Conjugate Heat and Mass Transfer for MHD Mixed Convection with Viscous Dissipation and Radiation Effect for Viscoelastic Fluid past a Stretching Sheet
In this study, an analysis has been performed for
conjugate heat and mass transfer of a steady laminar boundary-layer
mixed convection of magnetic hydrodynamic (MHD) flow with
radiation effect of second grade subject to suction past a stretching
sheet. Parameters E Nr, Gr, Gc, Ec and Sc represent the dominance of
the viscoelastic fluid heat and mass transfer effect which have
presented in governing equations, respectively. The similar
transformation and the finite-difference method have been used to
analyze the present problem. The conjugate heat and mass transfer
results show that the non-Newtonian viscoelastic fluid has a better heat
transfer effect than the Newtonian fluid. The free convection with a
larger r G or c G has a good heat transfer effect better than a smaller
r G or c G , and the radiative convection has a good heat transfer
effect better than non-radiative convection.
[1] J.P. Hartnett, Viscoelastic fluids: a new challenge in heat transfer,
Transactions of ASME, 296-303, (1992).
[2] K.R. Rajagopal, A.S. Gupta and T.Y. Na, A note on the Falkner-Skan
flows of a non-Newtonian fluid, Int. J. Non-linear Mech., 313-320,
(1983).
[3] M. Massoudi and M. Ramezan, Effect of injection or suction on the
Falkner-Skan flows of second grade fluids, Int. J. Non-linear Mech.,
221-227, (1989).
[4] K. R. Rajagopal, Boundary Layers in Non-linear Fluids, Pitman
Monographs and Surveys in Pure and Applied Mathematics, 209-218,
(1995).
[5] K. Vajravelu and E. Soewono, Fourth order non-Linear systems arising in
combined free and forced convection flow of a second order fluid, Int. J.
Non-Linear Mech. Vol. 29, No. 6, 861-869 (1994).
[6] A.A. Raptis, Heat Transfer From Flow of an Elastico Viscous Fluid, Int.
Comm. Heat Mass Transfer Vol. 16, 193-197, (1989).
[7] Sujit Kumar Khan, Heat transfer in a viscoelastic fluid flow over a
stretching surface with heat source/sink, suction/blowing and radiation,
International Journal of Heat and Mass Transfer, Volume 49, Issues 3-4,
February 2006, Pages 628-639.
[8] Sanjayanand, Emmanuel; Khan, Sujit Kumar, On heat and mass transfer
in a viscoelastic boundary layer flow over an exponentially stretching
sheet, International Journal of Thermal Sciences Volume: 45, Issue: 8,
August, 2006, pp. 819-828.
[9] Cortell, Rafael, MHD flow and mass transfer of an electrically conducting
fluid of second grade in a porous medium over a stretching sheet with
chemically reactive species, Chemical Engineering & Processing
Volume: 46, Issue: 8, August, 2007, pp. 721-728.
[10] Rafael Cortell Bataller, Viscoelastic fluid flow and heat transfer over a
stretching sheet under the effects of a non-uniform heat source, viscous
dissipation and thermal radiation International Journal of Heat and Mass
Transfer, Volume 50, Issues 15-16, July 2007, Pages 3152-3162.
[11] Seddeek, M.A., 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 Volume: 38, Issue:
4, February, 2007, pp. 781-787.
[12] Kai-Long Hsiao, Heat and Mass Transfer for Electrical Conducting
Mixed Convection with Radiation Effect for Viscoelastic Fluid past a
Stretching Sheet, Journal of Mechanics, Vol.24, No.2, June 2008,
(pp.N21-N27).
[13] Kai-Long Hsiao, MHD Mixed Convection of Viscoelastic Fluid over a
Stretching Sheet with Ohmic Dissipation, Journal of Mechanics, Vol.24,
No.3, September 2008, (pp.N29-N34).
[14] E. M. Sparrow and M. K. Chyu, Conjugate forced convection-conduction
analysis of heat transfer in a plate fin, ASME J. Heat Transfer, 104,
204-206 (1982).
