MHD Mass Transfer Flow past a Vertical Porous Plate Embedded in a Porous Medium in a Slip Flow Regime with Thermal Radiation and Chemical Reaction

ABSTRACT

This problem presents the effects of thermal radiation and chemical reaction on MHD unsteady mass transfer flow past a semi-infinite vertical porous plate embedded in a porous medium in a slip flow regime with variable suction. A magnetic field of uniform strength is assumed to be applied transversely to the direction of the main flow. Perturbation technique is applied to transform the non-linear coupled governing partial differential equations in dimensionless form into a system of ordinary differential equations. The resulting equations are solved analytically and the solutions for the velocity, temperature and concentration fields are obtained. The effects of various flow parameters on velocity, temperature and concentration fields are presented graphically. For different values of the flow parameters involved in the problem, the numerical calculations for the Nusselt number, Sherwood number and skin-friction co-efficient at the plate are performed in tabulated form. It is seen that chemical reaction causes the velocity field and concentration field to decrease and the chemical reaction decreases the rate of viscous drag at the plate.

Cite this paper

N. Ahmed and K. Kumar Das, "MHD Mass Transfer Flow past a Vertical Porous Plate Embedded in a Porous Medium in a Slip Flow Regime with Thermal Radiation and Chemical Reaction,"*Open Journal of Fluid Dynamics*, Vol. 3 No. 3, 2013, pp. 230-239. doi: 10.4236/ojfd.2013.33028.

N. Ahmed and K. Kumar Das, "MHD Mass Transfer Flow past a Vertical Porous Plate Embedded in a Porous Medium in a Slip Flow Regime with Thermal Radiation and Chemical Reaction,"

References

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[2] O. V. Trevisan and A. Bejan, “Natural Convection with Combined Heat and Mass Transfer Buoyancy Effects in a Porous Medium,” Heat and Mass Transfer, Vol. 28, No. 8, 1985, pp. 1597-1611. doi:10.1016/0017-9310(85)90261-3

[3] M. Acharya, G. C. Das and L. P. Singh, “Magnetic Field Effects on the Free Convection and Mass Transfer Flow through Porous Medium with Constant Suction and Con- stant Heat Flux,” Indian Journal Pure Applied Mathematics, Vol. 31, No. 1, 2000, pp. 1-18.

[4] A. Rapits and N. Kafousias, “Magneto Hydrodynamics Free Convective Flow and Mass Transfer through a Porous Medium Bounded by an Infinite Vertical Porous Plate with constant Heat Flux,” Canadian Journal of Physics, Vol. 60, No. 12, 1982, pp. 1724-1729.

[5] U. N. Das, N. Ahmed and D. Sharma, “Three-Dimensional Free Convective MHD Flow and Heat Transfer through Porous Medium,” FJAM, Vol. 4, No. 3, 2000, pp. 357- 369.

[6] H. P. G. Darcy, “Lee Fort Airs Publication La Villede Dijan Victor Dalonat,” Paris, Vol. 1, 1857, p. 41.

[7] R. Wooding, “Steady State Free Thermal Convection of Liquid in a Saturated Permeable Medium,” Journal of Fluid Mechanics, Vol. 2, No. 3, 1957, pp. 273-285. doi:10.1017/S0022112057000129

[8] H. C. Brickmam, “A Calculation of the Viscous Force Exerted by a Flowing Fluid on a Dense Swarm of Particles,” Applied Sciences Research, Vol. A1, 1947, pp. 27- 34.

[9] H. C. Brickman, “On the Permeability of Media Consisting of Closely Packed Porous Particles,” Applied Sciences Research, Vol. A1, 1947, pp. 81-86.

[10] R. C. Chaudhary and A. Jain, “Combined Heat and Mass Transfer Effects on MHD Free Convection Flow Past an Oscillating Plate Embedded in Porous Medium,” Romanian Journal of Physics, Vol. 52, No. 5-7, 2007, pp. 505- 524.

