Mixed Convection with Radiation Effect over a Nonlinearly Stretching Sheet
In this study, an analysis has been performed for
free convection with radiation effect over a thermal forming
nonlinearly stretching sheet. Parameters n, k0, Pr, G represent
the dominance of the nonlinearly effect, radiation effect, heat
transfer and free convection effects which have been presented
in governing equations, respectively. The similarity
transformation and the finite-difference methods have been
used to analyze the present problem. From the results, we find
that the effects of parameters n, k0, Pr, Ec and G to the
nonlinearly stretching sheet. The increase of Prandtl number Pr,
free convection parameter G or radiation parameter k0 resulting
in the increase of heat transfer effects, but increase of the
viscous dissipation number Ec will decrease of heat transfer
effect.
[1] B.C. Sakiadis, Boundary-layer behaviour on continuous solid surfaces,
AIChE J. 7 (1961), pp. 26-28.
[2] K. Sadeghy, A.H. Najafi and M. Saffaripour, Sakiadis flow of an
upper-convected Maxwell fluid, Int. J. Non-Linear Mech. 40 (2005), pp.
1220-1228.
[3] P.D. Ariel, T. Hayat and S. Asghar, The flow of an elasto-viscous fluid
past a stretching sheet with partial slip, Acta Mech. 187 (2006), pp.
29-35.
[4] S.J. Liao, An analytic solution of unsteady boundary-layer flows caused
by an impulsively stretching plate, Commun. Non-linear Sci. Numer.
Simul. 11 (2006), pp. 326-339.
[5] H. Xu, An explicit analytic solution for convective heat transfer in an
electrically conducting fluid at a stretching surface with uniform free
stream, Int. J. Eng. Sci. 43 (2005), pp. 859-874.
[6] R. Cortell, Effects of viscous dissipation and work done by deformation
on the MHD flow and heat transfer of a viscoelastic fluid over a stretching
sheet, Phys. Lett. A 357 (2006), pp. 298-305.
[7] R. Cortell, Flow and heat transfer of a fluid through a porous medium over
a stretching surface with internal heat generation/absorption and
suction/blowing, Fluid Dyn. Res. 37 (2005), pp. 231-245.
[8] R. Cortell, Effects of viscous dissipation and radiation on the thermal
boundary layer over a nonlinearly stretching sheet, Physics Letters A,
Volume 372, Issue 5, 28 January 2008, Pages 631-636.
[9] S. Awang Kechil and I. Hashim, Series solution of flow over nonlinearly
stretching sheet with chemical reaction and magnetic field, Physics
Letters A, In Press, 2007.
[10] R. Cortell Bataller, Similarity solutions for flow and heat transfer of a
quiescent fluid over a nonlinearly stretching surface, Journal of Materials
Processing Technology, In Press, 2007.
[11] R. Cortell, Viscous flow and heat transfer over a nonlinearly stretching
sheet, Applied Mathematics and Computation, Volume 184, Issue 2, 15
January 2007, Pages 864-873.
[12] K. Vajravelu, Viscous flow over a nonlinearly stretching sheet Applied
Mathematics and Computation, Volume 124, Issue 3, 15 December 2001,
Pages 281-288.
[13] Z. Abbas, T. Hayata, Radiation effects on MHD flow in a porous space,
International Journal of Heat and Mass Transfer, Volume 51, Issues 5-6,
March 2008, Pages 1024-1033.
[14] M.Q. Brewster, Thermal Radiative Transfer Properties, Wiley, New
York,1972.
[15] K.-L. Hsiao and G.-B. 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.
[16] K.-L. 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).
[17] 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).
[18] 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).
[19] K. Vajravelu, Convection Heat Transfer at a Stretching Sheet with
Suction and Blowing, J. of Mathematical Analysis and Application, 188,
1002-1011(1994).
[20] 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.
[21] 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.
[22] Chapra and Canale, Numerical Methods for Engineers, McGRAW-HILL,
2ed, 1990.
[1] B.C. Sakiadis, Boundary-layer behaviour on continuous solid surfaces,
AIChE J. 7 (1961), pp. 26-28.