[15] B. Sunden, The effect of Prandtl number on conjugate heat transfer from
rectangular fins, Int. Commun. Heat Mass Transfer, 12, 225-232 (1985).
[16] A. V. Luikov. V. A. Aleksashenko and A. A. Aleksashenko, Analytical
methods of solution of conjugated problems in convective heat transfer,
Int. J. Heat Mass Transfer 14, 1047--1056 (1971).
[17] A. V. Luikov, Conjugate convective heat transfer problems, Int. J. Heat
Mass Transfer 17, 257-265 (I974).
[18] 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, Volume 348, Issues 3-6, 2 January 2006, Pages
172-179.
[19] Mahmoud E.M. Ouaf, Exact solution of thermal radiation on MHD flow
over a stretching porous sheet, Applied Mathematics and Computation,
Volume 170, Issue 2, 15 November 2005, Pages 1117-1125
[20] Sujit Kumar Khan, Heat transfer in a viscoelastic fluid flow over a
stretching surface with heat source/sink, suction/blowing and radiation,
International Journal of Heat and Mass Transfer, in Press, Corrected
Proof, Available online 14 October 2005.
[21] P.G. Siddheshwar and U.S. Mahabaleswar, Effects of radiation and heat
source on MHD flow of a viscoelastic liquid and heat transfer over a
stretching sheet, International Journal of Non-Linear Mechanics, Volume
40, Issue 6, July 2005, Pages 807-820.
[22] Kai-Long Hsiao and Guan-Bang Chen, Conjugate Heat Transfer of Mixed
Convection for Viscoelastic Fluid Past A Stretching Sheet, Mathematical
Problems in Engineering, Volume 2007, Article ID 17058, 21 pages
doi:10.1155/2007/17058.
[23] Kai-Long Hsiao, Conjugate Heat Transfer of Magnetic Mixed Convection
with Radiative and Viscous Dissipation Effects for Second Grade
Viscoelastic Fluid past a Stretching Sheet, Applied Thermal Engineering,
27/11-12 pp. 1895-1903 (2007).
[24] R. S. Rivlin and J. L. Ericksen, Stress deformation relation for isotropic
materials, J. Rat. Mech. Analysis, 323-425, (1955).
[25] T. Cebeci and P. Bradshaw, Physical and Computational Aspects of
Convective Heat Transfer, Springer-Verlag, (1984).
[26] Kai-Long Hsiao, Heat and Mass Transfer for Electrical Conducting
Mixed Convection with Radiation Effect for Viscoelastic Fluid past a
Stretching Sheet, Journal of Mechanics, Vol.24, No.2, June 2008,
(pp.N21-N27).
[27] Kai-Long Hsiao, MHD Mixed Convection of Viscoelastic Fluid over a
Stretching Sheet with Ohmic Dissipation, Journal of Mechanics, Vol.24,
No.3, September 2008, (pp.N29-N34).
[28] Kai-Long Hsiao and C.H. Hsu, Conjugate heat transfer of mixed
convection for viscoelastic fluid past a horizontal flat-plate fin, Applied
Thermal Engineering, 29/1, pp 28-36, January 2009.
[29] Kai-Long Hsiao and C.H. Hsu, Conjugate heat transfer of mixed
convection for visco-elastic fluid past a triangular fin, Nonlinear Analysis
(Series B: Real World Applications), Vol.10/1, pp 130-143, February
2009.
[30] K. Vajravelu, Convection Heat Transfer at a Stretching Sheet with
Suction and Blowing, J. of Mathematical Analysis and Application, 188,
1002-1011(1994).
[31] Chapra and Canale, Numerical Methods for Engineers, McGRAW-HILL,
2ed, 1990.
[1] J.P. Hartnett, Viscoelastic fluids: a new challenge in heat transfer,
Transactions of ASME, 296-303, (1992).
