics, S.V. University, Tirupati-517 502, A.P., India, (e-mail: [email protected]). itself. A reaction is said to be of first order, if the rate of 52 International Conference on Advances in Marine, Industrial and Mechanical Engineering (ICAMIME'2014) April 15-16, 2014 Johannesburg (South Africa) reaction is directly proportional to the concentration itself, studied by Chamkha and Camille [23]. Raptis et al. [24] Cussler [9]. A few representative areas of interest in which studied the hydromagnetic free convection flow of an heat and mass transfer combined along with chemical optically thin gray gas taking into account the induced reaction play an important role in chemical industries like in magnetic field in the presence of radiation and the analytical food processing and polymer production. Chambre and solutions were obtained by perturbation technique. MHD Young [10] have analyzed a first order chemical reaction in mixed free-forced heat and mass convective incompressible the neighborhood of a horizontal plate. Apelblat [11] studied steady laminar boundary layer flow of a gray optically thick analytical solution for mass transfer with a chemical reaction electrically conducting viscous fluid past a semi-infinite of first order. Das et al. [12] have studied the effect of vertical plate have been considered by Emad and Gamel [25]. homogeneous first order chemical reaction on the flow past Orhan and Kaya [26] examined MHD mixed convective heat an impulsively started vertical plate with uniform heat flux transfer along a permeable vertical infinite plate in the and mass transfer. Again, mass transfer effects on moving presence of radiation and solutions are derived using Kellar isothermal vertical plate in the presence of chemical reaction box scheme and accurate finite-difference scheme. Zueco et studied by Das et al. [13]. The dimensionless governing al. [27] investigated thermophoretic effects on magneto equations were solved by the usual Laplace Transform hydrodynamic heat and mass transfer in boundary layer flow technique. along a flat plate with viscous heating, Joule heating and wall In all the above studies the authors have considered a very suction by employing the network simulation method. Ghosh small magnetic Reynolds numbers, allowing magnetic et al. [28] presented an exact solution for the hydromagnetic induction effects to be neglected. But the effect of induced free convection flow past an infinite vertical flat plate in the magnetic field must be considered for relatively large values presence of transverse magnetic field taking into account the of the magnetic Reynolds number. Glauert [14] presented a induced magnetic field. Sahin Ahmed [29] investigated the seminal analysis for hydromagnetic flat plate boundary layers study of influence of thermal radiation and magnetic Prandtl with uniform magnetic field in the stream direction at the number on the steady MHD heat and mass transfer mixed plate. Raptis and Soundalgekar [15] examined a problem of convection flow of a viscous, incompressible, electrically- study flow of an electrically conducting fluid past a moving conducting Newtonian fluid over a vertical porous plate with vertical infinite plate in presence of constant suction and heat induced magnetic field. Recently, Ahmed [30] investigated flux in the presence of induced magnetic field. Alom et al. the effects of thermal radiation and viscous/magnetic [16] studied MHD mixed convection heat and mass transfer dissipation on the steady MHD heat transfer flow over a study flow along a moving vertical porous plate taking into porous vertical plate with induced magnetic field. account induced magnetic field, thermal diffusion, constant In this paper, it is proposed to study the effects of viscous heat and mass fluxes with non-linear coupled equations and and magnetic dissipation on steady two-dimensional the obtained governing equations were solved by shooting magneto-hydrodynamic mixed convection heat and mass iteration technique. Beg et al. [17] presented local non- transfer flow of a Newtonian, electrically conducting and similarity numerical solutions for the velocity, temperature viscous incompressible radiative fluid over a porous vertical distributions in forced convection MHD boundary layers in plate taking into the account of induced magnetic field and the presence of magnetic Prandtl numbers and induction. The magnetic Prandtl number. The governing equations for this study of heat and mass transfer on free convective three investigation are formulated
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