Heat and Mass Transfer in MHD Visco-Elastic Fluid Flow through a Porous Medium over a Stretching Sheet with Chemical Reaction

ABSTRACT

This paper presents the study of convective heat and mass transfer characteristics of an incompressible MHD visco-elastic fluid flow immersed in a porous medium over a stretching sheet with chemical reaction and thermal stratification effects. The resultant governing boundary layer equations are highly non-linear and coupled form of partial differential equations, and they have been solved by using fourth order Runge-Kutta integration scheme with Newton Raphson shooting method. Numerical computations are carried out for the non-dimensional physical parameters. Here a numerical has been carried out to study the effect of different physical parameters such as visco-elasticity, permeability of the porous medium, magnetic field, Grashof number, Schmidt number, heat source parameter and chemical reaction parameter on the flow, heat and mass transfer characteristics.

This paper presents the study of convective heat and mass transfer characteristics of an incompressible MHD visco-elastic fluid flow immersed in a porous medium over a stretching sheet with chemical reaction and thermal stratification effects. The resultant governing boundary layer equations are highly non-linear and coupled form of partial differential equations, and they have been solved by using fourth order Runge-Kutta integration scheme with Newton Raphson shooting method. Numerical computations are carried out for the non-dimensional physical parameters. Here a numerical has been carried out to study the effect of different physical parameters such as visco-elasticity, permeability of the porous medium, magnetic field, Grashof number, Schmidt number, heat source parameter and chemical reaction parameter on the flow, heat and mass transfer characteristics.

KEYWORDS

Heat and Mass Transfer, Incompressible MHD, Visco-Elastic, Porous Medium, Chemical Reaction

Heat and Mass Transfer, Incompressible MHD, Visco-Elastic, Porous Medium, Chemical Reaction

Cite this paper

nullS. Alharbi, M. Bazid and M. Gendy, "Heat and Mass Transfer in MHD Visco-Elastic Fluid Flow through a Porous Medium over a Stretching Sheet with Chemical Reaction,"*Applied Mathematics*, Vol. 1 No. 6, 2010, pp. 446-455. doi: 10.4236/am.2010.16059.

nullS. Alharbi, M. Bazid and M. Gendy, "Heat and Mass Transfer in MHD Visco-Elastic Fluid Flow through a Porous Medium over a Stretching Sheet with Chemical Reaction,"

References

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[2] B. C. Sakiadis, “Boundary Layer Behavior on Continuous Solid Surfaces: II. Boundary Layer on a Continuous Flat Surface,” AICHE Journal, Vol. 7, 1961, pp. 221-225.

[3] F. K. Tsou, E. M. Sparrow and R. J. Goldstein, “Flow and Heat Transfer in the Boundary Layer on a Continuous Moving Surface,” International Journal of Heat and Mass Transfer, Vol. 10, 1967, pp. 219-223.

[4] L. J. Crane, “Flow past a Stretching Plate,” Zeitschrift für Angewandte Mathematik und Physik (ZAMP), Vol. 21, No. 4, 1970, pp. 645-647.

[5] A. Chakrabarti and A. S. Gupta, “Hydromagnetic flow and heat transfer over a stretching sheet,” Quarterly Journal of Mechanics and Applied Mathematics, Vol. 37, 1979, pp. 73-78.

[6] C. K. Chen and M. I. Char, “Heat Transfer of a Continuous Stretching Surface with Suction or Blowing,” Journal of Mathematical Analysis and Applications, Vol. 135, No. 2, November 1988, pp. 568-580.

[7] T. C. Chiam, “Heat Transfer in a Variable Conductivity in a Stagnation Point Flow towards a Stretching Sheet,” International Communications in Heat and Mass Transfer, Vol. 23, No. 2, March-April 1996, pp. 239-248.

[8] E. M. Abo Eldahab and M. S.El Gendy, “Radiation Effect on Convective Heat Transfer in an Electrically Conducting Fluid at a Stretching surface with Variable Viscosity and Uniform Free-Stream,” Physica Scripta, Vol. 62, No. 4, 2000, pp. 321-325.

