EFFECT OF CHEMICAL REACTION ON MHD FLOW OF A VISCO-ELASTIC (WALTER'S LIQUID MODEL-B) FLUID THROUGH POROUS MEDIUM WITH HEAT SOURCE
DOI:
https://doi.org/10.24297/ijct.v8i1.6816Keywords:
Chemical reaction, MHD, Visco-elastic, Walter, s Liquid Model-B, Heat source, Porous medium, UnsteadyAbstract
In this paper we have studied and discussed the problem of unsteady flow of a visco-elastic (walter’s liquid model B) fluid through porous medium in presence of a heat source and a uniform magnetic field with effect of chemical reaction parameter. The effect of chemical reaction parameter g, porous parameter K and magnetic parameter on fluid velocity, temperature and concentration with respect to vertical axis Y and time t are discussed graphically.
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References
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. 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.
5. Das, U.N., Ray, S.N. and Soundalgekar, V.M., Mass transfer effects on flow past an impulsively started infinite vertical plate with constant mass flux and exact solution. Heat and Mass Transfer, 31, 163-167 (1996).
6. 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.
7. 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.
8. 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.
9. A. Megahed, S. R. Komy and A. A. Afify, “Similarity Analysis in Magneto hydrodynamics 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.
10. 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.
11. 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.
12. 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
13. 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.
14. 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.
15. 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.
16. Gebhart, B. and Pera, L., The nature of vertical natural convection flows resulting from the combined buoyancy effects of thermal and mass transfer and mass diffusion. Int. J. Heat Mass Transfer, 14, 2025-2050 (1971).
17. Muthucumaraswamy, R., Genesan, P. and Soundalgekar, V.M., Heat and Mass transfer effects on flow past an impulsively started vertical plate. Acta Mech., 146, 1-8 (2001).
18. 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 Visco-elastic Fluid past a Stretching Surface,†Acta Mechanica, Vol. 95, 1992, pp. 227- 230.
19. 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.
20. 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.
ISSN 22773061
729 | P a g e J u n e 1 5 , 2 0 1 3
21. 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.
22. S. Abel and N. Mahesha, “Heat Transfer in MHD Visco-elastic 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.
23. K. V. Prasad, D. Pal, V. Umesh and N. S. Prasanna Rao, “The Effect of Variable Viscosity on MHD Visco-elastic 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.
24. D. A. Nield and A. Bejan, “Convection in Porous Media,†2nd Edition, Springer-Verlag, New York, 1999.
25. E. R. G. Eckert and R. M. Drake, “Analysis of Heat and Mass Transfer,†McGraw-Hill, New York, 1972.
26. 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.
27. R. Kandasamy, K. Periasamy and K. K. S. 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.
28. 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.
29. 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.
30. 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.
31. 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.
32. T. Y. Na, “Computational Methods in Engineering Boundary Value Problems,†Academic Press, New York, 1979.
33. Soundalgekar, V.M., Free convection effects on the Stokes problem for an infinite vertical plate. Trans. ASME. J. Heat Transfer, Vol. 99, p. 499-501 (1977).
34. Soundalgekar, V.M., Effects of mass transfer and free convection on the flow pastan impulsively started vertical plate. ASMEJ. Appl. Mech., 46, 757-760 (1979).
35. Stokes, G.G., On the effects of the internal friction of fluids on the motion of pendulums. Camber. Phil. IX, 8-106 (1851).
36. Kumar, P., Jha, R. and Singh, U.R., MHD flow of a visco-elastic (Walter’s liquid model-B) fluid through porous medium. Acta Ciencia Indica, Vol. XXXIV M, No. 2, 759-764 (2008).
37. Bhagwat Swarup and Kuldeep, MHD flow of a visco-elastic (Walter’s liquid model-B) fluid through porous medium. Acta Ciencia Indica, Vol. XXXV M, No. 2, 605-610 (2010).
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. 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.
5. Das, U.N., Ray, S.N. and Soundalgekar, V.M., Mass transfer effects on flow past an impulsively started infinite vertical plate with constant mass flux and exact solution. Heat and Mass Transfer, 31, 163-167 (1996).
6. 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.
7. 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.
8. 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.
9. A. Megahed, S. R. Komy and A. A. Afify, “Similarity Analysis in Magneto hydrodynamics 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.
10. 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.
11. 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.
12. 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
13. 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.
14. 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.
15. 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.
16. Gebhart, B. and Pera, L., The nature of vertical natural convection flows resulting from the combined buoyancy effects of thermal and mass transfer and mass diffusion. Int. J. Heat Mass Transfer, 14, 2025-2050 (1971).
17. Muthucumaraswamy, R., Genesan, P. and Soundalgekar, V.M., Heat and Mass transfer effects on flow past an impulsively started vertical plate. Acta Mech., 146, 1-8 (2001).
18. 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 Visco-elastic Fluid past a Stretching Surface,†Acta Mechanica, Vol. 95, 1992, pp. 227- 230.
19. 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.
20. 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.
ISSN 22773061
729 | P a g e J u n e 1 5 , 2 0 1 3
21. 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.
22. S. Abel and N. Mahesha, “Heat Transfer in MHD Visco-elastic 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.
23. K. V. Prasad, D. Pal, V. Umesh and N. S. Prasanna Rao, “The Effect of Variable Viscosity on MHD Visco-elastic 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.
24. D. A. Nield and A. Bejan, “Convection in Porous Media,†2nd Edition, Springer-Verlag, New York, 1999.
25. E. R. G. Eckert and R. M. Drake, “Analysis of Heat and Mass Transfer,†McGraw-Hill, New York, 1972.
26. 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.
27. R. Kandasamy, K. Periasamy and K. K. S. 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.
28. 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.
29. 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.
30. 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.
31. 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.
32. T. Y. Na, “Computational Methods in Engineering Boundary Value Problems,†Academic Press, New York, 1979.
33. Soundalgekar, V.M., Free convection effects on the Stokes problem for an infinite vertical plate. Trans. ASME. J. Heat Transfer, Vol. 99, p. 499-501 (1977).
34. Soundalgekar, V.M., Effects of mass transfer and free convection on the flow pastan impulsively started vertical plate. ASMEJ. Appl. Mech., 46, 757-760 (1979).
35. Stokes, G.G., On the effects of the internal friction of fluids on the motion of pendulums. Camber. Phil. IX, 8-106 (1851).
36. Kumar, P., Jha, R. and Singh, U.R., MHD flow of a visco-elastic (Walter’s liquid model-B) fluid through porous medium. Acta Ciencia Indica, Vol. XXXIV M, No. 2, 759-764 (2008).
37. Bhagwat Swarup and Kuldeep, MHD flow of a visco-elastic (Walter’s liquid model-B) fluid through porous medium. Acta Ciencia Indica, Vol. XXXV M, No. 2, 605-610 (2010).
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Published
2013-06-23
How to Cite
Chaturvedi, R., Shrivatav, D., & Ahemad, D. S. (2013). EFFECT OF CHEMICAL REACTION ON MHD FLOW OF A VISCO-ELASTIC (WALTER’S LIQUID MODEL-B) FLUID THROUGH POROUS MEDIUM WITH HEAT SOURCE. INTERNATIONAL JOURNAL OF COMPUTERS &Amp; TECHNOLOGY, 8(1), 721–729. https://doi.org/10.24297/ijct.v8i1.6816
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