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Influence of Chemical Reaction, Heat Source, Soret and Dufour Effects on Heat And Mass Transfer in Boundary Layer Flow Over a Stretching Cylinder Embedded in a Porous Medium using Brinkman-Forchheimer Extended Darcy Model

Bishwa Ram Sharma1 and Animesh Aich2
  1. Professor, Department of Mathematics, Dibrugarh University, Dibrugarh, Assam, India
  2. Research Scholar, Department of Mathematics, Dibrugarh University, Dibrugarh, Assam, India
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Abstract

Heat and mass transfer characteristics by boundary layer flow over a stretching cylinder embedded in a porous medium subjected to a chemical reaction and heat source is investigated numerically by taking into account the soret and dufour effects using Brinkman-Forchheimer extended Darcy model.The concentration profile is drawn for various values of Reynold’s number , Darcy number , chemical reaction parameter, Prandtl number, Schmidt number , heat source , nondarcy parameter , Soret and Dufour numbers. Numerical results of rate of mass transfer for different parameters are presented in tabular form.

Keywords
Heat and Mass Transfer, Porous Medium, Stretching Cylinder, Soret and Dufour effects, Chemical Reaction, Heat Source, Brinkman-Forchheimer equation.

INTRODUCTION
Convective flow through porous media has attracted considerable attention in last several decades due to its many important engineering, environmental and geophysical applications. Recent books by Nield and Bejan [1], Ingham and Pop [2] present a comprehensive account of available information in the field. The combined heat and mass transfer problems with chemical reactions have received a considerable amount of attention in recent years. Das [3] have studied the effects of chemical reaction and mass transfer on flow past an impulsively infinite vertical plate with constant heat flux. Andersson [4] have studied the flow and mass diffusion of a chemical species with first order and higher order reactions over a linearly stretching surface. Anjalidevi and Kandasamy [5] have analysed the steady laminar flow along a semi- infinite horizontal plate in the presence of a species concentration and chemical reaction. Muthucumaraswamy [6] has studied the effect of chemical reaction on a moving isothermal vertical infinitely long surface with suction. Chamkha [7] discussed the analytical solutions for heat and mass transfer on MHD mass flow of a uniformly stretched vertical permeable surface with the effects of heat generation/absorption and chemical reaction . El-Kabeir and Modather [8] has studied the effect of chemical reaction on heat and mass transfer by MHD flow over a vertical cone surface in micropolar fluids with heat generation / absorption . Partha [9] obtained similarity solutions for double dispersion effects on free convection hydromagnetic heat and mass transfer in a non-Darcy porous medium with Soret and Dufour effects , showing that in both aiding and opposing buoyancies, Dufour and Soret numbers considerably affect the wall mass transfer rates , both of which are also reduced with stronger magnetic field. Aziz [10] studied the thermal – diffusion and diffusion –thermo effects on the heat and mass transfer characteristics of free convection past a continuously stretching permeable surface in the presence of magnetic field and radiation. Postelnicu [11] has discussed the influence of chemical reaction on heat and mass transfer by natural convection from vertical surfaces embedded in fluid – saturated porous medium considering Soret and Dufour effects . Cheng [12] studied the Soret and Dufour effects on natural convection heat and mass transfer from a vertical cone in a porous medium. Pal and Mondal [13] analysed the effects of Soret and Dufour numbers , chemical reaction and thermal radiation on MHD non-Darcy unsteady mixed convective heat and mass transfer over a stretchingsheet . Sharma [14] has analysed the Soret and Dufour effects on separation of binary fluid mixture in MHD natural convection in porous media. El.Kabeir (2011) has studied the Soret and Dufour effects on heat and mass transfer due to a stretching cylinder saturated porous medium with chemically-reactive species.
The objective of this paper is to study the chemical reaction , heat source, thermaldiffusion and diffusion-thermo effects on heat and mass transfer due to a stretching cylinder embedded in a porous medium using the Brinkman-Forchheimer extented Darcy model.

