Aligned Magnetic Field Effect on Unsteady MHD Natural Convection Flow of a Chemically Reacting, Radiative and Dissipative Fluid Past a Porous Vertical Plate in the Presence of Constant Heat and Mass Flux

R.Chandra Sekhar Reddy*, K.Jayarami Reddy**, M.S.N. Reddy***
* Department of Mathematics, Priyadarshini Institute of Technology, Tirupati, A.P, India.
** Department of Mathematics, K.L University, Guntur, A.P, India.
*** Department of Mathematics, JNTUA College of engineering, Pulivendula, A.P, India.
Periodicity:October - December'2014
DOI : https://doi.org/10.26634/jmat.3.4.3186

Abstract

The analytical results are investigated for an unsteady MHD free convection heat and mass transfer flow of a viscous, dissipative incompressible fluid past an infinite vertical plate through porous medium. The presence of thermal radiation, chemical reaction, joules heating are considered along with aligned magnetic field effect and constant heat and mass flux. The non dimensional governing equations are reduced to a set of ordinary differential equation by using a multiple parameter perturbation technique. The expansion for the velocity, the temperature and the concentration are obtained with reference to the assumed boundary conditions. The expressions for Skin friction, Nusselt number and Sherwood number are also derived. The consequences of varied physical parameters like magnetic parameter (M), Radiation parameter (R), Grashof number (Gr), Sharewood number (Gm), Prandtl number (Pr), Eckert number (Ec), and heat source parameter on the flow quantified are studied numerically with the help of tables and graphs.

Keywords

MHD Flow, Free Convection, Heat and Mass Transfer, Aligned Magnetic Field, Heat Flux, Mass Flux, Chemical Reaction, Radiation, Joule effect, Viscous Dissipation.

How to Cite this Article?

Reddy, R.C.S., Reddy, K.J., and Reddy, M.S.N. (2014). Aligned Magnetic Field Effect on Unsteady MHD Natural Convection Flow of a Chemically Reacting, Radiative and Dissipative Fluid Past a Porous Vertical Plate in the Presence of Constant Heat and Mass Flux. i-manager’s Journal on Mathematics, 3(4), 27-41. https://doi.org/10.26634/jmat.3.4.3186