[9] E. M. Abo Eldahab and M. S. El Gendy, “Convective Heat Transfer past a Continuously Moving Plate Embedded in a Non-Darcian Porous Medium in the Presence of a Magnetic Field,” Canadian Journal of Physics, Vol. 79, 2001, pp. 1031-1038.

[10] A. A. Megahed, S. R. Komy and A. A. Afify, “Similarity Analysis in Magnetohydrodynamics Hall Effect on Free Convection Flow and Mass Transfer past Semi Infinite Vertical Flat Plate,” International Journal of Non-Linear Mechanics, Vol. 38, 2003, pp. 513-520.

[11] M. A. Seddeek, “Effects of Non-Darcian on Forced Convection Heat Transfer over a Flat Plate in a Porous Medium-with Temperature Dependent Viscosity,” International Communications in Heat and Mass Transfer, Vol. 32, 2005, pp. 258-265.

[12] M. A. Seddeek and M. S. Abdelmeguid, “Effects of Radiation and Thermal Diffusivity on Heat Transfer over a Stretching Surface with Variable Heat Flux,” Physics Letters A, Vol. 348, No. 3-6, January 2006, pp. 172-179.

[13] A. A. Afify, “Similarity Solution in MHD: Effects of Thermal Diffusion and Diffusion Thermo on Free Convective Heat and Mass Transfer over a Stretching Surface Considering Suction or Injection,” Communications in Nonlinear Science and Numerical Simulation, Vol. 14, No. 5, May 2009, pp. 2202-2214.

[14] M. A. Seddeek, S. N. Odda and M. S. Abdelmeguid, “Numerical Study for the Effects of Thermophoresis and Variable Thermal Conductivity on Heat and Mass Transfer over an Accelerating Surface with Heat Source,” Computational Materials Science, Vol. 47, No. 1, 2009, pp. 93-98.

[15] K. R. Rajagopal, T. Y. Na and A. S. Gupta, “Flow of Visco-Elastic Fluid over a Stretching Sheet,” Rheol Acta, Vol. 23, 1984, pp. 213-215.

[16] B. Siddappa and S. Abel, “Non-Newtonian flow past a stretching plate,” Zeitschrift für Angewandte Mathematik und Physik (ZAMP), Vol. 36, 1985, pp. 890-892.

[17] S. Abel and P. H. Veena, “Visco-Elastic Fluid Flow and Heat Transfer in Porous Medium over a Stretching Sheet,” International Journal of Non-Linear Mechanics, Vol. 33, 1998, pp. 531-540.

[18] A. Chakrabarti and A. S. Gupta, “Hydromagnetic Flow and Heat Transfer over a Stretching Sheet,” Quarterly Journal of Mechanics and Applied Mathematics, Vol. 37, 1979, pp. 73-78.

[19] T. Sarpakaya, “Flow of Non-Newtonian Fluids in Magnetic Field,” AICHE Journal, Vol. 7, 1961, pp. 324-328.

[20] H. I. Andersson, “MHD Flow of Viscoelastic Fluid past a Stretching Surface,” Acta Mech, Vol. 95, 1992, pp. 227- 230.

[21] S. Abel, A. Joshi and R. M. Sonth, “Heat Transfer in a MHD Visco-Elastic Fluid over a Stretching Surface,” Journal of Applied Mathematics and Mechanics, Vol. 81, 2001, pp. 691-698.

[22] S. Abel, P. H. Veena, K. Rajgopal and V. K. Pravin, “Non-Newtonian Magneto Hydrodynamic Flow over a Stretching Surface with Heat and Mass Transfer,” International Journal of Non-Linear Mechanics, Vol. 39, 2004, pp. 1067-1078.

[23] M. A. Seddeek, “Heat and Mass Transfer on a Stretching Sheet with a Magnetic Field in a Visco-Elastic Fluid Flow through a Porous Medium with Heat Source or Sink,” Computational Materials Science, Vol. 38, 2007, pp. 781-787.

