Conjugate Heat transfer over an Unsteady Stretching Sheet Mixed Convection with Magnetic Effect

A conjugate heat transfer for steady two-dimensional mixed convection with magnetic hydrodynamic (MHD) flow of an incompressible quiescent fluid over an unsteady thermal forming stretching sheet has been studied. A parameter, M, which is used to represent the dominance of the magnetic effect has been presented in governing equations. The similar transformation and an implicit finite-difference method have been used to analyze the present problem. The numerical solutions of the flow velocity distributions, temperature profiles, the wall unknown values of f''(0) and '(θ (0) for calculating the heat transfer of the similar boundary-layer flow are carried out as functions of the unsteadiness parameter (S), the Prandtl number (Pr), the space-dependent parameter (A) and temperature-dependent parameter (B) for heat source/sink and the magnetic parameter (M). The effects of these parameters have also discussed. At the results, it will produce greater heat transfer effect with a larger Pr and M, S, A, B will reduce heat transfer effects. At last, conjugate heat transfer for the free convection with a larger G has a good heat transfer effect better than a smaller G=0.

Authors:



References:
[1] B.C. Sakiadis, Boundary layer behavior on continuous solid surfaces:
boundary layer on a continuous flat surface, American Institute of
Chemical Engineers Journal, 7 (1961) 221-225.
[2] K. Vajravelu, T. Roper, Flow and heat transfer in a second grade fluid
over a stretching sheet, International Journal of Non-Linear Mechanics,
34 (6) (1999) 1031-1036.
[3] K. Vajravelu, Viscous flow over a nonlinearly stretching sheet, Applied
Mathematics and Computation 124 (3) (2001) 281-288.
[4] I.C. Liu, Flow and heat transfer of an electrically conducting fluid of
second grade over a stretching sheet subject to a transverse magnetic field,
International Journal of Heat and Mass Transfer 47 (19-20) (2004)
4427-4437.
[5] M. Sajid, T. Hayat, Influence of thermal radiation on the boundary layer
flow due to an exponentially stretching sheet, International
Communications in Heat and Mass Transfer 35 (3) (2008) 347-356.
[6] E.M. Abo-Eldahab, M.A.E. Aziz, Blowing/suction effect on
hydromagnetic heat transfer by mixed convection from an inclined
continuously stretching surface with internal heat generation/absorption,
International Journal of Thermal Sciences, 43 (7) (2004) 709-719.
[7] M.S. Abel, P.G. Siddheshwar, M.M. Nandeppanavar, Heat transfer in a
viscoelastic boundary layer flow over a stretching sheet with viscous
dissipation and non-uniform heat source, International Journal of Heat
and Mass Transfer, 50 (5-6), (2007) 960-966.
[8] R.C. 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 50
(15-16) (2007) 3152-3162.
[9] S. Mukhopadhyay, G.C. Layek, Sk.A. Samad, Study of MHD boundary
layer flow over a heated stretching sheet with variable viscosity,
International Journal of Heat and Mass Transfer 48 (21-22) (2005)
4460-4466.
[10] A. Pantokratoras, Study of MHD boundary layer flow over a heated
stretching sheet with variable viscosity: a numerical reinvestigation,
International Journal of Heat and Mass Transfer, 51 (1-2) (2008)
104-110.
[11] S. Mukhopadhyay, G.C. Layek, Effects of thermal radiation and variable
fluid viscosity on free convective flowand heat transfer past a porous
stretching surface, International Journal of Heat and Mass Transfer, 51
(9-10) (2008) 2167-2178.
[12] K. R. Rajagopal, A. S. Gupta and T. Y. Na(1983), A note on the
falkner-skan flows of a non-newtonian fluid International Journal of
Non-Linear Mechanics, Volume 18, Issue 4, Pages 313-320.
[13] K. R. Rajagopal(1982), A note on unsteady unidirectional flows of a
non-Newtonian fluid International Journal of Non-Linear Mechanics,
