Commenced in January 2007
Paper Count: 30172
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.
Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1332450Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1549
 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.
 J.H. Merkin, Free convection boundary layer on cylinders of elliptic cross-section, ASME, Journal of Heat Transfer, 99 (1977) 453-457.
 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.
 S. Bhattacharyya, I. Pop, Free convection from cylinders of elliptic cross section in micropolar fluids, International Journal of Engineering Science 34 (1996) 1301-1310.
 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.
 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.
 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.
 W. Jitchote, AM. Robertson. Flow of second order fluids in curved pipes. J Non-Newtonian Fluid Mech 2000;90(1):91-116.
 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.
 L.A. Da├évalos-Orozco and E. Va├ézquez Luis, Natural convection of a viscoelastic fluid with deformable free surface, J. Non-Newtonian Fluid Mech. 85 (1999) 257-271.
 HK. Rasmussen, O. Hassager Simulation of transient viscoelastic flow with second order time integration. J Non-Newtonian Fluid Mech 1995;56(1):65-84.
 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.
 ] 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-.
 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.
 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.
 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
 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).
 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
 T. Cebeci, P. Bradshaw, Physical and Computational Aspects of Convective heat Transfer, Springer, New York 1984.
 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.
 M. Kumari, H.S. Takhar, G. Nath, Nonsimilar mixed convection flow
 of a non-Newtonian fluid past a vertical wedge, Acta Mechanica 113
 (1995) 205 - 213.
 M. M. Molla et al. Natural Convection Flow from a Horizontal
 Circular Cylinder with Uniform Heat Flux in the Presence of Heat
 Generation, Applied Mathematics Modelling 33 (2009) 3226-3236
 M. Katagiri et al. transient free convection from an isothermal horizontal circular cylinder, Warme-und Stoffubertragung 12 (1979) 73-8