[2] K.R. Rajagopal, A.S. Gupta and T.Y. Na, A note on the Falkner-Skan
flows of a non-Newtonian fluid, Int. J. Non-linear Mech., 313-320,
(1983).
[3] M. Massoudi and M. Ramezan, Effect of injection or suction on the
Falkner-Skan flows of second grade fluids, Int. J. Non-linear Mech.,
221-227, (1989).
[4] K. R. Rajagopal, Boundary Layers in Non-linear Fluids, Pitman
Monographs and Surveys in Pure and Applied Mathematics, 209-218,
(1995).
[5] K. Vajravelu and E. Soewono, Fourth order non-Linear systems arising in
combined free and forced convection flow of a second order fluid, Int. J.
Non-Linear Mech. Vol. 29, No. 6, 861-869 (1994).
[6] A.A. Raptis, Heat Transfer From Flow of an Elastico Viscous Fluid, Int.
Comm. Heat Mass Transfer Vol. 16, 193-197, (1989).
[7] Sujit Kumar Khan, Heat transfer in a viscoelastic fluid flow over a
stretching surface with heat source/sink, suction/blowing and radiation,
International Journal of Heat and Mass Transfer, Volume 49, Issues 3-4,
February 2006, Pages 628-639.
[8] Sanjayanand, Emmanuel; Khan, Sujit Kumar, On heat and mass transfer
in a viscoelastic boundary layer flow over an exponentially stretching
sheet, International Journal of Thermal Sciences Volume: 45, Issue: 8,
August, 2006, pp. 819-828.
[9] Cortell, Rafael, MHD flow and mass transfer of an electrically conducting
fluid of second grade in a porous medium over a stretching sheet with
chemically reactive species, Chemical Engineering & Processing
Volume: 46, Issue: 8, August, 2007, pp. 721-728.
[10] Rafael Cortell Bataller, Viscoelastic fluid flow and heat transfer over a
stretching sheet under the effects of a non-uniform heat source, viscous
dissipation and thermal radiation International Journal of Heat and Mass
Transfer, Volume 50, Issues 15-16, July 2007, Pages 3152-3162.
[11] Seddeek, M.A., 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 Volume: 38, Issue:
4, February, 2007, pp. 781-787.
[12] Kai-Long Hsiao, Heat and Mass Transfer for Electrical Conducting
Mixed Convection with Radiation Effect for Viscoelastic Fluid past a
Stretching Sheet, Journal of Mechanics, Vol.24, No.2, June 2008,
(pp.N21-N27).
[13] Kai-Long Hsiao, MHD Mixed Convection of Viscoelastic Fluid over a
Stretching Sheet with Ohmic Dissipation, Journal of Mechanics, Vol.24,
No.3, September 2008, (pp.N29-N34).
[14] E. M. Sparrow and M. K. Chyu, Conjugate forced convection-conduction
analysis of heat transfer in a plate fin, ASME J. Heat Transfer, 104,
204-206 (1982).
[15] B. Sunden, The effect of Prandtl number on conjugate heat transfer from
rectangular fins, Int. Commun. Heat Mass Transfer, 12, 225-232 (1985).
[16] A. V. Luikov. V. A. Aleksashenko and A. A. Aleksashenko, Analytical
methods of solution of conjugated problems in convective heat transfer,
Int. J. Heat Mass Transfer 14, 1047--1056 (1971).
[17] A. V. Luikov, Conjugate convective heat transfer problems, Int. J. Heat
Mass Transfer 17, 257-265 (I974).
[18] 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, Volume 348, Issues 3-6, 2 January 2006, Pages
172-179.
[19] Mahmoud E.M. Ouaf, Exact solution of thermal radiation on MHD flow
over a stretching porous sheet, Applied Mathematics and Computation,
Volume 170, Issue 2, 15 November 2005, Pages 1117-1125
[20] Sujit Kumar Khan, Heat transfer in a viscoelastic fluid flow over a
stretching surface with heat source/sink, suction/blowing and radiation,
International Journal of Heat and Mass Transfer, in Press, Corrected
Proof, Available online 14 October 2005.
