Lie group solution for free convective flow of a nanofluid past a chemically reacting horizontal plate in a porous media

Mathematical Problems in Engineering

Volumn 2014, Issue , 2014, Pages

  Rashidi, M M ^a,b   Momoniat, E ^c   Ferdows, M ^d   Basiriparsa, A ^a,e  

^a BU ALI SINA UNIVERSITY   (Iran)

^b SHANGHAI JIAO TONG UNIVERSITY   (China)

^c UNIVERSITY OF THE WITWATERSRAND   (South Africa)

^d UNIVERSITY OF DHAKA   (Bangladesh)

^e ISLAMIC AZAD UNIVERSITY   (Iran)

Author keywords

[No Author keywords available]

Indexed keywords

INCOMPRESSIBLE FLOW; NANOPARTICLES; NATURAL CONVECTION; NUMERICAL METHODS; POROUS MATERIALS; RUNGE KUTTA METHODS; VOLUME FRACTION;

CONTROLLING PARAMETERS; DIMENSIONLESS VELOCITY; HEAT GENERATION/ABSORPTION; NANOPARTICLE VOLUME FRACTIONS; NUMERICAL COMPUTATIONS; OPTIMAL HOMOTOPY ANALYSIS METHODS; RUNGE-KUTTA-FEHLBERG; SIMILARITY TRANSFORMATION;

NANOFLUIDICS;

EID: 84896275161     PISSN: 1024123X     EISSN: 15635147     Source Type: Journal    
DOI: 10.1155/2014/239082     Document Type: Article

References (54)

