Scaling Transformation for the Effect of Temperature-Dependent Fluid Viscosity with Thermophoresis Particle Deposition on MHD-Free Convective Heat and Mass Transfer Over a Porous Stretching Surface

Transport in Porous Media

Volumn 84, Issue 2, 2010, Pages 549-568

  Kandasamy, R ^a   Muhaimin, I ^a  

^a UNIVERSITI TUN HUSSEIN ONN MALAYSIA   (Malaysia)

Author keywords

Lie group analysis; Magnetic field; Temperature dependent fluid viscosity; Thermophoresis particle deposition

Indexed keywords

CONCENTRATION BOUNDARY LAYER; CONVECTIVE HEAT; DIFFUSION EQUATIONS; EFFECT OF TEMPERATURE; FLUID VELOCITIES; FLUID VISCOSITY; GOVERNING EQUATIONS; INCOMPRESSIBLE FLUID; LIE GROUP ANALYSIS; LINEAR FUNCTIONS; MOMENTUM EQUATION; PARTICLE DEPOSITIONS; SCALING GROUP; SCALING TRANSFORMATION; SECOND-ORDER ORDINARY DIFFERENTIAL EQUATIONS; STRETCHING SHEET; STRETCHING SURFACE; TEMPERATURE INCREASE; TEMPERATURE-DEPENDENT FLUID VISCOSITY; THIRD-ORDER ORDINARY DIFFERENTIAL EQUATIONS; TRANSVERSE MAGNETIC FIELD; TWO-DIMENSIONAL FLOW;

BOUNDARY CONDITIONS; DYNAMICAL SYSTEMS; FLUIDS; INCOMPRESSIBLE FLOW; MAGNETIC FIELDS; MASS TRANSFER; THERMOPHORESIS; VISCOSITY;

ORDINARY DIFFERENTIAL EQUATIONS;

BOUNDARY CONDITION; INCOMPRESSIBLE FLOW; MAGNETIC FIELD; MASS TRANSFER; POROUS MEDIUM; STEADY FLOW; TEMPERATURE GRADIENT; TWO-DIMENSIONAL FLOW;

EID: 77955849884     PISSN: 01693913     EISSN: None     Source Type: Journal    
DOI: 10.1007/s11242-009-9519-6     Document Type: Article

References (45)