References

[1]. Al-Badawi, Y. M. & Duwairi, H. M. (2010). MHD natural convection with Joule and viscous heating effects in iso-flux porous medium-filled enclosures, Appl. Math. Mech. -Engl. Ed., Vol. 31(9), pp.1105–1112, DOI 10.1007/s10483-010-1346-6.
[2]. Rudra, Kt. Deka, & Bhaben Ch. Neog. (2009). Unsteady natural convection flow past an accelerated vertical plate in a thermally stratified fluid, Theoret. Appl. Mech., Vol. 36(4), pp.261-274.
[3]. Narahari, M. & Yunus Nayan, M. (2011). Free convection flow past an impulsively started infinite vertical plate with Newtonian heating in the presence of thermal radiation and mass diffusion, Turkish J. Eng. Env. Sci., Vol. 35, pp.187 – 198.
[4]. Sengupta, S. & Ahmed N. (2014). MHD free convective chemically reactive flow of a dissipative fluid with thermal diffusion, fluctuating wall temperature and concentrations in velocity slip regime, Int. J. of Appl. Math and Mech., Vol. 10 (4), pp.27-54. (4), pp.1–8.
[5]. Nandkeolyar, R., Seth, G. S., Makinde, O. D., Sibanda, P. & Ansari, M. S. ( 2013). Unsteady hydromagnetic natural convection flow of a dusty fluid past an impulsively moving vertical plate with ramped temperature in the presence of thermal radiation, ASME-Journal of Applied Mechanics, Vol. 80, No. 6, Article ID 061003, 9 pages,
[6]. Miraj, M., Alim, M. A. & Mamun, M. A. H. ( 2010). Effect of Radiation on Natural Convection Flow on a Sphere in Presence of Heat Generation, International communications in heat and mass transfer, Vol. 37, No. 6, pp.660-665.
[7]. Anajali Devi, S. P. & Ganga, B. (2009). Effects of Viscous and Joules dissipation on MHD flow, heat and mass transfer past a stretching porous surface embedded in a porous medium, Nonlinear Analysis: Modelling and Control, Vol. 14(3), pp.303- 314.
[8]. Jha, B.K. & Apere, C.A. (2011). Magneto hydrodynamic Free Convective Couette Flow with Suction and Injection. Journal of Heat Transfer, Vol. 133(9), pp.214-219.
[9]. Raja Shekar, M. N. & Karunakar Reddy, S. (2012). Heat and Mass Transfer past a Continuously Moving Porous Boundary in the Presence of a Magnetic Field, International Journal of Computer Applications, Vol. 39, No.12, pp.13-16.
[10]. Sun, Z., Guo, M., Vleugels, J., van der Biest, O. & Blanpain, B. (2010). Strong magnetic field induced segregation and self-assembly of micrometer sized non- magnetic particles, Progress In Electromagnetics Research B, Vol. 23, pp.199-214.
[11]. Raja Shekar, M. N. & Karunakar Reddy, S. (2012). Heat and Mass Transfer past a Continuously Moving Porous Boundary in the Presence of a Magnetic Field, International Journal of Computer Applications, Vol. 39, No.12, pp.13-16.
[12]. Seddeek, M. A. (2002). Effects of radiation and variable viscosity on a MHD free convection flow past a semi-infinite flat plate with an aligned magnetic field in the case of unsteady flow, International Journal of Heat and Mass Transfer, Vol.45, pp.931-935.
[13]. Krishna, P. M., Sandeep, N. & Sugunamma, V. (2014). Effects of radiation and chemical reaction on MHD convective flow over a permeable stretching surface with suction and heat generation, Walailak Journal of Science and Technology, Vol. 11, No. 12, pp.141-148.
[14]. Kandasamy, R., Hayat, T. & Obaidat, S. (2011). Group theory transformation for Soret and Dufour effects on free convective heat and mass transfer with thermophoresis and chemical reaction over a porous stretching surface in the presence of heat source/sink, Nucl. Eng. Des., Vol. 241, No.6, pp.2155–2161.
[15]. Ravikumar, V. Raju, M.C. Varma, S.V.K. & Chamkha, A.J. (2013). MHD double diffusive and chemically reactive flow through porous medium bounded by two vertical plates, International Journal of Energy & Technology, Vol.5
[16]. Joneidi, A.A., Domairry, G. & Babaelahi, M. (2010). Analytical treatment of MHD free convective flow and mass transfer over a stretching sheet with chemical reaction, J. Taiwan Inst. Chem. Eng., Vol. 41, No.1, pp.35–43.
[17]. Sahin, A. (2010). Influence of chemical reaction on transient MHD free convection flow over a vertical plate in slip-flow regime, Emirates Journal for Engineering Research, Vol.15(1), pp.25 -34.