1. Abu-Nada E., Hakan F. O., Pop I., Buoyancy induced flow in a nanofluid filled enclosure partially exposed to forced convection. Superlattices and Microstructures 2012 51 3 381 395 2-s2.0-84857367845 10.1016/j.spmi.2012.01.002
2. Kakaç S., Pramuanjaroenkij A., Review of convective heat transfer enhancement with nanofluids. International Journal of Heat and Mass Transfer 2009 52 13-14 3187 3196 2-s2.0-64749113545 10.1016/j.ijheatmasstransfer.2009.02. 006
3. Eastman J. A., Choi S. U. S., Li S., Yu W., Thompson L. J., Anomalously increased effective thermal conductivities of ethylene glycol-based nanofluids containing copper nanoparticles. Applied Physics Letters 2001 78 6 718 720 2-s2.0-0001435905 10.1063/1.1341218 (Pubitemid 33630327)
4. Xuan Y., Li Q., Heat transfer enhancement of nanofluids. International Journal of Heat and Fluid Flow 2000 21 1 58 64 2-s2.0-0034069053 10.1016/S0142-727X(99)00067-3 (Pubitemid 30192457)
5. Das S. K., Putra N., Thiesen P., Roetzel W., Temperature dependence of thermal conductivity enhancement for nanofluids. Journal of Heat Transfer 2003 125 4 567 574 2-s2.0-0042418742 10.1115/1.1571080 (Pubitemid 37078524)
6. Kumar D. H., Patel H. E., Kumar V. R. R., Sundararajan T., Pradeep T., Das S. K., Model for heat conduction in nanofluids. Physical Review Letters 2004 93 14 144301 2-s2.0-18844430431 10.1103/PhysRevLett.93.144301
7. Patel H. E., Sundararajan T., Pradeep T., Dasgupta A., Dasgupta N., Das S. K., A micro-convection model for thermal conductivity of nanofluids. Pramana 2005 65 5 863 869 2-s2.0-30844452941 10.1007/BF02704086 (Pubitemid 43104339)
8. Kuznetsov A. V., Non-oscillatory and oscillatory nanofluid bio-thermal convection in a horizontal layer of finite depth. European Journal of Mechanics 2011 30 2 156 165 2-s2.0-79551484503 10.1016/j.euromechflu.2010.10.007
9. Napoli M., Eijkel J. C. T., Pennathur S., Nanofluidic technology for biomolecule applications: a critical review. Lab on a Chip 2010 10 8 957 985 2-s2.0-77950389176 10.1039/b917759k
10. Crepeau J. C., Clarksean R., Similarity solutions of natural convection with internal heat generation. Journal of Heat Transfer 1997 119 1 183 185 2-s2.0-0000012209 (Pubitemid 127567206)
11. Şahin A. Z., Transient heat conduction in semi-infinite solid with spatially decaying exponential heat generation. International Communications in Heat and Mass Transfer 1992 19 3 349 358 2-s2.0-0026861667
12. Makind O. D., Aziz A., Mixed convection from a convectively heated vertical plate to a fluid with internal heat generation. Journal of Heat Transfer 2011 133 6 122501
13. Buongiorno J., Convective transport in nanofluids. Journal of Heat Transfer 2006 128 3 240 250 2-s2.0-33645634748 10.1115/1.2150834
14. Kuznetsov A. V., Nield D. A., Natural convective boundary-layer flow of a nanofluid past a vertical plate. International Journal of Thermal Sciences 2010 49 2 243 247 2-s2.0-71649085635 10.1016/j.ijthermalsci.2009.07.015
15. Godson L. B., Raja D., Mohan L. D., Wongwisesc S., Enhancement of heat transfer using nanofluids-an overview. Renewable and Sustainable Energy Reviews 2010 14 2 629 641 2-s2.0-72149089590 10.1016/j.rser.2009.10.004
16. Nield D. A., Bejan A., Convection in Porous Media 2006 3rd New York, NY, USA Springer
17. Vadasz P., Emerging Topics in Heat and Mass Transfer in Porous Media 2008 New York, NY, USA Springer
18. Vafai K., Porous Media: Applications in Biological Systems and Biotechnology 2010 New York, NY, USA CRC Press
19. 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 Geophysical Research 1977 82 14 2040 2044 2-s2.0-0017493606
20. 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 and Mass Transfer 2009 52 25-26 5792 5795 2-s2.0-77649338479 10.1016/j.ijheatmasstransfer.2009.07.024
21. Cheng P., Chang I. D., Buoyancy induced flows in a saturated porous medium adjacent to impermeable horizontal surfaces. International Journal of Heat and Mass Transfer 1976 19 11 1267 1272 2-s2.0-49349139478
22. Chang I. D., Cheng P., Matched asymptotic expansions for free convection about an impermeable horizontal surface in a porous medium. International Journal of Heat and Mass Transfer 1983 26 2 163 174 2-s2.0-0020707531 (Pubitemid 13504406)
23. 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 and Mass Transfer 1986 29 4 611 623 2-s2.0-0022695298 (Pubitemid 16546169)
24. Merkin J. H., Zhang G., On the similarity solutions for free convection in a saturated porous medium adjacent to impermeable horizontal surfaces. Wärme- und Stoffübertragung 1990 25 3 179 184 2-s2.0-0004140912 10.1007/BF01590149 (Pubitemid 20695479)
25. Chaudhary M. A., Merkin J. H., Pop I., Natural convection from a horizontal permeable surface in a porous medium-numerical and asymptotic solutions. Transport in Porous Media 1996 22 3 327 344 2-s2.0-0029676323 (Pubitemid 126709645)
26. Gorla R. S. R., Chamkha A., Natural convective boundary layer flow over a nonisothermal vertical plate embedded in a porous medium saturated with a nanofluid. Nanoscale and Microscale Thermophysical Engineering 2011 15 2 81 94 2-s2.0-79957595168 10.1080/15567265.2010.549931
27. Khan W. A., Pop I., Free convection boundary layer flow past a horizontal flat plate embedded in a porous medium filled with a nanofluid. Journal of Heat Transfer 2011 133 9 2-s2.0-79960533729 10.1115/1.4003834 094501
28. Aziz A., Khan W. A., Pop I., Free convection boundary layer flow past a horizontal flat plate embedded in porous medium filled by nanofluid containing gyrotactic microorganisms. International Journal of Thermal Sciences 2012 56 48 57 2-s2.0-84858278180 10.1016/j.ijthermalsci.2012.01.011