[11] P. L. Chambre and J. D. Young, “On the Diffusion of a Chemically Reactive Species in a Laminar Boundary Layer Flow,” Physics of Fluids, Vol. 1, No. 1, 1958, pp. 48-54. doi:10.1063/1.1724336

[12] R. Muthucumaraswamy, “Effects of a Chemical on a Moving Isothermal Surface with Suction,” Acta Mechanica, Vol. 155, No. 1-2, 2002, pp. 65-70. doi:10.1007/BF01170840

[13] R. Muthucumaraswamy and S. Meenakshisundaram, “Theroretical Study of Chemical Reaction Effects on Vertical Oscillating Plate with Variable Temperature,” Theoretical and Applied Mechanics, Vol. 33, No. 3, 2006, pp. 245-257.

[14] M. A. Hussain and H. S. Takhar, “Radiation Effect on Mixed Convection along a Vertical Plate in Presence of Heat Generation or Absorption,” Journal of Heat Transfer, Vol. 31, No. 4, 1996, pp. 243-248.

[15] N. Ahmed and H. K. Sarmah, “The Radiation Effect on a Transient MHD Flow Mass Transfer Past an Impulsively Fixed Infinite Vertical Plate,” International Journal of Applied Mathematics and Mechanics, Vol. 5, No. 5, 2009, pp. 87-98.

[16] V. Rajesh and S. V. K. Varma, “Radiation Effects on MHD Flow through a Porous Medium with Variable Tem- perature and Mass Diffusion,” International Journal of Applied Mathematics and Mechanics, Vol. 6, No. 11, 2010, pp. 39-57.

[17] D. Pal and H. Mondal, “Radiation Effects on Combined Convection over a Vertical Flat Plate Embedded in a Porous Medium of Variable Porosity,” Meccanica, Vol. 44, No. 2, 2009, pp. 133-144. doi:10.1007/s11012-008-9156-0

[18] A. M. D. Samad and M. M. Rahman, “Thermal Radiation Interaction with Unsteady MHD Flow past a Vertical Porous plate immersed in a porous medium, Journal of Naval Architecture and Marine Engineering, Vol. 3, No. 1, 2006, pp. 7-14.

[19] S. Karthikeyan, S. Sivasankaran and S. Rajan, “Thermal Radiation Effects on MHD Convective Flow over a Vertical Porous Plate Embedded in a Porous Medium by Perturbation Technique,” Proceedings of International Con- ference on Fluid Dynamics and Its Applications, Bangalore, 20-22 July 2010, pp. 484-491.

[20] S. Das, M. Jana and R. N. Jana, “Radiation Effect on Natural Convection near a Vertical Plate Embedded in Porous Medium with Ramped Wall Temperature,” Open Journal of Fluid Dynamics, Vol. 1, No. 1, 2011, pp. 1-11.

[21] D. Pal and B. Talukdar, “Perturbation Analysis of Unsteady Magnetohydrodynamic Convective Heat and Mass Transfer in a Boundary Layer Slip Flow past a Vertical Permeable Plate with Thermal Radiation Chemical Reaction,” Communications in Nonlinear Science and Numerical Simulation, Vol. 15, No. 7, 2010, pp. 1813-1830.

[22] C. L. M. H. Navier, “Memoire Surles du Movement des,” Mem Acad. Sci. Inst. France, Vol. 1, No. 6, 1823, pp. 414-416.

[23] S. Yu and T. A. Ahem, “Slip Flow Heat Transfer in Rectangular Micro Channel,” International Journal of Heat and Mass Transfer, Vol. 44, No. 22, 2002, pp. 4225-4234. doi:10.1016/S0017-9310(01)00075-8

[24] S. Goldstein, “Modern Development in Fluid Dynamics,” Vol. 2, Dover, New York, 1965, p. 676.

[25] K. Watannebe and Y. H. Mizunuma, “Slip of Newtonian Fluids at Solid Boundary,” JSME International Journal Series B, Vol. 41, No. 3, 1998, p. 525.

[26] S. R. Jain and P. K. Sharma, “Effect of Viscous Heating on Flow past a Vertical Plate in Slip-Flow Regime without Periodic Temperature Variations,” Journal of Rajasthan Academy of Physical Sciences, Vol. 5, No. 4, 2006, pp. 383-398.

