Lie group analysis of natural convective flow from a convectively heated upward facing radiating permeable horizontal plate in porous media filled with nanofluid

Journal of Applied Mathematics

Volumn 2012, Issue , 2012, Pages

  Uddin, Md Jashim ^a   Khan, W A ^b   Ismail, A I Md ^a  

^a SCHOOL OF PHYSICS   (Malaysia)

^b NATIONAL UNIVERSITY OF SCIENCES AND TECHNOLOGY   (Pakistan)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 84864920053     PISSN: 1110757X     EISSN: 16870042     Source Type: Journal    
DOI: 10.1155/2012/648675     Document Type: Article

References (44)

1. Kaka S., zerin S., Yazcolu A. G., Enhanced thermal conductivity of nanofluids: a state-of-the-art review Microfluid Nanofluid 2010 8 145 170
2. Maxwell J. C., A Treatise on Electricity and Magnetism 1981 2nd Oxford, UK Clarendon Press
3. Choi S. U. S., Siginer D. A., Wang H. P., Enhancing thermal conductivity of fluids with nanoparticles Developments and Applications of Non-Newtonian Flows 1995 Baltimore, Md, USA American Society of Mechanical Engineers 99 105
4. Schaefer H., Nanoscience: The Science of the Small in Physics, Engineering. Chemistry, Biology and Medicine (Nanoscience and Technology) 2010 Springer
5. Sharma R. P. E., Nanostructuring Operations in Nanoscale Science and Engineering 2010 Kal.Mcgraw Hill
6. Buongiorno J., Convective transport in nanofluids ASME Journal of Heat Transfer 2006 128 240 250
7. Khan W. A., Aziz A., Natural convection flow of a nanofluid over a vertical plate with uniform surface heat flux International Journal of Thermal Science 2011 50 1207 1214
8. Cheng P., Minkowycz W. J., Free convection about a vertical flat plate embedded in a porous medium with application to heat transfer from a dike Journal of Geophysics Research 1977 82 14 2040 2044
9. Nield D. A., Kuznetsov A. V., The Cheng-Minkowycz problem for natural convective boundary-layer flow in a porous medium saturated by a nanofluid International Journal of Heat Mass Transfer 2009 52 5792 5795
10. Kuznetsov A. V., Nield D. A., Natural convective boundary-layer flow of a nanofluid past a vertical plate International Journal of Thermal Science 2010 49 243 247
11. Kuznetsov A. V., Nield D. A., Thermal instability in a porous medium layer saturated by a nanofluid: brinkman model Transport in Porous Media 2010 81 3 409 422
12. Kuznetsov A. V., Nield D. A., Effect of local thermal non-equilibrium on the onset of convection in a porous medium layer saturated by a nanofluid Transport in Porous Media 2010 83 425 436
13. Godson L. B., Raja D., Mohan D. L., Wongwisesc S., Enhancement of heat transfer using nanofluidsan overview Renewable and Sustainable Energy Reviews 2010 14 629 641
14. Vajravelu K., Prasad K. V., Lee J., Lee C., Pop I., van Gorder R. A., Convective heat transfer in the flow of viscous Ag water and Cu water nanofluids over a stretching surface International Journal of Thermal Sciences 2011 50 843 851
15. Noghrehabadi A., Rashid P., Mohammad G., Effect of partial slip boundary condition on the flow and heat transfer of nanofluids past stretching sheet prescribed constant wall temperature International Journal of Thermal Sciences 2012 54 253 261
16. Aziz A., Khan W. A., Natural convective boundary layer flow of a nanofluid past a convectively heated vertical plate International Journal of Thermal Science 2012 52 83 90
17. Aboeldahab E. M., Azzam G. E. A., Thermal radiation effects on MHD flow past a semi-infinite inclined plate in the presence of mass diffusion Heat and Mass Transfer 2005 41 12 1056 1065
18. Cortell R., Suction, viscous dissipation and thermal radiation effects on the flow and heat transfer of a power-law fluid past an infinite porous plate Chemical Engineering Research and Design 2011 89 85 93
19. Bataller R. C., Radiation effects in the Blasius flow Applied Mathematics and Computation 2008 198 1 333 338
20. Ishak A., Yacob N. A., Bachok N., Radiation effects on the thermal boundary layer flow over a moving plate with convective boundary condition Meccanica 2011 46 4 795 801