ANALYSIS
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RESULTS AND DISCUSSIONS
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CaseIX:
Fig. 9 exhibit concentration profile for various values of α0. The value of the concentration is more near the surface of the cylinder than its value at the end of the boundary layer. It depicts that concentration decreases near the surface of the cylinder with increase in the values of parameter α0 but at about n = 4 onwards, reverse effect is observed.
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CONCLUSION
In this work, chemical reaction , heat source, thermal-diffusion and diffusion-thermo effects on heat and mass transfer due to a stretching cylinder embedded in a Porous medium using the Brinkman-Forchheimer extended Darcy model has been investigated. From this paper as obvious from table 1 , we can conclude that the rate of mass transfer decreases inImage

References
  1. Nield, D.A., and Bejan, A., Convection in porous media , 2nd edition, Springer , New York, 1999.
  2. Ingham, D.B., and Pop, I., Transport phenomena in porous media I, Pergamon, Oxford, 1999.
  3. Das, U.N., Deka, R., and Soundalgekar, V.M., “Effects of mass transfer on flow past an impulsive started infinite vertical plate with constant heat flux and chemical reac tion,” Forschung Im Ingenieurwesen-Engineering Research Bd, vol. 60, pp. 284-287, 1994.
  4. Andersson, K.I., Hansen, O.R., and Holmedal, B., “Diffusion of a chemically reactive species from a stretching sheet,” Int. J. Heat Mass Transfer , vol. 37 , pp. 659-664, 1994.
  5. Anjalidevi, S.P., and Kandasamy, R., “Effect of chemical reaction, heat and mass transfer on laminar flow along a semi infinite horizontal plate,” Heat Mass Transfer , vol. 35, pp. 465-467, 1999.
  6. Muthucumaraswamy, R., “Effects of chemical reaction on a moving isothermal vertical surface with suction,” Acta Mechanica,vol. 155, pp. 65-70, 2002.
  7. Chamkha, A.J., “MHD flow of a uniformly stretched vertical permeable sirface in the presence of heat generation/absorption and a chemical reaction,” Int. Comm. Heat Mass Transfer, vol. 30, pp. 413-422, 2003.
  8. El Kabeir, S.M.M., and Modather, M., “Chemical reaction,heat and mass transfer on MHD flow over a vertical isothermal cone surface in micropolar fluids with heat generation/absorption,” Applied Mathematical Sciences, vol. 1, pp. 1663-1674, 2007.
  9. Partha, M.K., Murthy, P.V.S.N., and Raja Sekhar, G.P., “Soret and Dufour Effects in a Non-Darcy Porous Medium,” ASME J. Heat Transfer, vol. 128, pp. 605-610, 2006.
  10. Abd El-Aziz, M., “Thermal-diffusion and diffusion-thermo effects on combined heat and mass transfer by hydromagnetic three dimensional free convection over a permeable stretching surface with radiation,” Physics Letters A, vol. 372, pp.263-272, 2008.
  11. Postelnicu, A., “Influence of chemical reaction on heat and mass transfer by natural convection from vertical surfaces in porous media considering Soret and Dufour effects,” Heat Mass Transfer, vol. 43, pp.595-602, 2007.
  12. Cheng, C.Y., “Soret and Dufour effects on natural convection heat and mass transfer from a vertical cone in a porous medium,” Int.Commun. Heat and Mass Transfer, vol. 36 , pp. 1020-1024, 2009.
  13. Pal, D. , and Mondal, H., “Effects of Soret, Dufour, chemical reaction and thermal radiation on MHD non Darcy unsteady mixed convective heat and mass transfer over a stretching sheet ,” Commun. Nonlinear Sci Numer. Simulat., vol. 16, pp. 1942-1958 , 2011.
  14. Sharma, B.R., “Soret and Dufour effects on separation of a binary fluid mixture in MHD natural convection flow in porous media.” Mathematical Forum, vol. 24 , pp.17-27, 2011.
  15. El.Kabeir, S.M.M.,“Soret and Dufour effects on heat and mass transfer due to a stretching cylinder saturated porous medium with chemically-reactive species.” Lat. Am. Appl. Res, vol. 41, No 4 , pp.331-337, 2011.