Free Convection Boundary Layer Flow of a Viscoelastic Fluid in the Presence of Heat Generation
The present paper considers the steady free
convection boundary layer flow of a viscoelastics fluid with constant
temperature in the presence of heat generation. The boundary layer
equations are an order higher than those for the Newtonian (viscous)
fluid and the adherence boundary conditions are insufficient to
determine the solution of these equations completely. The governing
boundary layer equations are first transformed into non-dimensional
form by using special dimensionless group. Computations are
performed numerically by using Keller-box method by augmenting
an extra boundary condition at infinity and the results are displayed
graphically to illustrate the influence of viscoelastic K, heat
generation γ , and Prandtl Number, Pr parameters on the velocity
and temperature profiles. The results of the surface shear stress in
terms of the local skin friction and the surface rate of heat transfer in
terms of the local Nusselt number for a selection of the heat
generation parameterγ (=0.0, 0.2, 0.5, 0.8, 1.0) are obtained and
presented in both tabular and graphical formats. Without effect of the
internal heat generation inside the fluid domain for which we take
γ = 0.0, the present numerical results show an excellent agreement
with previous publication.
[1] D.A. Saville, S.W. Churchill, Laminar free convection in boundary
layers near horizontal cylinders and vertical axisymmetric bodies,
Journal of Fluid Mechanics 29 (1967) 391-399.
[2] J.H. Merkin, Free convection boundary layer on cylinders of elliptic
cross-section, ASME, Journal of Heat Transfer, 99 (1977) 453-457.
[3] F.S. Lien, T.M. Chen, C.K. Chen, Analysis of a free- convection
micropolar boundary layer about a horizontal permeable cylinder at a
non-uniform thermal condition, ASME Journal of Heat Transfer 112
(1990) 504-506.
[4] S. Bhattacharyya, I. Pop, Free convection from cylinders of elliptic
cross section in micropolar fluids, International Journal of
Engineering Science 34 (1996) 1301-1310.
[5] M.A. Mansour, M.A. El-Hakiem, S.M. El Kabeir, Heat and mass
transfer in magnetohydrodynamic flow of micropolar fluid on a
circular cylinder with uniform heat and mass flux, Journal of
Magnetism and Magnetic Materials 220 (2000) 259-270.
[6] C.Y. Cheng, Free convection heat and mass transfer from a
horizontal cylinder of elliptic cross section in micropolar fluids,
International Communications in Heat and Mass Transfer 33 (2006)
311-318.
[7] M.A.Hossain, M.A. Alim,D.A.S. Rees, Effect of thermal radiation on
natural convection over cylinders of elliptic cross section, Acta
Mechanica 129 (1998) 177-186.
[8] W. Jitchote, AM. Robertson. Flow of second order fluids in curved
pipes. J Non-Newtonian Fluid Mech 2000;90(1):91-116.
[9] PD. Ariel, I. Teipel On dual solutions of stagnation point flow of a
viscoelastic fluid. Zeitschrift f├╝r Angewandte Mathematik und
Mechanik (ZAMM) 1994;74(8):341-7.
[10] L.A. DaÂvalos-Orozco and E. VaÂzquez Luis, Natural convection of
a viscoelastic fluid with deformable free surface, J. Non-Newtonian
Fluid Mech. 85 (1999) 257-271.
[11] HK. Rasmussen, O. Hassager Simulation of transient viscoelastic
flow with second order time integration. J Non-Newtonian Fluid
Mech 1995;56(1):65-84.
[12] WP. Wood Transient viscoelastic helical flows in pipes of circular
and annular cross-section. J Non-Newtonian Fluid Mech 2001;100(1-
3):115-26.
[13] ] T. B. Chang et al. Numerical study of transient free convective
mass transfer in a Walters-B viscoelastic flow with wall suction,
Commun Nonlinear Sci Numer Simulat, ÔÇÿarticle in press-.
[14] K. Vajravelu, A. Hadjinicolaou, Heat transfer in a viscous fluid over
a stretching sheet with viscous dissipation and internal heat
generation, International Communication Heat Mass Transfer 20
(1993) 417- 430.