[27] A. R. A. Khaled and K. Vafai, “The Effect of the Slip Condition on Stokes and Couette Flows Due to an Oscillating Wall, Exact Solutions,” International Journal of Non-Linear Mechanics, Vol. 39, No. 5, 2004, pp. 759-809. doi:10.1016/S0020-7462(03)00043-X

[28] H. Poonia and R. C. Chaudhary, “The Influence of Radiative Heat Transfer on MHD Osciallating Flow in a Planner Channel with Slip Condition,” International Journal of Energy & Technology, Vol. 4, No. 2, 2012, pp. 1-7.

[29] A. C. L. Cogley, W. G. Vincenti and E. S. Giles, “Differential Approximation for Radiative Heat Transfer in a Non-Grey Gas near Equilibrium,” American Institute of Aeronautics and Astronautics, Vol. 6, No. 3, 1968, pp. 551- 553. doi:10.2514/3.4538

[1] A. Bejan and K. R. Khair, “Heat and Mass Transfer in Porous Medium,” International Journal of Heat and Mass Transfer, Vol. 28, No. 5, 1985. 902-918.

[2] O. V. Trevisan and A. Bejan, “Natural Convection with Combined Heat and Mass Transfer Buoyancy Effects in a Porous Medium,” Heat and Mass Transfer, Vol. 28, No. 8, 1985, pp. 1597-1611. doi:10.1016/0017-9310(85)90261-3

[3] M. Acharya, G. C. Das and L. P. Singh, “Magnetic Field Effects on the Free Convection and Mass Transfer Flow through Porous Medium with Constant Suction and Con- stant Heat Flux,” Indian Journal Pure Applied Mathematics, Vol. 31, No. 1, 2000, pp. 1-18.

[4] A. Rapits and N. Kafousias, “Magneto Hydrodynamics Free Convective Flow and Mass Transfer through a Porous Medium Bounded by an Infinite Vertical Porous Plate with constant Heat Flux,” Canadian Journal of Physics, Vol. 60, No. 12, 1982, pp. 1724-1729.

[5] U. N. Das, N. Ahmed and D. Sharma, “Three-Dimensional Free Convective MHD Flow and Heat Transfer through Porous Medium,” FJAM, Vol. 4, No. 3, 2000, pp. 357- 369.

[6] H. P. G. Darcy, “Lee Fort Airs Publication La Villede Dijan Victor Dalonat,” Paris, Vol. 1, 1857, p. 41.

[7] R. Wooding, “Steady State Free Thermal Convection of Liquid in a Saturated Permeable Medium,” Journal of Fluid Mechanics, Vol. 2, No. 3, 1957, pp. 273-285. doi:10.1017/S0022112057000129

[8] H. C. Brickmam, “A Calculation of the Viscous Force Exerted by a Flowing Fluid on a Dense Swarm of Particles,” Applied Sciences Research, Vol. A1, 1947, pp. 27- 34.

[9] H. C. Brickman, “On the Permeability of Media Consisting of Closely Packed Porous Particles,” Applied Sciences Research, Vol. A1, 1947, pp. 81-86.

[10] R. C. Chaudhary and A. Jain, “Combined Heat and Mass Transfer Effects on MHD Free Convection Flow Past an Oscillating Plate Embedded in Porous Medium,” Romanian Journal of Physics, Vol. 52, No. 5-7, 2007, pp. 505- 524.

[11] P. L. Chambre and J. D. Young, “On the Diffusion of a Chemically Reactive Species in a Laminar Boundary Layer Flow,” Physics of Fluids, Vol. 1, No. 1, 1958, pp. 48-54. doi:10.1063/1.1724336

[12] R. Muthucumaraswamy, “Effects of a Chemical on a Moving Isothermal Surface with Suction,” Acta Mechanica, Vol. 155, No. 1-2, 2002, pp. 65-70. doi:10.1007/BF01170840

[13] R. Muthucumaraswamy and S. Meenakshisundaram, “Theroretical Study of Chemical Reaction Effects on Vertical Oscillating Plate with Variable Temperature,” Theoretical and Applied Mechanics, Vol. 33, No. 3, 2006, pp. 245-257.

[14] M. A. Hussain and H. S. Takhar, “Radiation Effect on Mixed Convection along a Vertical Plate in Presence of Heat Generation or Absorption,” Journal of Heat Transfer, Vol. 31, No. 4, 1996, pp. 243-248.