21. Gbadeyan J. A., Olanrewaju M. A., Olanrewaju P. O., Boundary layer flow of a nanofluid past a stretching sheet with a convective boundary condition in the presence of magnetic field and thermal radiation Australian Journal of Basic and Applied Sciences 2011 5 9 1323 1334
22. Chamkha A. J., Abbasbandy S., Rashad A. M., Vajravelu K., Radiation effects on mixed convection over a wedge embedded in a porous medium filled with a nanofluid Transport in Porous Media 2012 91 261 279
23. Khan W. A., Pop I., Free convection boundary layer flow past a horizontal flat plate embedded in a porous medium filled with a nanofluid ASME Journal of Heat Transfer 2011 133 9 4
24. Nield D. A., Bejan A., Convection in Porous Media 2006 3rd New York, NY, USA Springer
25. Vadasz P., Emerging Topics in Heat and Mass Transfer in Porous Media 2008 New York, NY, USA Springer
26. Vafai K., Porous Media: Applications in Biological Systems and Biotechnology 2010 New York, NY, USA CRC Press
27. Cheng P., Chang I. D., Buoyancy induced flows in a saturated porous medium adjacent to impermeable horizontal surfaces International Journal of Heat Mass Transfer 1976 19 1267 1272
28. Chang I. D., Cheng P., Matched asymptotic expansions for free convection about an impermeable horizontal surface in a porous medium International Journal of Heat Mass Transfer 1983 26 163 173
29. Shiunlin D. S., Gebhart B., Buoyancy-induced flow adjacent to a horizontal surface submerged in porous medium saturated with cold water International Journal of Heat Mass Transfer 1986 29 611 623 (Pubitemid 16546169)
30. Merkin J. H., Zhang G., On the similarity solutions for free convection in a saturated porous medium adjacent to impermeable horizontal surfaces Wrme-und Stoffbertragung 1990 25 179 184 (Pubitemid 20695479)
31. Chaudhary M. A., Merkin J. H., Pop I., Natural convection from a horizontal permeable surface in porous medium-numerical and asymptotic solutions Transport in Porous Media 1996 22 3 327 344 (Pubitemid 126709645)
32. Gorla R. S. R., Chamkha A., Natural convective boundary layer flow over a horizontal plate embedded in a porous medium saturated with a nanofluid Journal of Modern Physics 2011 2 62 71
33. Aziz A., A similarity solution for laminar thermal boundary over a flat plate with a convective boundary condition Communication in Nonlinear Science and Numerical Simulation 2009 14 1064 1068
34. Yao S., Fang T., Zhong Y., Heat transfer of a generalized stretching/shrinking wall problem with convective boundary conditions Communication in Nonliear Science and Numerical Simulation 2011 16 752 760
35. Uddin M. J., Khan W. A., Ismail A. I. M., Free convection boundary layer flow from a heated upward facing horizontal flat plate embedded in a porous medium filled by a nanofluid and with a convective boundary condition Transport in Porous Media 2012 92 3 867 881
36. Magyari E., Comment on a similarity solution for laminar thermal boundary layer over a flat plate with a convective surface boundary condition by A. Aziz, Comm.Non.Sci. Numer. Simul.' (2009).14, 1064'68 Communications in Nonlinear Science and Numerical Simulation 2011 19 599 601
37. Yacob N. A., Ishak A., Pop I., Falkner-Skan problem for a static or moving wedge in nanofluids International Journal of Thermal Sciences 2011 50 133 139
38. Bluman G. W., Kumei S., Symmetries and Differential Equations 1989 81 New York, NY, USA Springer Applied Mathematical Sciences
39. Jalil M., Asghar S., Mushtaq M., Lie group analysis of mixed convection flow with mass transfer over a stretching surface with suction or injection Mathematical Problems in Engineering 2010 2010 14
40. Pakdemirli M., Yurusoy M., Similarity transformations for partial differential equations SIAM Review 1998 40 1 96 101 (Pubitemid 128628444)
41. Bluman G. W., Anco S. C., Symmetry and Integration Methods for Differential Equations 2009 New York, NY, USA Springer
42. Olver P. J., Applications of Lie Groups to Differential Equations 1986 107 New York, NY, USA Springer Graduate Texts in Mathematics
43. Ibragimov H., Kovalev V. F., Approximate and Re-Norm Group symmetry 2009 New York, NY, USA Springer
44. 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 Mechanica 2001 151 1 14 (Pubitemid 33613855)