[15] A.J. Chamkha, Camille Issa, Effects of heat generation/absorption
and the thermophoresis on hydromagnetic flow with heat and mass
transfer over a flat plate, International Journal of Numerical
Methods for Heat & Fluid Flow 10 (4) (2000) 432-448.
[16] F. Mendez, C. Trevino, The conjugate conduction- natural
convection heat transfer along a thin vertical plate with non-uniform
internal heat generation, International Journal of Heat Mass Transfer
43 (2000) 2739-2748
[17] J.H. Merkin, Free convection boundary layer on an isothermal
horizontal circular cylinders, ASME/AIChE, Heat Transfer
Conference, St. Louis, Mo., August 9-11 (1976).
[18] M.M. Molla, M.A. Hossain, M.C. Paul, Natural convection flow
from an isothermal horizontal circular cylinder in presence of heat
generation. International Journal of Engineering Science 44 (2006)
949-958
[19] T. Cebeci, P. Bradshaw, Physical and Computational Aspects of
Convective heat Transfer, Springer, New York 1984.
[20] M. M. Molla, M. A. Hossain, R. S. R. Gorla, Natural convection flow
from an isothermal horizontal circular cylinder with temperature
dependent viscosity, Heat and Mass Transfer, 41 (2005) 594-598.
[21] M. Kumari, H.S. Takhar, G. Nath, Nonsimilar mixed convection
flow
[22] of a non-Newtonian fluid past a vertical wedge, Acta Mechanica 113
[23] (1995) 205 - 213.
[24] M. M. Molla et al. Natural Convection Flow from a Horizontal
[25] Circular Cylinder with Uniform Heat Flux in the Presence of Heat
[26] Generation, Applied Mathematics Modelling 33 (2009) 3226-3236
[27] M. Katagiri et al. transient free convection from an isothermal
horizontal circular cylinder, Warme-und Stoffubertragung 12 (1979)
73-8
[1] D.A. Saville, S.W. Churchill, Laminar free convection in boundary
layers near horizontal cylinders and vertical axisymmetric bodies,
Journal of Fluid Mechanics 29 (1967) 391-399.
[2] J.H. Merkin, Free convection boundary layer on cylinders of elliptic
cross-section, ASME, Journal of Heat Transfer, 99 (1977) 453-457.
[3] F.S. Lien, T.M. Chen, C.K. Chen, Analysis of a free- convection
micropolar boundary layer about a horizontal permeable cylinder at a
non-uniform thermal condition, ASME Journal of Heat Transfer 112
(1990) 504-506.
[4] S. Bhattacharyya, I. Pop, Free convection from cylinders of elliptic
cross section in micropolar fluids, International Journal of
Engineering Science 34 (1996) 1301-1310.
[5] M.A. Mansour, M.A. El-Hakiem, S.M. El Kabeir, Heat and mass
transfer in magnetohydrodynamic flow of micropolar fluid on a
circular cylinder with uniform heat and mass flux, Journal of
Magnetism and Magnetic Materials 220 (2000) 259-270.
[6] C.Y. Cheng, Free convection heat and mass transfer from a
horizontal cylinder of elliptic cross section in micropolar fluids,
International Communications in Heat and Mass Transfer 33 (2006)
311-318.
[7] M.A.Hossain, M.A. Alim,D.A.S. Rees, Effect of thermal radiation on
natural convection over cylinders of elliptic cross section, Acta
Mechanica 129 (1998) 177-186.
[8] W. Jitchote, AM. Robertson. Flow of second order fluids in curved
pipes. J Non-Newtonian Fluid Mech 2000;90(1):91-116.
[9] PD. Ariel, I. Teipel On dual solutions of stagnation point flow of a
viscoelastic fluid. Zeitschrift f├╝r Angewandte Mathematik und
Mechanik (ZAMM) 1994;74(8):341-7.
[10] L.A. DaÂvalos-Orozco and E. VaÂzquez Luis, Natural convection of
a viscoelastic fluid with deformable free surface, J. Non-Newtonian
Fluid Mech. 85 (1999) 257-271.
[11] HK. Rasmussen, O. Hassager Simulation of transient viscoelastic
flow with second order time integration. J Non-Newtonian Fluid
Mech 1995;56(1):65-84.
