Thermal Stratification Effects on Hiemenz Flow of Nanofluid Over a Porous Wedge Sheet in the Presence of Suction/Injection Due to Solar Energy: Lie Group Transformation

Transport in Porous Media

Volumn 94, Issue 1, 2012, Pages 399-416

  Kandasamy, R ^a   Muhaimin, I ^a   Ram, N Siva ^b   Prabhu, K K Sivagnana ^b  

^a UNIVERSITI TUN HUSSEIN ONN MALAYSIA   (Malaysia)

^b R M K ENGINEERING COLLEGE   (India)

Author keywords

Hiemenz flow; Nanofluids; Porous wedge; Thermal stratification and solar energy

Indexed keywords

BUOYANCY FORCES; FLOW AND HEAT TRANSFER; HIEMENZ FLOW; INCIDENT RADIATION; LIE GROUP TRANSFORMATION; LIE SYMMETRIES; NANOFLUIDS; POROUS MEDIUM; POROUS WEDGE; POWER LAW VARIATION; SHOOTING METHODS; SUCTION/INJECTION; SYSTEM OF ORDINARY DIFFERENTIAL EQUATIONS; WALL SUCTION; WALL TEMPERATURES;

NANOFLUIDICS; ORDINARY DIFFERENTIAL EQUATIONS; PARTIAL DIFFERENTIAL EQUATIONS; POROUS MATERIALS; RUNGE KUTTA METHODS; THERMAL STRATIFICATION;

LIE GROUPS;

CONVECTIVE SYSTEM; INCOMPRESSIBLE FLOW; POROSITY; POROUS MEDIUM; SOLAR POWER; STRATIFICATION; TEMPERATURE EFFECT;

EID: 84864096803     PISSN: 01693913     EISSN: None     Source Type: Journal    
DOI: 10.1007/s11242-012-0011-3     Document Type: Article

References (50)