[18]. Chamkha, A.J., Mohamed, R.A., & Ahmed, S.E. (2011). Unsteady MHD natural convection from a heated vertical porous plate in a micropolar fluid with Joule heating, chemical reaction and radiation effects, Meccanica, Vol.46, pp.390- 399.
[19]. Mohamed, R.A., Osman, A-N.A. & Abo-Dahab, S.M. (2013). Unsteady MHD double-diffusive convection boundarylayer flow past a radiate hot vertical surface in porous media in the presence of chemical reaction and heat sink, Meccanica, Vol. 48, pp.931-936.
[20]. Rajput, U. S. & Kumar, S. (2012). Radiation effects on MHD flow past an impulsively started vertical plate with variable heat and mass transfer, Int. J. of Appl. Math. and Mech., Vol. 8(1), pp.66-85.
[21]. Rajput, U. S. & Kumar, S. (2011). Combined effects of rotation and radiation on MHD flow past an impulsively started vertical plate with variable temperature, International Journal of Mathematical Analysis, Vol. 5, No. 24, pp.1155–1163.
[22]. Vijayalakshmi, A. R. (2010). Radiation effects on free-convection flow past an impulsively started vertical plate in a rotating fluid, Theoretical and Applied Mechanics, Vol. 37, No. 2, pp.79–95.
[23]. Muthucumaraswamy R. & Janakiraman. (2006). MHD and Radiation effects on moving isothermal vertical plate with variable mass diffusion, Theoret. Appl. Mech., Vol.33(1), pp.17-29.
[24]. Ahmedsahin & Tridip, K.K. (2010). Thermal radiation and magneto hydrodynamics effects on heat and Mass transfer chemically reacting fluid with periodic suction, International Journal of Applied mathematics, Vol. 23 (5), pp.778-789.
[25]. Dulal Pal & Babulal Talukdar. (2010). Perturbation analysis of unsteady magneto hydrodynamic convective heat and mass transfer in a boundary layer slip flow past a vertical permeable plate with thermal radiation and chemical reaction, CNSNS, pp.1813-1830.
[26]. Umamaheswar, M., Varma, S. V. K. & Raju, M. C. (2013). Unsteady MHD Free Convective Visco-Elastic Fluid Flow Bounded by an Infinite Inclined Porous Plate in the Presence of Heat Source, Viscous Dissipation and Ohmic Heating, International Journal of Advanced Science and Technology, Vol.61, pp.39- 52.
[27]. Sandeep, N. & Sugunamma, V. (2013). Effect of inclined magnetic field on unsteady free convective flow of dissipative fluid past a vertical plate, World Applied Sciences Journal, Vol. 22, No. 7, pp.975–984.
[28]. Seshaiah B., Varma, S.V.K. & Raju, M.C. (2013). Induced magnetic field effects on free convective flow of radiative, dissipative fluid past a porous plate with temperature gradient heat source, International Journal of Engineering Science and Technology (IJEST), Vol. 5. No.07, pp.1397-1412, ISSN: 0975-5462.
[29]. Ahmed, S. (2012). Mathematical model of induced magnetic field with viscous/magnetic dissipation bounded by a porous vertical plate in the presence of radiation, International Journal of Mathematic and Mechanics, Vol. 8 (1), pp.86- 104.
[30]. Pal, D. & Talukdar, B. (2011). Combined effects of Joule heating and chemical reaction on unsteady magneto hydrodynamic mixed convection of a viscous dissipating fluid over a vertical plate in porous media with thermal radiation, Math. Comput. Modelling, Vol. 54, No.11, pp.3016–3036.
[31]. Zahan, I. & Samad, M.A. (2013). Radiative heat and mass transfer of an MHD free convection flow along a stretching sheet with chemical reaction, heat generation and viscous dissipation, Dhaka Univ. J. Sci., Vol.61(1), pp.27-34.
[32]. Abdul Hamid, R., Arifin, N.M. & Nazar, R. (2013). Effects of Radiation, Joule Heating and Viscous Dissipation on MHD Marangoni Convection over a Flat Surface with Suction and Injection, World Applied Sciences Journal, Vol.21, pp.933- 938.
[33]. Miraj, M., Alim, M. A. & Mamun, M. A. H. ( 2010). Effect of Radiation on Natural Convection Flow on a Sphere in Presence of Heat Generation, International communications in heat and mass transfer, Vol. 37, No. 6, pp.660-665.