[12] WP. Wood Transient viscoelastic helical flows in pipes of circular
and annular cross-section. J Non-Newtonian Fluid Mech 2001;100(1-
3):115-26.
[13] ] T. B. Chang et al. Numerical study of transient free convective
mass transfer in a Walters-B viscoelastic flow with wall suction,
Commun Nonlinear Sci Numer Simulat, ÔÇÿarticle in press-.
[14] K. Vajravelu, A. Hadjinicolaou, Heat transfer in a viscous fluid over
a stretching sheet with viscous dissipation and internal heat
generation, International Communication Heat Mass Transfer 20
(1993) 417- 430.
[15] A.J. Chamkha, Camille Issa, Effects of heat generation/absorption
and the thermophoresis on hydromagnetic flow with heat and mass
transfer over a flat plate, International Journal of Numerical
Methods for Heat & Fluid Flow 10 (4) (2000) 432-448.
[16] F. Mendez, C. Trevino, The conjugate conduction- natural
convection heat transfer along a thin vertical plate with non-uniform
internal heat generation, International Journal of Heat Mass Transfer
43 (2000) 2739-2748
[17] J.H. Merkin, Free convection boundary layer on an isothermal
horizontal circular cylinders, ASME/AIChE, Heat Transfer
Conference, St. Louis, Mo., August 9-11 (1976).
[18] M.M. Molla, M.A. Hossain, M.C. Paul, Natural convection flow
from an isothermal horizontal circular cylinder in presence of heat
generation. International Journal of Engineering Science 44 (2006)
949-958
[19] T. Cebeci, P. Bradshaw, Physical and Computational Aspects of
Convective heat Transfer, Springer, New York 1984.
[20] M. M. Molla, M. A. Hossain, R. S. R. Gorla, Natural convection flow
from an isothermal horizontal circular cylinder with temperature
dependent viscosity, Heat and Mass Transfer, 41 (2005) 594-598.
[21] M. Kumari, H.S. Takhar, G. Nath, Nonsimilar mixed convection
flow
[22] of a non-Newtonian fluid past a vertical wedge, Acta Mechanica 113
[23] (1995) 205 - 213.
[24] M. M. Molla et al. Natural Convection Flow from a Horizontal
[25] Circular Cylinder with Uniform Heat Flux in the Presence of Heat
[26] Generation, Applied Mathematics Modelling 33 (2009) 3226-3236
[27] M. Katagiri et al. transient free convection from an isothermal
horizontal circular cylinder, Warme-und Stoffubertragung 12 (1979)
73-8
@article{"International Journal of Engineering, Mathematical and Physical Sciences:53650", author = "Abdul Rahman Mohd Kasim and Mohd Ariff Admon and Sharidan Shafie", title = "Free Convection Boundary Layer Flow of a Viscoelastic Fluid in the Presence of Heat Generation", abstract = "The present paper considers the steady free
convection boundary layer flow of a viscoelastics fluid with constant
temperature in the presence of heat generation. The boundary layer
equations are an order higher than those for the Newtonian (viscous)
fluid and the adherence boundary conditions are insufficient to
determine the solution of these equations completely. The governing
boundary layer equations are first transformed into non-dimensional
form by using special dimensionless group. Computations are
performed numerically by using Keller-box method by augmenting
an extra boundary condition at infinity and the results are displayed
graphically to illustrate the influence of viscoelastic K, heat
generation γ , and Prandtl Number, Pr parameters on the velocity
and temperature profiles. The results of the surface shear stress in
terms of the local skin friction and the surface rate of heat transfer in
terms of the local Nusselt number for a selection of the heat
generation parameterγ (=0.0, 0.2, 0.5, 0.8, 1.0) are obtained and
presented in both tabular and graphical formats. Without effect of the
internal heat generation inside the fluid domain for which we take
γ = 0.0, the present numerical results show an excellent agreement
with previous publication.", keywords = "Free Convection, Boundary Layer, CircularCylinder, Viscoelastic Fluid, Heat Generation", volume = "5", number = "3", pages = "325-8", }