1. Abdel-Rahman G. M.: Thermal-diffusion and MHD for Soret and Dufour's effects on Hiemenz flow and mass transfer of fluid flow through porous medium onto a stretching surface. Phys. B 405, 2560-2569 (2010).
2. Aminossadati S. M., Ghasemi B.: Natural convection cooling of a localized heat source at the bottom of a nanofluid-filled enclosure. Eur. J. Mech. B. Fluids 28, 630-640 (2009).
3. Anjali Devi S. P., Kandasamy R.: Effects of heat and mass transfer on MHD laminar boundary layer flow over a wedge with suction or injection. J. Energy Heat Mass Transf. 23, 167-178 (2001).
4. 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).
5. Chamkha A. J., Khaled A.-R. A.: Similarity for hydromagnetic mixed convection heat and mass transfer for Hiemenz flow through porous media. Int. J. Numer. Methods Heat Fluid Flow 10, 94-115 (2000).
6. Chamkha A. J., Khaled A.-R. A.: Similarity solutions for hydro magnetic simultaneous heat and mass transfer. Heat Mass Transf. 37, 117-125 (2001).
7. Bluman G. W., Kumei S.: Symmetries and Differential Equations. Springer, New York (1989).
8. Birkoff G.: Mathematics for engineers. J. Electr. Eng. 67, 1185 (1948).
9. Birkoff G.: Hydrodynamics. Princeton University Press, New Jersey (1960).
10. Brewster M. Q.: Thermal Radiative Transfer Properties. Wiley, New York (1972).
11. Buongiorno J.: Convective transport in nanofluids. ASME J. Heat Transf. 128, 240-250 (2006).
12. Buongiorno J., Hu W.: Nanofluid coolants for advanced nuclear power plants. In: Proceedings of ICAPP '05, Seoul, 15-19, Paper no. 5705 (2005).
13. Cheng W. T., Lin H. T.: Non-similarity solution and correlation of transient heat transfer in laminar boundary layer flow over a wedge. Int. J. Eng. Sci. 40, 531-540 (2002).
14. Cheng P., Minkowycz W.: Free convection about a vertical flat plate embedded in a porous medium with application to heat transfer from a dike. J. Geophys. Res. 82, 2040-2044 (1977).
15. Choi, S.: Enhancing thermal conductivity of fluids with nanoparticle. In: Siginer, D. A., Wang, H. P. (eds.) Developments and Applications of Non-Newtonian Flows. ASME MD, vol. 231 and FED, vol. 66, pp. 99-105 (1995).
16. Fathalah K. A., Elsayed M. M.: Natural convection due to solar radiation over a non absorbing plate with and without heat losses. Int. J. Heat Fluid Flow 2, 41-45 (1980).
17. Gill S.: A process for the step-by-step integration of differential equations in an automatic digital computing machine. Proc. Cambr. Philos. Soc. 47, 96-108 (1951).
18. Hakiem M. A. E. L., Mohammadeian A. A., Kaheir S. M. M. E. L., Gorla R. S. R.: Joule heating effects on MHD free convection flow of a micro polar fluid. Int. Comms. Heat Mass Transf. 26, 219-226 (1999).
19. Hiemenz K.: Die Grenzschicht an einem in den gleichfoÈrmigen FluÈssigkeitsstrom eingetauchten geraden Kreiszylinder. Dingl. Poltechnol. J. 326, 321-410 (1911).
20. Hossian M. A.: Viscous and Joule heating effects on MHD free convection flow with variable plate temperature. Int. J. Heat Mass Transf. 35, 3485-3492 (1992).
21. Hunt, A. J.: Small particle heat exchangers. Lawrence Berkeley Laboratory Report No. LBL-7841. J. Renew. Sustain. Energy (1978).
22. Ibragimov N. H.: Elementary Lie Group Analysis and Ordinary Differential Equations. Wiley, New York (1999).
23. Kafoussias N. G., Nanousis N. D.: Magnetohydrodynamic laminar boundary layer flow over a wedge with suction or injection. Can. J. Phys. 75, 733 (1997a).
24. Kafoussias N. G., Nanousis N. D.: Magnetohydrodynamic laminar boundary layer flow over a wedge with suction or injection. Can. J. Phys. 75, 733-781 (1997b).
25. Kandasamy R., Loganathan P., Puvi Arasu P.: Scaling group transformation for MHD boundary-layer flow of a nanofluid past a vertical stretching surface in the presence of suction/injection. Nucl. Eng. Des. 241, 2053-2059 (2011).
26. Kuo B.-L.: Heat transfer analysis for the Falkner-Skan wedge flow by the differential transformation method. Int. J. Heat Mass Transf. 48, 5036-5042 (2005).
27. Kuznetsov A. V., Nield D. A.: Natural convective boundary-layer flow of a nanofluid past a vertical plate. Int. J. Therm. Sci. 49, 243-247 (2010).
28. Lai F. C., Kulacki F. A.: The influence of lateral mass flux on mixed convection over inclined surface in saturated porous media. ASME J. Heat Transf. 21, 515-518 (1990).
29. Maxwell J. C.: A Treatise on Electricity and Magnetism: Unabridged, vol. 2, 3rd edn. Clarendon Press, Oxford (1891).
30. Nakayama A., Koyama H.: Hitoshi Similarity solutions for buoyancy induced flows over a non-isothermal curved surface in a thermally stratified porous medium. Appl. Sci. Res. 46, 309-314 (1989).
31. Nield D. A., Kuznetsov A. V.: 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).
32. Ovsiannikov L. V.: Group Analysis of Differential Equations. Academic Press, New York (1982).
33. Oztop H. F., Abu-Nada E.: Numerical study of natural convection in partially heated rectangular enclosures filled with nanofluids. Int. J. Heat Fluid Flow 29, 1326-1336 (2008).
34. Rana R., Bhargava R.: Numerical study of heat transfer enhancement in mixed convection flow along a vertical plate with heat source/sink utilizing nanofluids. Commun. Nonlinear Sci. Numer. Simul. 16, 4318-4334 (2011).
35. Raptis A.: Radiation and free convection flow through a porous medium. Int. Commun. Heat Mass Transf. 25, 289-295 (1998).
36. Rosmila A.-K., Kandasamy K., Muhaimin I.: Scaling group transformation for boundary-layer flow of a nanofluid past a porous vertical stretching surface in the presence of chemical reaction with heat radiation. Comput. Fluids 52, 15-21 (2011).
37. Schlichting, H.: Boundary Layer Theory, vol. 9, pp. 164-165. McGraw Hill Inc, New York (1979).
38. Seddeek M. A., Darwish A. A., Abdelmeguid M. S.: Effects of chemical reaction and variable viscosity on hydromagnetic mixed convection heat and mass transfer for Hiemenz flow through porous media with radiation. Commun. Nonlinear Sci. Numer. Simul. 12, 195-213 (2007).
39. Sharma A., Tyagi V. V., Chen C. R., Buddhi D.: Review on thermal energy storage with phase change materials and applications. Renew. Sustain. Energy Rev. 13, 318-345 (2009).
40. Sparrow, E. M., Cess, R. D.: Radiation Heat Transfer. Hemisphere, Washington (1978).
41. Tien C. L., Hong J. T. et al.: Natural convection in porous media under non-Darcian and non-uniform permeability conditions. In: Kakac, S. (eds) Natural Convection, Hemisphere, Washington (1985).
42. Tsai R., Huang J. S.: Heat and mass transfer for Soret and Dufour's effects on Hiemenz flow through porous medium onto a stretching surface. Int. J. Heat Mass Transf. 52, 2399-2406 (2009).
43. Vafai K., Alkire R. L., Tien C. L.: An experimental investigation of heat transfer in variable porosity media. ASME J. Heat Transf. 107, 642-647 (1985).
44. Vajravelu K., Prasad K. V., Jinho L., Changhoon L., Pop I., van Gorder R. A.: Convective heat transfer in the flow of viscous Ag-water and cu-water nanofluids over a stretching surface. Int. J. Therm. Sci. 50, 843-851 (2011).
45. Watanabe T.: Thermal boundary layer over a wedge with uniform suction or injection in forced flow. Acta Mech. 83, 119-126 (1990).
46. Yih K. A.: The effect of uniform suction/blowing on heat transfer of Magnetohydrodynamic Hiemenz flow through porous media. Acta Mech. 130, 147-158 (1998).
47. 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).
48. Yurusoy M., Pakdemirli M.: Exact solutions of boundary layer equations of a special non-Newtonian fluid over a stretching sheet. Mech. Res. Commun. 26, 171-175 (1999a).
49. 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 (1999b).
50. Yurusoy M., Pakdemirli M., Noyan O. F.: Lie group analysis of creeping flow of a second grade fluid. Int. J. Non-Linear Mech. 36, 955-960 (2001).