[2] K. Sadeghy, A.H. Najafi and M. Saffaripour, Sakiadis flow of an
upper-convected Maxwell fluid, Int. J. Non-Linear Mech. 40 (2005), pp.
1220-1228.
[3] P.D. Ariel, T. Hayat and S. Asghar, The flow of an elasto-viscous fluid
past a stretching sheet with partial slip, Acta Mech. 187 (2006), pp.
29-35.
[4] S.J. Liao, An analytic solution of unsteady boundary-layer flows caused
by an impulsively stretching plate, Commun. Non-linear Sci. Numer.
Simul. 11 (2006), pp. 326-339.
[5] H. Xu, An explicit analytic solution for convective heat transfer in an
electrically conducting fluid at a stretching surface with uniform free
stream, Int. J. Eng. Sci. 43 (2005), pp. 859-874.
[6] R. Cortell, Effects of viscous dissipation and work done by deformation
on the MHD flow and heat transfer of a viscoelastic fluid over a stretching
sheet, Phys. Lett. A 357 (2006), pp. 298-305.
[7] R. Cortell, Flow and heat transfer of a fluid through a porous medium over
a stretching surface with internal heat generation/absorption and
suction/blowing, Fluid Dyn. Res. 37 (2005), pp. 231-245.
[8] R. Cortell, Effects of viscous dissipation and radiation on the thermal
boundary layer over a nonlinearly stretching sheet, Physics Letters A,
Volume 372, Issue 5, 28 January 2008, Pages 631-636.
[9] S. Awang Kechil and I. Hashim, Series solution of flow over nonlinearly
stretching sheet with chemical reaction and magnetic field, Physics
Letters A, In Press, 2007.
[10] R. Cortell Bataller, Similarity solutions for flow and heat transfer of a
quiescent fluid over a nonlinearly stretching surface, Journal of Materials
Processing Technology, In Press, 2007.
[11] R. Cortell, Viscous flow and heat transfer over a nonlinearly stretching
sheet, Applied Mathematics and Computation, Volume 184, Issue 2, 15
January 2007, Pages 864-873.
[12] K. Vajravelu, Viscous flow over a nonlinearly stretching sheet Applied
Mathematics and Computation, Volume 124, Issue 3, 15 December 2001,
Pages 281-288.
[13] Z. Abbas, T. Hayata, Radiation effects on MHD flow in a porous space,
International Journal of Heat and Mass Transfer, Volume 51, Issues 5-6,
March 2008, Pages 1024-1033.
[14] M.Q. Brewster, Thermal Radiative Transfer Properties, Wiley, New
York,1972.
[15] K.-L. Hsiao and G.-B. 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.
[16] K.-L. 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).
[17] 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).
[18] 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).
[19] K. Vajravelu, Convection Heat Transfer at a Stretching Sheet with
Suction and Blowing, J. of Mathematical Analysis and Application, 188,
1002-1011(1994).
[20] 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.
[21] 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.
[22] Chapra and Canale, Numerical Methods for Engineers, McGRAW-HILL,
2ed, 1990.
@article{"International Journal of Mechanical, Industrial and Aerospace Sciences:60886", author = "Kai-Long Hsiao", title = "Mixed Convection with Radiation Effect over a Nonlinearly Stretching Sheet", abstract = "In this study, an analysis has been performed for
free convection with radiation effect over a thermal forming
nonlinearly stretching sheet. Parameters n, k0, Pr, G represent
the dominance of the nonlinearly effect, radiation effect, heat
transfer and free convection effects which have been presented
in governing equations, respectively. The similarity
transformation and the finite-difference methods have been
used to analyze the present problem. From the results, we find
that the effects of parameters n, k0, Pr, Ec and G to the
nonlinearly stretching sheet. The increase of Prandtl number Pr,
free convection parameter G or radiation parameter k0 resulting
in the increase of heat transfer effects, but increase of the
viscous dissipation number Ec will decrease of heat transfer
effect.", keywords = "Nonlinearly stretching sheet, Free convection,Finite-difference, Radiation effect.", volume = "4", number = "2", pages = "251-5", }