[21] P.G. Siddheshwar and U.S. Mahabaleswar, Effects of radiation and heat
source on MHD flow of a viscoelastic liquid and heat transfer over a
stretching sheet, International Journal of Non-Linear Mechanics, Volume
40, Issue 6, July 2005, Pages 807-820.
[22] Kai-Long Hsiao and Guan-Bang Chen, Conjugate Heat Transfer of Mixed
Convection for Viscoelastic Fluid Past A Stretching Sheet, Mathematical
Problems in Engineering, Volume 2007, Article ID 17058, 21 pages
doi:10.1155/2007/17058.
[23] Kai-Long Hsiao, Conjugate Heat Transfer of Magnetic Mixed Convection
with Radiative and Viscous Dissipation Effects for Second Grade
Viscoelastic Fluid past a Stretching Sheet, Applied Thermal Engineering,
27/11-12 pp. 1895-1903 (2007).
[24] R. S. Rivlin and J. L. Ericksen, Stress deformation relation for isotropic
materials, J. Rat. Mech. Analysis, 323-425, (1955).
[25] T. Cebeci and P. Bradshaw, Physical and Computational Aspects of
Convective Heat Transfer, Springer-Verlag, (1984).
[26] Kai-Long Hsiao, Heat and Mass Transfer for Electrical Conducting
Mixed Convection with Radiation Effect for Viscoelastic Fluid past a
Stretching Sheet, Journal of Mechanics, Vol.24, No.2, June 2008,
(pp.N21-N27).
[27] Kai-Long Hsiao, MHD Mixed Convection of Viscoelastic Fluid over a
Stretching Sheet with Ohmic Dissipation, Journal of Mechanics, Vol.24,
No.3, September 2008, (pp.N29-N34).
[28] Kai-Long Hsiao and C.H. Hsu, Conjugate heat transfer of mixed
convection for viscoelastic fluid past a horizontal flat-plate fin, Applied
Thermal Engineering, 29/1, pp 28-36, January 2009.
[29] Kai-Long Hsiao and C.H. Hsu, Conjugate heat transfer of mixed
convection for visco-elastic fluid past a triangular fin, Nonlinear Analysis
(Series B: Real World Applications), Vol.10/1, pp 130-143, February
2009.
[30] K. Vajravelu, Convection Heat Transfer at a Stretching Sheet with
Suction and Blowing, J. of Mathematical Analysis and Application, 188,
1002-1011(1994).
[31] Chapra and Canale, Numerical Methods for Engineers, McGRAW-HILL,
2ed, 1990.
@article{"International Journal of Mechanical, Industrial and Aerospace Sciences:64266", author = "Kai-Long Hsiao and BorMing Lee", title = "Conjugate Heat and Mass Transfer for MHD Mixed Convection with Viscous Dissipation and Radiation Effect for Viscoelastic Fluid past a Stretching Sheet", abstract = "In this study, an analysis has been performed for
conjugate heat and mass transfer of a steady laminar boundary-layer
mixed convection of magnetic hydrodynamic (MHD) flow with
radiation effect of second grade subject to suction past a stretching
sheet. Parameters E Nr, Gr, Gc, Ec and Sc represent the dominance of
the viscoelastic fluid heat and mass transfer effect which have
presented in governing equations, respectively. The similar
transformation and the finite-difference method have been used to
analyze the present problem. The conjugate heat and mass transfer
results show that the non-Newtonian viscoelastic fluid has a better heat
transfer effect than the Newtonian fluid. The free convection with a
larger r G or c G has a good heat transfer effect better than a smaller
r G or c G , and the radiative convection has a good heat transfer
effect better than non-radiative convection.", keywords = "Conjugate heat and mass transfer, Radiation effect,Magnetic effect, Viscoelastic fluid, Viscous dissipation, Stretchingsheet.", volume = "4", number = "2", pages = "267-8", }