[24] S. Abel and N. Mahesha, “Heat Transfer in MHD Viscoelastic Fluid Flow over a Stretching Sheet with Variable Thermal Conductivity, Non-Uniform Heat Source and Radiation,” Applied Mathematical Modelling, Vol. 32, 2008, pp. 1965-1983.

[25] K. V. Prasad, D. Pal, V. Umesh and N. S. Prasanna Rao, “The Effect of Variable Viscosity on MHD Viscoelastic Fluid Flow and Heat Transfer over a Stretching Sheet,” Communications in Nonlinear Science and Numerical Simulation, Vol. 15, No. 2, February 2010, pp. 331-344.

[26] D. A. Nield and A. Bejan, “Convection in Porous Media,” 2nd Edition, Springer-Verlag, New York, 1999.

[27] E. R. G. Eckert and R. M. Drake, “Analysis of Heat and Mass Transfer,” McGraw-Hill, New York, 1972.

[28] R. Kandasamy, K. Periasamy and K. K. Sivagnana Prabhu, "Chemical Reaction, Heat and Mass Transfer on MHD Flow over a Vertical Stretching Surface with Heat Source and Thermal Stratification Effects," International Journal of Heat and Mass Transfer, Vol. 48, No. 21-22, October 2005, pp. 4557-4561

[29] R. Kandasamy, K. Periasamy and K. K. Sivagnana Prabhu, "Effect of Chemical Reaction, Heat and Mass Transfer along a Wedge with Heat Source and Concentration in the Presence of Suction or Injection," International Journal of Heat and Mass Transfer, Vol. 48, No. 7, March 2005, pp. 1388-1394.

[30] M. A. Seddeek, “Thermal Radiation and Buoyancy Effects on MHD Free Convection Heat Generation Flow over an Accelerating Permeable Surface with Temperature Dependent Viscosity,” Canadian Journal of Physics, Vol. 79, 2001, pp. 725-732.

[31] M. A. Seddeek, A. A. Darwish and M. S. Abdelmeguid, “Effect of Chemical Reaction and Variable Viscosity on Hydromagnetic Mixed Convection Heat and Mass Transfer for Hiemenz Flow through Porous Media with Radiation” Communications in Nonlinear Science and Numerical Simulation, Vol. 12, No. 2, March 2007, pp. 195-213.

[32] M. A. Seddeek and A. M. Salem, “The Effect of an Axial Magnetic Field on The Flow and Heat Transfer about a Fluid Underlying the Axisymmetric Spreading Surface with Temperature Dependent Viscosity and Thermal Diffusivity,” Computional Mechanics, Vol. 39, No. 4, 2007, pp. 401-408.

[33] M. A. Seddeek, F. A. Salama, “The Effects of Temperature Dependent Viscosity and Thermal Conductivity on Unsteady MHD Convective Heat Transfer Past a Semi-Infinite Vertical Porous Moving Plate with Variable Suction,” Computational Materials Science, Vol. 40, No. 2, August 2007, pp. 186-192.

[34] T. Y. Na, “Computational Methods in Engineering Boundary Value Problems,” Academic Press, New York, 1979.

[1] B. C. Sakiadis, “Boundary Layer Behavior on Continuous Solid Surfaces: I. Boundary Layer Equations for Two Dimensional and Axisymmetric Flow,” AICHE Journal, Vol. 7, No. 1, March 1961, pp. 26-28.

[2] B. C. Sakiadis, “Boundary Layer Behavior on Continuous Solid Surfaces: II. Boundary Layer on a Continuous Flat Surface,” AICHE Journal, Vol. 7, 1961, pp. 221-225.

[3] F. K. Tsou, E. M. Sparrow and R. J. Goldstein, “Flow and Heat Transfer in the Boundary Layer on a Continuous Moving Surface,” International Journal of Heat and Mass Transfer, Vol. 10, 1967, pp. 219-223.

[4] L. J. Crane, “Flow past a Stretching Plate,” Zeitschrift für Angewandte Mathematik und Physik (ZAMP), Vol. 21, No. 4, 1970, pp. 645-647.