Volume 17, Issues 5-6, Pages 369-373.
[14] H.I. Andersson, J.B. Aarseth, B.S. Dandapat, Heat transfer in a fluid film
on an unsteady stretching surface, International Journal of Heat and Mass
Transfer, 43 (1) (2000) 69-74.
[15] B.S. Dandapat, B. Santra, H.I. Andersson, Thermocapillarity in a liquid
film on an unsteady stretching surface, International Journal of Heat and
Mass Transfer, 46 (16) (2003) 3009-3015.
[16] M.E. Ali, E. Magyari, Unsteady fluid and heat flow induced by a
submerged stretching surface while its steady motion is slowed down
gradually, International Journal of Heat and Mass Transfer, 50 (1-2)
(2007) 188-195.
[17] B.S. Dandapat, B. Santra, K. Vajravelu, The effects of variable fluid
properties and thermocapillarity on the flow of a thin film on an unsteady
stretching sheet, International Journal of Heat and Mass Transfer, 50
(5-6) (2007) 991-996.
[18] M. Sajid, I. Ahmad, T. Hayat, M. Ayub, Series solution for unsteady
axisymmetric flow and heat transfer over a radially stretching sheet,
Communications in Nonlinear Science and Numerical Simulation,
Volume 13, Issue 10, December 2008, Pages 2193-2202.
[19] Ahmer Mehmood, Asif Ali, Tariq Shah, Heat transfer analysis of unsteady
boundary layer flow by homotopy analysis method, Communications in
Nonlinear Science and Numerical Simulation, Volume 13, Issue 5, July
2008, Pages 902-912.
[20] I.-Chung Liu, Helge I. Andersson, Heat transfer in a liquid film on an
unsteady stretching sheet, International Journal of Thermal Sciences,
Volume 47, Issue 6, June 2008, Pages 766-772.
[21] M. Sajid, I. Ahmad, T. Hayat, M. Ayub, Unsteady flow and heat transfer
of a second grade fluid over a stretching sheet, Communications in
Nonlinear Science and Numerical Simulation, Volume 14, Issue 1,
January 2009, Pages 96-108.
[22] Z. Abbas, Y. Wang, T. Hayat, M. Oberlack, Hydromagnetic flow in a
viscoelastic fluid due to the oscillatory stretching surface, International
Journal of Non-Linear Mechanics, Volume 43, Issue 8, October 2008,
Pages 783-793
[23] I. Ahmad, M. Sajid, T. Hayat, M. Ayub, Unsteady axisymmetric flow of a
second-grade fluid over a radially stretching sheet, Computers &
Mathematics with Applications, Volume 56, Issue 5, September 2008,
Pages 1351-1357.
[24] T. Hayat, S. Saif, Z. Abbas, The influence of heat transfer in an MHD
second grade fluid film over an unsteady stretching sheet, Physics Letters
A, Volume 372, Issue 30, 21 July 2008, Pages 5037-5045.
[25] R. Tsai, K.H. Huang, J.S. Huang, Flow and heat transfer over an unsteady
stretching surface with non-uniform heat source, International
Communications in Heat and Mass Transfer, In Press, Uncorrected Proof,
Available online 3 August 2008.
[26] T. Cebeci and P. Bradshaw, Physical and Computational Aspects of
Convective Heat Transfer, Springer-Verlag, (1984).
[27] K. Vajravelu, Convection heat transfer at a stretching sheet with suction
and blowing, J. of Mathematical Analysis and Application, 188,
1002-1011(1994).
[28] Vajravelu. K, Viscous flow over a nonlinearly stretching sheet, Applied
Mathematics and Computation, Volume: 124, Issue: 3, December 15,
2001, pp. 281-288.
[29] Vajravelu. K, Rollins. D., Hydromagnetic flow of a second grade fluid
over a stretching sheet, Applied Mathematics and Computation, Volume:
148, Issue: 3, January 30, 2004, pp.783-791.
[30] Chapra and Canale, Numerical Methods for Engineers, McGRAW-HILL,
2ed, 1990.
[31] 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.
[32] 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).
[33] 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).
[34] 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).
[35] 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.
[36] 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.