Dufour and Soret Effects on Melting from a Vertical Plate Embedded in Saturated Porous Media

Thermal-diffusion and diffusion-thermo effects on combined heat and mass transfer in mixed convection boundary layer flow with aiding and opposing external flows from a vertical plate embedded in a liquid saturated porous medium with melting are investigated. The resulting system of nonlinear ordinary differential equations is solved numerically using Runge Kutta-Fehlberg with shooting techniques. Numerical results are obtained for the velocity, temperature, and concentration distributions, as well as the Nusselt number and Sherwood number for several values of the parameters, namely, the buoyancy parameter, melting parameter, Dufour effect, Soret effect, and Lewis number. The obtained results are presented graphically and in tabular form and the physical aspects of the problem are discussed.

[1]  Yogesh Jaluria,et al.  Natural Convection: Heat and Mass Transfer , 1980 .

[2]  W. Cheng,et al.  Transient mixed convective heat transfer with melting effect from the vertical plate in a liquid saturated porous medium , 2006 .

[3]  A. Y. Bakier Aiding and Opposing Mixed Convection Flow in Melting From a Vertical Flat Plate Embedded in a Porous Medium , 1997 .

[4]  Y. Zhai,et al.  Soret and Dufour effects in strongly endothermic chemical reaction system of porous media , 2006 .

[5]  A. Rashad,et al.  Group method analysis of melting effect on MHD mixed convection flow from radiate vertical plate embedded in a saturated porous media , 2009 .

[6]  H. Schlichting Boundary Layer Theory , 1955 .

[7]  A. Postelnicu,et al.  Influence of a magnetic field on heat and mass transfer by natural convection from vertical surfaces in porous media considering Soret and Dufour effects , 2004 .

[8]  Ian Proudman,et al.  Boundary Layer Theory (fourth edition). By H. SCHLICHTINO. New York: McGraw-Hill, 1960. 647 pp. £6. 8s. , 1962, Journal of Fluid Mechanics.

[9]  I. A. Hassanien,et al.  Mixed Convection Effect on Melting from a Vertical Plate in a Porous Medium , 1999 .

[10]  J. Bear Dynamics of Fluids in Porous Media , 1975 .

[11]  J. C. Jaeger,et al.  Conduction of Heat in Solids , 1952 .

[12]  V. Ambethkar NUMERICAL SOLUTIONS OF HEAT AND MASS TRANSFER EFFECTS OF AN UNSTEADY MHD FREE CONVECTIVE FLOW PAST AN INFINITE VERTICAL PLATE WITH CONSTANT SUCTION AND HEAT SOURCE OR SINK , 2009 .

[13]  M. B. K. Moorthy,et al.  Soret and Dufour Effects on Natural Convection Flow Past a Vertical Surface in a Porous Medium with Variable Viscosity , 2012, J. Appl. Math..

[14]  P. S. Gupta,et al.  Heat and mass transfer on a stretching sheet with suction or blowing , 1977 .

[15]  Marcelo F. Alfradique,et al.  Boundary layer flows with Dufour and Soret effects: I: Forced and natural convection , 2006 .

[16]  Shariful Alam,et al.  Dufour and Soret Effects on Steadv MHD Combined Free-Forced Convective and Mass Transfer Flow Past a Semi-Infinite Vertical Plate , 2006 .

[17]  E. Osalusi,et al.  Thermal-diffusion and diffusion-thermo effects on combined heat and mass transfer of a steady MHD convective and slip flow due to a rotating disk with viscous dissipation and Ohmic heating☆ , 2008 .

[18]  L. Roberts On the melting of a semi-infinite body of ice placed in a hot stream of air , 1958, Journal of Fluid Mechanics.

[19]  W. Cheng,et al.  Unsteady mass transfer in mixed convective heat flow from a vertical plate embedded in a liquid-saturated porous medium with melting effect , 2008 .

[20]  M. S. Malashetty,et al.  An analytical study of linear and non-linear double diffusive convection with Soret and Dufour effects in couple stress fluid , 2007 .

[21]  M. M. Rahman,et al.  MHD Free Convective Heat and Mass Transfer Flow Past an Inclined Surface with Heat Generation , 2006 .

[22]  Stanford Shateyi,et al.  Thermal Radiation and Buoyancy Effects on Heat and Mass Transfer over a Semi-Infinite Stretching Surface with Suction and Blowing , 2008, J. Appl. Math..

[23]  E. Williams,et al.  Thermal-diffusion and diffusion-thermo effects on mixed free-forced convective and mass transfer boundary layer flow with temperature dependent viscosity , 1995 .

[24]  I. Pop,et al.  Heat and mass transfer for Soret and Dufour’s effect on mixed convection boundary layer flow over a stretching vertical surface in a porous medium filled with a viscoelastic fluid , 2010 .

[25]  Bourhan Tashtoush,et al.  Magnetic and buoyancy effects on melting from a vertical plate embedded in saturated porous media , 2005 .

[26]  G. Walker Climate Change 2007: A world melting from the top down , 2007, Nature.

[27]  S. M. Uppal,et al.  Magnetohydrodynamic free convection heat and mass transfer of a heat generating fluid past an impulsively started infinite vertical porous plate with Hall current and radiation absorption , 2001 .

[28]  S. Motsa On the onset of convection in a porous layer in the presence of Dufour and Soret effects , 2008 .

[29]  Adrian Bejan,et al.  The problem of time-dependent natural convection melting with conduction in the solid , 1989 .

[30]  M. M. Rahman,et al.  Dufour and Soret Effects on Mixed Convection Flow Past a Vertical Porous Flat Plate with Variable Suction , 2006 .

[31]  Wen-Jeng Chang,et al.  Natural convection for the melting of ice in porous media in a rectangular enclosure , 1996 .

[32]  W. Cheng,et al.  Melting effect on mixed convective heat transfer with aiding and opposing external flows from the vertical plate in a liquid-saturated porous medium , 2007 .