[5] A. Chakrabarti and A. S. Gupta, “Hydromagnetic flow and heat transfer over a stretching sheet,” Quarterly Journal of Mechanics and Applied Mathematics, Vol. 37, 1979, pp. 73-78.

[6] C. K. Chen and M. I. Char, “Heat Transfer of a Continuous Stretching Surface with Suction or Blowing,” Journal of Mathematical Analysis and Applications, Vol. 135, No. 2, November 1988, pp. 568-580.

[7] T. C. Chiam, “Heat Transfer in a Variable Conductivity in a Stagnation Point Flow towards a Stretching Sheet,” International Communications in Heat and Mass Transfer, Vol. 23, No. 2, March-April 1996, pp. 239-248.

[8] E. M. Abo Eldahab and M. S.El Gendy, “Radiation Effect on Convective Heat Transfer in an Electrically Conducting Fluid at a Stretching surface with Variable Viscosity and Uniform Free-Stream,” Physica Scripta, Vol. 62, No. 4, 2000, pp. 321-325.

[9] E. M. Abo Eldahab and M. S. El Gendy, “Convective Heat Transfer past a Continuously Moving Plate Embedded in a Non-Darcian Porous Medium in the Presence of a Magnetic Field,” Canadian Journal of Physics, Vol. 79, 2001, pp. 1031-1038.

[10] A. A. Megahed, S. R. Komy and A. A. Afify, “Similarity Analysis in Magnetohydrodynamics Hall Effect on Free Convection Flow and Mass Transfer past Semi Infinite Vertical Flat Plate,” International Journal of Non-Linear Mechanics, Vol. 38, 2003, pp. 513-520.

[11] M. A. Seddeek, “Effects of Non-Darcian on Forced Convection Heat Transfer over a Flat Plate in a Porous Medium-with Temperature Dependent Viscosity,” International Communications in Heat and Mass Transfer, Vol. 32, 2005, pp. 258-265.

[12] M. A. Seddeek and M. S. Abdelmeguid, “Effects of Radiation and Thermal Diffusivity on Heat Transfer over a Stretching Surface with Variable Heat Flux,” Physics Letters A, Vol. 348, No. 3-6, January 2006, pp. 172-179.

[13] A. A. Afify, “Similarity Solution in MHD: Effects of Thermal Diffusion and Diffusion Thermo on Free Convective Heat and Mass Transfer over a Stretching Surface Considering Suction or Injection,” Communications in Nonlinear Science and Numerical Simulation, Vol. 14, No. 5, May 2009, pp. 2202-2214.

[14] M. A. Seddeek, S. N. Odda and M. S. Abdelmeguid, “Numerical Study for the Effects of Thermophoresis and Variable Thermal Conductivity on Heat and Mass Transfer over an Accelerating Surface with Heat Source,” Computational Materials Science, Vol. 47, No. 1, 2009, pp. 93-98.

[15] K. R. Rajagopal, T. Y. Na and A. S. Gupta, “Flow of Visco-Elastic Fluid over a Stretching Sheet,” Rheol Acta, Vol. 23, 1984, pp. 213-215.

[16] B. Siddappa and S. Abel, “Non-Newtonian flow past a stretching plate,” Zeitschrift für Angewandte Mathematik und Physik (ZAMP), Vol. 36, 1985, pp. 890-892.

[17] S. Abel and P. H. Veena, “Visco-Elastic Fluid Flow and Heat Transfer in Porous Medium over a Stretching Sheet,” International Journal of Non-Linear Mechanics, Vol. 33, 1998, pp. 531-540.

[18] A. Chakrabarti and A. S. Gupta, “Hydromagnetic Flow and Heat Transfer over a Stretching Sheet,” Quarterly Journal of Mechanics and Applied Mathematics, Vol. 37, 1979, pp. 73-78.

[19] T. Sarpakaya, “Flow of Non-Newtonian Fluids in Magnetic Field,” AICHE Journal, Vol. 7, 1961, pp. 324-328.