1. Afify A. A.: MHD free convective flow and mass transfer over a stretching sheet with chemical reaction. Heat Mass Transf. 40, 495-500 (2004).
2. Asghar S., Hayat T., Kara A. H.: Exact solutions of thin film flows. Nonlinear Dyn. 50, 229-233 (2007).
3. Avramenko A. A., Kobzar S. G., Shevchuk I. V., Kuznetsov A. V., Iwanisov L. T.: Symmetry of turbulent boundary layer flows: investigation of different Eddy viscosity models. Acta Mech. 151, 1-14 (2001).
4. Batchelor G. K.: An Introduction to Fluid Dynamics. Cambridge University Press, London (1987).
5. Bluman G. W., Kumei S.: Symmetries and Differential Equations. Springer, New York (1989).
6. Chakrabarti A., Gupta A. S.: Hydromagnetic flow heat and mass transfer over a stretching sheet. Q. Appl. Math. 33, 73-78 (1979).
7. Chamka A., Pop I.: Effect of thermophoresis particle deposition in free convection boundary layer from a vertical flat plate embedded in a porous medium. Int. Commun. Heat Mass Transf. 31, 421-430 (2004).
8. Chamka A., Jaradat M., Pop I.: Thermophoresis free convection from a vertical cylinder embedded in a porous medium. Int. J. Appl. Mech. Eng. 9, 471-481 (2004).
9. Chen C.-L., Chan K.-C.: Combined effects of thermophoresis and electrophoresis on particle deposition onto a wavy surface disk. Int. J. Heat Mass Transf. 51, 2657-2664 (2008).
10. EL-Hakiem M. A.: Radiation effects on hydromagnetic free convective and mass transfer flow of a gas past a circular cylinder with uniform heat and mass flux. Int. J. Numer. Methods Heat Fluid Flow 19, 445-458 (2009).
11. EL-Hakiem M. A., Rashad A. M.: The effect of radiation on non-Darcy free convection from a vertical cylinder embedded in a fluid-saturated porous medium with a temperature dependent viscosity. J. Porous Media 10, 209-218 (2007).
12. EL-Kabeir S. M. M., EL-Hakiem M. A., Rashad A. M.: Lie group analysis of unsteady MHD three dimensional by natural convection from an inclined stretching surface saturated porous medium. J. Comput. Appl. Math. 213, 582-603 (2008).
13. Epstein M., Hauser G. M., Henry R. E.: Thermophoretic deposition of particles in natural convection flow from vertical plate. ASME J. Heat Transf. 107, 272-276 (1985).
14. Garg V. K., Jayaraj S.: Thermophoresis of aerosol particles in laminar flow over inclined plates. Int. J. Heat Mass Transf. 31, 875-890 (1988).
15. Gary J., Kassoy D. R., Tadjeran H., Zebib A.: The effects of significant viscosity variation on convective heat transport in water saturated porous medium. J. Fluid Mech. 117, 233-241 (1982).
16. Gill S.: A process for the step-by-step integration of differential equations in an automatic digital computing machine. Proc. Camb. Philos. Soc. 47, 96-108 (1951).
17. Goren S. L.: Thermophoresis of aerosol particles in laminar boundary layer on a flat plate. J. Colloid Interface Sci. 61, 77-85 (1977).
18. Hayat T., Mahomed F. M.: Note on an exact solution for the pipe flow of a third-grade fluid. Acta Mech. 190, 233-236 (2007).
19. Hayat T., Kara A. H., Momoniat E.: Exact flow of a third-grade fluid on a porous wall. Int. J. Non-Linear Mech. 38, 1533-1537 (2003).
20. Hayat T., Kara A. H., Momoniat E.: The unsteady flow of a fourth-grade fluid past a porous plate. Math. Comput. Model. 41, 1347-1353 (2005).
21. Hayat T., Ellahi R., Asghar S.: Unsteady magnetohydrodynamic non-Newtonian flow due to non-coaxial rotations of disk and a fluid at infinity. Chem. Eng. Commun. 194, 37-49 (2007).
22. Ibragimov N. H.: Elementary Lie Group Analysis and Ordinary Differential Equations. Wiley, New York (1999).
23. Ingham D., Pop I.: Transport Phenomena in Porous Media I. Pergamon, Oxford (1998).
24. Ingham D., Pop I.: Transport Phenomena in Porous Media II. Pergamon, Oxford (2002).
25. Jayaraj S., Dinesh K. K., Pillai K. L.: Thermophoresis in natural convection with variable properties. Heat Mass Transf. 34, 469-475 (1999).
26. Ling J. X., Dybbs A.: Forced Convection Over a Flat Plate Submersed in a Porous Medium: Variable Viscosity Case Paper 87-WA/HT-23. American Society of Mechanical Engineers, New York (1987).
27. Mehta K. N., Sood S.: Transient free convection flow with temperature-dependent viscosity in a fluid saturated porous medium. Int. J. Eng. Sci. 30, 1083-1087 (1992).
28. Mohyuddin M. R., Hayat T., Mahomed F. M., Asghar S., Siddiqui A. M.: On solutions of some non-linear differential equations arising in Newtonian and non-Newtonian fluids. Nonlinear Dyn. 35, 229-248 (2004).
29. Mukhopadhyay S., Layek G. C.: Effects of thermal radiation and variable fluid viscosity on free convective flow and heat transfer past a porous stretching surface. Int. J. Heat Mass Transf. 51, 2167-2178 (2008).
30. Mukhopadhyay S., Layek G. C., Samad S. A.: Study of MHD boundary layer flow over a heated stretching sheet with variable viscosity. Int. J. Heat Mass Transf. 48, 4460-4466 (2005).
31. Nield D. A., Bejan A.: Convection in Porous Media. 3rd edn. Springer, New York (2006).
32. Nield D. A., Bejan A.: The Cheng-Minkowycz problem for natural convective boundary layer flow in a porous medium saturated by a nanofluid. Int. J. Heat Mass Transf. 52, 5792-5795 (2009).
33. Nield D. A., Kuznetsov A. V.: Natural convection about a vertical plate embedded in a bidisperse porous medium. Int. J. Heat Mass Transf. 51, 1658-1664 (2008).
34. Ovsiannikov L. V.: Group Analysis of Differential Equations. Academic Press, New York (1982).
35. Rees D. A., Nield D. A., Kuznetsov A. V.: Vertical free convective boundary-layer flow in a bidisperse porous medium. ASME J. Heat Transf. 130, 1-9 (2008).
36. Sharma P. R., Mathur P.: Steady laminar free convection flow of an electrically conducting fluid along a porous hot vertical plate in the presences of heat source/sink. Indian J. Pure Appl. Math. 26, 1125-1134 (1995).
37. Sivasankaran S., Bhuvaneswari M., Kandaswamy P., Ramasami E. K.: Lie group analysis of natural convection heat and mass transfer in an inclined surface. Nonlinear Anal. Model. Control 11, 201-212 (2006a).
38. Sivasankaran S., Bhuvaneswari M., Kandaswamy P., Ramasami E. K.: Lie group analysis of natural convection heat and mass transfer in an inclined porous surface with heat generation. Int. J. Appl. Math. Mech. 2, 34-40 (2006b).
39. Soh C. W.: Invariant solutions of the unidirectional flow of an electrically charged power-law non-Newtonian fluid over a flat plate in presence of a transverse magnetic field. Commun. Nonlinear Sci. Numer. Simul. 10, 537-548 (2005).
40. Soh C. W., Phiri P. A., Pooe C. A.: Nonequivalent similarity reductions of steady 2D thermal boundary layer equations for an incompressible laminar flow over a continuous moving hot surface. Fluid Dyn. Res. 37, 430-442 (2005).
41. Vajravelu K., Hadjinicolaou A.: Convective heat transfer in an electrically conducting fluid at a stretching surface in uniform free stream. Int. J. Eng. Sci. 35, 1237-1244 (1997).
42. Wang C. C.: Combined effects of inertia and thermophoresis on particle deposition onto a wafer with wavy surface. Int. J. Heat Mass Transf. 49, 1395-1402 (2006).
43. Wang C. C., Chen C. K.: Thermophoresis deposition of particles from a boundary layer flow onto a continuously moving wavy surface. Acta Mech. 181, 139-151 (2006).
44. Yurusoy M., Pakdemirli M.: Symmetry reductions of unsteady three-dimensional boundary layers of some non-Newtonian fluids. Int. J. Eng. Sci. 35, 731-740 (1997).
45. Yurusoy M., Pakdemirli M.: Group classification of a non-Newtonian fluid model using classical approach and equivalence transformations. Int. J. Non-Linear Mech. 34, 341-346 (1999).