[15] N. Ahmed and H. K. Sarmah, “The Radiation Effect on a Transient MHD Flow Mass Transfer Past an Impulsively Fixed Infinite Vertical Plate,” International Journal of Applied Mathematics and Mechanics, Vol. 5, No. 5, 2009, pp. 87-98.

[16] V. Rajesh and S. V. K. Varma, “Radiation Effects on MHD Flow through a Porous Medium with Variable Tem- perature and Mass Diffusion,” International Journal of Applied Mathematics and Mechanics, Vol. 6, No. 11, 2010, pp. 39-57.

[17] D. Pal and H. Mondal, “Radiation Effects on Combined Convection over a Vertical Flat Plate Embedded in a Porous Medium of Variable Porosity,” Meccanica, Vol. 44, No. 2, 2009, pp. 133-144. doi:10.1007/s11012-008-9156-0

[18] A. M. D. Samad and M. M. Rahman, “Thermal Radiation Interaction with Unsteady MHD Flow past a Vertical Porous plate immersed in a porous medium, Journal of Naval Architecture and Marine Engineering, Vol. 3, No. 1, 2006, pp. 7-14.

[19] S. Karthikeyan, S. Sivasankaran and S. Rajan, “Thermal Radiation Effects on MHD Convective Flow over a Vertical Porous Plate Embedded in a Porous Medium by Perturbation Technique,” Proceedings of International Con- ference on Fluid Dynamics and Its Applications, Bangalore, 20-22 July 2010, pp. 484-491.

[20] S. Das, M. Jana and R. N. Jana, “Radiation Effect on Natural Convection near a Vertical Plate Embedded in Porous Medium with Ramped Wall Temperature,” Open Journal of Fluid Dynamics, Vol. 1, No. 1, 2011, pp. 1-11.

[21] D. Pal and B. Talukdar, “Perturbation Analysis of Unsteady Magnetohydrodynamic Convective Heat and Mass Transfer in a Boundary Layer Slip Flow past a Vertical Permeable Plate with Thermal Radiation Chemical Reaction,” Communications in Nonlinear Science and Numerical Simulation, Vol. 15, No. 7, 2010, pp. 1813-1830.

[22] C. L. M. H. Navier, “Memoire Surles du Movement des,” Mem Acad. Sci. Inst. France, Vol. 1, No. 6, 1823, pp. 414-416.

[23] S. Yu and T. A. Ahem, “Slip Flow Heat Transfer in Rectangular Micro Channel,” International Journal of Heat and Mass Transfer, Vol. 44, No. 22, 2002, pp. 4225-4234. doi:10.1016/S0017-9310(01)00075-8

[24] S. Goldstein, “Modern Development in Fluid Dynamics,” Vol. 2, Dover, New York, 1965, p. 676.

[25] K. Watannebe and Y. H. Mizunuma, “Slip of Newtonian Fluids at Solid Boundary,” JSME International Journal Series B, Vol. 41, No. 3, 1998, p. 525.

[26] S. R. Jain and P. K. Sharma, “Effect of Viscous Heating on Flow past a Vertical Plate in Slip-Flow Regime without Periodic Temperature Variations,” Journal of Rajasthan Academy of Physical Sciences, Vol. 5, No. 4, 2006, pp. 383-398.

[27] A. R. A. Khaled and K. Vafai, “The Effect of the Slip Condition on Stokes and Couette Flows Due to an Oscillating Wall, Exact Solutions,” International Journal of Non-Linear Mechanics, Vol. 39, No. 5, 2004, pp. 759-809. doi:10.1016/S0020-7462(03)00043-X

[28] H. Poonia and R. C. Chaudhary, “The Influence of Radiative Heat Transfer on MHD Osciallating Flow in a Planner Channel with Slip Condition,” International Journal of Energy & Technology, Vol. 4, No. 2, 2012, pp. 1-7.

[29] A. C. L. Cogley, W. G. Vincenti and E. S. Giles, “Differential Approximation for Radiative Heat Transfer in a Non-Grey Gas near Equilibrium,” American Institute of Aeronautics and Astronautics, Vol. 6, No. 3, 1968, pp. 551- 553. doi:10.2514/3.4538