[20] H. I. Andersson, “MHD Flow of Viscoelastic Fluid past a Stretching Surface,” Acta Mech, Vol. 95, 1992, pp. 227- 230.

[21] S. Abel, A. Joshi and R. M. Sonth, “Heat Transfer in a MHD Visco-Elastic Fluid over a Stretching Surface,” Journal of Applied Mathematics and Mechanics, Vol. 81, 2001, pp. 691-698.

[22] S. Abel, P. H. Veena, K. Rajgopal and V. K. Pravin, “Non-Newtonian Magneto Hydrodynamic Flow over a Stretching Surface with Heat and Mass Transfer,” International Journal of Non-Linear Mechanics, Vol. 39, 2004, pp. 1067-1078.

[23] M. A. Seddeek, “Heat and Mass Transfer on a Stretching Sheet with a Magnetic Field in a Visco-Elastic Fluid Flow through a Porous Medium with Heat Source or Sink,” Computational Materials Science, Vol. 38, 2007, pp. 781-787.

[24] S. Abel and N. Mahesha, “Heat Transfer in MHD Viscoelastic Fluid Flow over a Stretching Sheet with Variable Thermal Conductivity, Non-Uniform Heat Source and Radiation,” Applied Mathematical Modelling, Vol. 32, 2008, pp. 1965-1983.

[25] K. V. Prasad, D. Pal, V. Umesh and N. S. Prasanna Rao, “The Effect of Variable Viscosity on MHD Viscoelastic Fluid Flow and Heat Transfer over a Stretching Sheet,” Communications in Nonlinear Science and Numerical Simulation, Vol. 15, No. 2, February 2010, pp. 331-344.

[26] D. A. Nield and A. Bejan, “Convection in Porous Media,” 2nd Edition, Springer-Verlag, New York, 1999.

[27] E. R. G. Eckert and R. M. Drake, “Analysis of Heat and Mass Transfer,” McGraw-Hill, New York, 1972.

[28] R. Kandasamy, K. Periasamy and K. K. Sivagnana Prabhu, "Chemical Reaction, Heat and Mass Transfer on MHD Flow over a Vertical Stretching Surface with Heat Source and Thermal Stratification Effects," International Journal of Heat and Mass Transfer, Vol. 48, No. 21-22, October 2005, pp. 4557-4561

[29] R. Kandasamy, K. Periasamy and K. K. Sivagnana Prabhu, "Effect of Chemical Reaction, Heat and Mass Transfer along a Wedge with Heat Source and Concentration in the Presence of Suction or Injection," International Journal of Heat and Mass Transfer, Vol. 48, No. 7, March 2005, pp. 1388-1394.

[30] M. A. Seddeek, “Thermal Radiation and Buoyancy Effects on MHD Free Convection Heat Generation Flow over an Accelerating Permeable Surface with Temperature Dependent Viscosity,” Canadian Journal of Physics, Vol. 79, 2001, pp. 725-732.

[31] M. A. Seddeek, A. A. Darwish and M. S. Abdelmeguid, “Effect of Chemical Reaction and Variable Viscosity on Hydromagnetic Mixed Convection Heat and Mass Transfer for Hiemenz Flow through Porous Media with Radiation” Communications in Nonlinear Science and Numerical Simulation, Vol. 12, No. 2, March 2007, pp. 195-213.

[32] M. A. Seddeek and A. M. Salem, “The Effect of an Axial Magnetic Field on The Flow and Heat Transfer about a Fluid Underlying the Axisymmetric Spreading Surface with Temperature Dependent Viscosity and Thermal Diffusivity,” Computional Mechanics, Vol. 39, No. 4, 2007, pp. 401-408.

[33] M. A. Seddeek, F. A. Salama, “The Effects of Temperature Dependent Viscosity and Thermal Conductivity on Unsteady MHD Convective Heat Transfer Past a Semi-Infinite Vertical Porous Moving Plate with Variable Suction,” Computational Materials Science, Vol. 40, No. 2, August 2007, pp. 186-192.

[34] T. Y. Na, “Computational Methods in Engineering Boundary Value Problems,” Academic Press, New York, 1979.