29. Bluman G. W., Anco S. C., Symmetry and Integration Methods for Differential Equations 2009 New York, NY, USA Springer
30. 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 1-2 1 14 2-s2.0-0040750347 10.1007/BF01272521 (Pubitemid 33613855)
31. Kuznetsov A. V., Avramenko A. A., Geng P., Analytical investigation of a falling plume caused by bioconvection of oxytactic bacteria in a fluid saturated porous medium. International Journal of Engineering Science 2004 42 5-6 557 569 2-s2.0-0346724624 10.1016/j.ijengsci.2003.08.004
32. 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 2-s2.0-78650719723 10.1155/2010/264901 264901
33. Hamad M. A. A., Uddin M. J., Ismail A. I. M., Radiation effects on heat and mass transfer in MHD stagnation-point flow over a permeable flat plate with thermal convective surface boundary condition, temperature dependent viscosity and thermal conductivity. Nuclear Engineering and Design 2012 242 194 200 2-s2.0-84355162903 10.1016/j.nucengdes.2011.09.005
34. Aziz A., Uddin M. J., Hamad M. A. A., Md. Ismail A. I., MHD flow over an inclined radiating plate with the temperature-dependent thermal conductivity, variable reactive index, and heat generation. Heat Transfer 2012 41 3 241 259 2-s2.0-84859922834 10.1002/htj.20409
35. Hansen A. G., Similarity Analysis of Boundary Layer Problems in Engineering 1964 Englewood Cliffs, NJ, USA Prentice Hall
36. Ames W. F., Nonlinear Partial Differential Equations in Engineering 1972 New York, NY, USA Academic Press
37. Seshadri R., Na T. Y., Group Invariance in Engineering Boundary Value Problems 1985 New York, NY, USA Springer
38. Shang D., Theory of Heat Transfer with Forced Convection Film Flows 2010 3 Heat and Mass Transfer
39. Nayfeh A. H., Perturbation Methods 2000 New York, NY, USA Wiley
40. Erfani E., Rashidi M. M., Parsa A. B., The modified differential transform method for solving off-centered stagnation flow toward a rotating disc. International Journal of Computational Methods 2010 7 4 655 670 2-s2.0-79551678644 10.1142/S0219876210002404
41. Rashidi M. M., Laraqi N., Basiri Parsa A., Analytical modeling of heat convection in magnetized micropolar fluid by using modified differential transform method. Heat Transfer 2011 40 3 187 204 2-s2.0-79954992368 10.1002/htj.20337
42. Rashidi M. M., Keimanesh M., Using differential transform method and padé approximant for solving mhd flow in a laminar liquid film from a horizontal stretching surface. Mathematical Problems in Engineering 2010 2010 14 2-s2.0-77952515880 10.1155/2010/491319 491319
43. Rashidi M. M., Domairry G., New analytical solution of the three-dimensional NavierStokes equations. Modern Physics Letters B 2009 23 26 3147 3155 2-s2.0-70350289848 10.1142/S0217984909021193
44. Rashidi M. M., Keimanesh M., Bég O. A., Hung T. K., Magnetohydrodynamic biorheological transport phenomena in a porous medium: a simulation of magnetic blood flow control and filtration. International Journal for Numerical Methods in Biomedical Engineering 2011 27 6 805 821 2-s2.0-79957603034 10.1002/cnm.1420
45. Liao S. J., The proposed homotopy analysis technique for the solution of nonlinear problems [Ph.D. thesis] 1992 Shanghai Jiao Tong University
46. Rashidi M. M., Domairry G., Dinarvand S., Approximate solutions for the Burger and regularized long wave equations by means of the homotopy analysis method. Communications in Nonlinear Science and Numerical Simulation 2009 14 3 708 717 2-s2.0-50249117853 10.1016/j.cnsns.2007.09.015
47. Ziabakhsh Z., Domairry G., Analytic solution of natural convection flow of a non-Newtonian fluid between two vertical flat plates using homotopy analysis method. Communications in Nonlinear Science and Numerical Simulation 2009 14 5 1868 1880 2-s2.0-56049101853 10.1016/j.cnsns.2008.09.022
48. Rashidi M. M., Mohimanian Pour S. A., Hayat T., Obaidat S., Analytic approximate solutions for steady flow over a rotating disk in porous medium with heat transfer by homotopy analysis method. Computers and Fluids 2012 54 1 1 9 2-s2.0-82455164141 10.1016/j.compfluid.2011.08.001
49. Sajid M., Hayat T., Asghar S., Comparison between the HAM and HPM solutions of thin film flows of non-Newtonian fluids on a moving belt. Nonlinear Dynamics 2007 50 1-2 27 35 2-s2.0-34548230554 10.1007/s11071-006-9140-y (Pubitemid 47327530)
50. Nield D. A., Kuznetsov A. V., The Cheng-Minkowycz problem for the double-diffusive natural convective boundary layer flow in a porous medium saturated by a nanofluid. International Journal of Heat and Mass Transfer 2011 54 1-3 374 378 2-s2.0-78449272982 10.1016/j.ijheatmasstransfer.2010.09.034
51. Vajravelu K., Hadjinicolaou A., Convective heat transfer in an electrically conducting fluid at a stretching surface with uniform free stream. International Journal of Engineering Science 1997 35 1237 1244 2-s2.0-0031221950 (Pubitemid 127371419)
52. Mukhopadhyay S., Layek G. C., Effects of variable fluid viscosity on flow past a heated stretching sheet embedded in a porous medium in presence of heat source/sink. Meccanica 2012 47 4 863 876 2-s2.0-79960329645 10.1007/s11012-011- 9457-6
53. Liao S. J., An optimal homotopy-analysis approach for strongly nonlinear differential equations. Communications in Nonlinear Science and Numerical Simulation 2010 15 8 2003 2016 2-s2.0-76049117931 10.1016/j.cnsns.2009.09.002
54. Aziz A., A similarity solution for laminar thermal boundary layer over a flat plate with a convective surface boundary condition. Communications in Nonlinear Science and Numerical Simulation 2009 14 4 1064 1068 2-s2.0-55549142170 10.1016/j.cnsns.2008.05.003