Abstract
This article considers the problem of mixed convection stagnation-point flow towards a vertical plate embedded in a porous medium with prescribed surface heat flux. It is assumed that the free stream velocity and the surface heat flux vary linearly from the stagnation point. Using a similarity transformation, the governing system of partial differential equations is transformed into a system of ordinary differential equations, before being solved numerically by a finite-difference method. The features of the flow and the heat transfer characteristics are analyzed and discussed. It is found that dual solutions exist for both buoyancy assisting and opposing flows.
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References
Bejan A., Kraus A.D.: Heat Transfer Handbook. Wiley, New York (2003)
Bejan A., Dincer I., Lorente S., Miguel A.F., Reis A.H.: Porous and Complex Flow Structures in Modern Technologies. Springer, New York (2004)
Brinkmann H.C.: On the permeability of media consisting of closely packed porous particles. Appl. Sci. Res. 1, 81–86 (1947)
Brouwers H.J.H.: Heat transfer between fluid-saturated porous medium and a permeable wall with fluid injection or withdrawal. Int. J. Heat Mass Transf. 37, 989–996 (1994)
Cebeci T., Bradshaw P.: Physical and Computational Aspects of Convective Heat Transfer. Springer, New York (1988)
Du Z.-G., Bilgen E.: Natural convection in vertical cavities with internal heat generating porous medium. Wärme- und Stoffübertr. 27, 149–155 (1992)
Gebhart B., Jaluria Y., Mahajan R.L., Sammakia B.: Buoyancy-Induced Flows and Transport. Hemisphere, New York (1988)
Harris S.D., Ingham D.B., Pop I.: Mixed convection boundary-layer flow near the stagnation point on a vertical surface in a porous medium: Brinkman model with slip. Transp. Porous Media 77, 267–285 (2009)
Hong J.T., Tien C.L., Kaviany M.: Non-Darcy effects on vertical-plate natural convection in porous media with high porosities. Int. J. Heat Mass Transf. 28, 2149–2157 (1985)
Hong J.T., Yamada Y., Tien C.L.: Effects of non-Darcian and nonuniform porosity on vertical-plate natural convection in porous media. ASME J. Heat Transf. 109, 356–362 (1987)
Ingham, D.B., Pop, I. (eds): Transport Phenomenon in Porous Media III. Pergamon, Oxford (2005)
Ishak A., Nazar R., Pop I.: Dual solutions in mixed convection flow near a stagnation point on a vertical surface in a porous medium. Int. J. Heat Mass Transf. 51, 1150–1155 (2008a)
Ishak A., Nazar R., Pop I.: Post-stagnation-point boundary layer flow and mixed convection heat transfer over a vertical, linearly stretching sheet. Arch. Mech. 60, 303–322 (2008b)
Kaviany M.: Boundary-layer treatment of forced convection heat transfer from a semi-infinite flat plate embedded in porous media. ASME J. Heat Transf 109, 345–349 (1987)
Lauriat G., Prasad V.: Natural convection in a vertical porous cavity: a numerical study for Brinkman-extended Darcy formulation. ASME J. Heat Transf. 109, 688–696 (1987)
Magyari E., Pop I., Keller B.: Exact dual solutions occurring in the Darcy mixed convection flow. Int. J. Heat Mass Transf. 44, 4563–4566 (2001)
Merkin J.H.: On dual solutions occurring in mixed convection in a porous medium. J. Eng. Math. 20, 171–179 (1985)
Merkin J.H., Mahmood T.: Mixed convection boundary layer similarity solutions: prescribed wall heat flux. J. Appl. Math. Phys. (ZAMP) 40, 51–68 (1989)
Merrill K., Beauchesne M., Previte J., Paullet J., Weidman P.: Final steady flow near a stagnation point on a vertical surface in a porous medium. Int. J. Heat Mass Transf. 49, 4681–4686 (2006)
Nakayama A.: PC-Aided Numerical Heat Transfer and Convective Flow. CRC Press, Tokyo (1995)
Nield D.A.: ASME J. Heat Transf. 129, 1459–1963 (2007)
Nield D.A., Bejan A.: Convection in Porous Media (3rd edition). Springer, New York (2006)
Paullet J., Weidman P.: Analysis of stagnation point flow towards a stretching sheet. Int. J. Non-Linear Mech. 42, 1084–1091 (2007)
Pop I., Ingham D.B.: Convective Heat Transfer: Mathematical and Computational Modelling of Viscous Fluids and Porous Media. Pergamon, Oxford (2001)
Postelnicu A., Pop I.: Falkner-Skan boundary layer flow of a power-law fluid past a stretching wedge. Appl. Math. Comput. 217, 4359–4368 (2011)
Raptis A.: Flow through a porous medium bounded by a semi-infinite surface. Mech. Res. Commun. 11, 277–279 (1984)
Raptis A., Perdikis C.: Unsteady flow through a porous medium in the presence of free convection. Int. Commun. Heat Mass Transf. 12, 697–704 (1985)
Raptis A., Takhar H.S.: Flow through a porous medium. Mech. Res. Commun. 14, 327–329 (1987)
Ridha A.: Aiding flows non-unique similarity solutions of mixed convection boundary-layer equations. J. Appl. Math. Phys. 47, 341–352 (1996)
Sathiyamoorthy M., Basak T., Roy S., Pop I.: Steady natural convection flow in a square cavity filled with a porous medium for linearly heated side wall (s). Int. J. Heat Mass Transf. 50, 1892–1901 (2007)
Schlichting H., Gersten K.: Boundary-Layer Theory. Springer, Berlin (2000)
Vadasz, P. (eds): Emerging Topics in Heat and Mass Transfer in Porous Media. Springer, New York (2008)
Vafai, K. (eds): Handbook of Porous Media (2nd edition). Taylor & Francis, New York (2005)
Vafai K.: Porous Media: Applications in Biological Systems and Biotechnology. CRC Press, Boca Raton, FL (2010)
Vafai K., Tien C.L.: Boundary and inertia effects on flow and heat transfer in porous media. Int. J. Heat Mass Transf. 24, 195–203 (1981)
Weidman P.D., Kubitschek D.G., Davis A.M.J.: The effect of transpiration on self-similar boundary layer flow over moving surface. Int. J. Eng. Sci. 44, 730–737 (2006)
Yamamoto K., Iwamura N.: Flow with convective acceleration through a porous medium. J. Eng. Math. 10, 41–54 (1976)
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Rosali, H., Ishak, A. & Pop, I. Mixed Convection Stagnation-Point Flow Over a Vertical Plate with Prescribed Heat Flux Embedded in a Porous Medium: Brinkman-Extended Darcy Formulation. Transp Porous Med 90, 709–719 (2011). https://doi.org/10.1007/s11242-011-9809-7
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DOI: https://doi.org/10.1007/s11242-011-9809-7