[34]. Parand, K., Delafkar, Z., Rad, J. A. & Kazem, S. (2012). Numerical Study on Wall Temperature and Surface Heat Flux Natural Convection Equations Arising in Porous Media by Rational Legendre Collocation Approach, International Journal of Nonlinear Science, Vol.13, No.1, pp.39-50.
[35]. Cheng, C.Y. (2009). Soret and Dufour effects on natural convection heat and mass transfer from a vertical cone in a porous medium. Int. Commun. Heat. Mass. Transf., Vol.36. pp.1020–1024.
[36]. Ahn H. S. (2007). Mass (Heat) Transfer Downstream of Blockages with Round and Elongated Holes in a Rectangular Channel, Transactions of ASME, Journal of Heat Transfer, Vol. 129, pp.1676-1680.
[37]. Wang Liangbi, (2008). Tube Transverse Pitch Effect on Heat/Mass Transfer Chacteristics of Flat Tube Bank Fin Mounted with Vortex Generators, Journal of Heat Transfer, (ASME), Vol. 130, pp.064502-1-3.
[38]. Mojtaba Balaj, Ehsan Roohi, Hassan Akhlaghi, & Rho Shin Myong. (2014). Investigation of convective heat transfer through constant wall heat flux micro/nano channels using DSMC, International Journal of Heat and Mass Transfer, Vol. 71, pp.633–638.
[39]. Sethuraman Eashwar. (2009). Mass/Heat Transfer in Rotating smooth, High Aspect Ratio (4:1) Coolant Channels With Curved Walls, Journal of Turbomachinery (ASME), Vol. 131, pp 0210021.
[40]. Vikas Chander. & Kitab Singh. (2014). Experimental study of dryout heat flux and mass transfer coefficient effect on a Single Horizontal Copper tube of an Evaporative Tubular Heat Dissipator, International Journal of Latest Trends in Engineering and Technology (IJLTET), Vol. 3, Issue 4, pp.372-337.
[41]. Ogulu, A., & Makinde, O. D. (2009). Unsteady hydromagnetic free convection flow of a dissipative and radiating fluid past a vertical plate with constant heat flux. Chem. Eng. Comm., Vol.196, pp.454–462.
[42]. Chien-Hsiung Lee, Lih-Wu Hourng and Kuo-Wei Lin (2012). Mathematical model predicting the critical heat flux of nuclear reactors, Journal of Computer Science, Vol.8 (12), pp.1996-2007
[43]. Sohouli, A.R., Famouri, M., Kimiaeifar, A. & Domairry, G.(2010). Application of homotopy analysis method for natural convection of Darcian fluid about a vertical full cone embedded in pours media prescribed surface heat flux, Commun. Nonlinear. Sci. Numer. Simulat., Vol. 15, pp.1691–1699.
[44]. Sharma, P. R. & Gurminder Singh. (2010). Effects of variable thermal conductivity, viscous dissipation on steady MHD natural convection flow of low Prandtl fluid on an inclined porous plate with Ohmic heating, Meccanica, Vol.45, pp. 237–247.
[45]. Singh, A. K. & Gorla, R. S. R. (2009). Free convective heat and mass transfer with Hall current, Joule heating and thermal diffusion, Heat and Mass Transfer, Vol.45, pp. 1341-1349.
[46]. Umamaheswar, M. Varma, S. V. K. & Raju, M. C. (2013). Unsteady MHD free convective visco-elastic fluid flow bounded by an infinite inclined porous plate in the presence of heat source, viscous dissipation and ohmic heating, International Journal of Advanced Science and Technology, Vol. 61, pp. 39-52.
[47]. Bermudez, A., Munoz-Sola, R. & Vazquez, R. (2010). Analysis of two stationary magneto hydrodynamics systems of equations including Joule heating, J. Math. Anal. Appl., Vol.368, pp.444–468.
[48]. Alam, M.S., Rahman, M.M. & Sattar, M.A. (2009). On the effectiveness of viscous dissipation and Joule heating on steady Magnetohydrodynamic heat and mass transfer flow over an inclined radiate isothermal permeable surface in the presence of thermophoresis, Commun Nonlinear Sci Numer Simulat, Vol. 14, pp. 2132–2143.
[49]. Bikash Sahoo. (2009). Effects of partial slip, viscous dissipation and Joule heating on Von Karman flow and heat transfer of an electrically conducting non-Newtonian fluid, Commun Nonlinear Sci Numer Simulat, Vol.14, pp. 2982–2998.
[50]. Raju, K.V.S., Sudhakar Reddy, T., Raju, M.C., Satya Narayana P.V. & Venkataramana, S. (2014). MHD convective flow through porous medium in a horizontal channel with insulated and impermeable bottom wall in the presence of viscous dissipation and Joule heating, Ain Shams Engineering Journal, Vol.5, pp.543–551.
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