Variable Fluid Properties and Thermal Radiation Effects on the Flow and Heat Transfer in a Micropolar Fluid Film Past a Moving Permeable Infinite Flat Plate With Slip Velocity

Mostafa A.A.Mahmoud; Shimaa E.Waheed

doi:10.3879/j.issn.1000-0887.2012.05.010

Volume 33 Issue 5

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Mostafa A.A.Mahmoud, Shimaa E.Waheed. Variable Fluid Properties and Thermal Radiation Effects on the Flow and Heat Transfer in a Micropolar Fluid Film Past a Moving Permeable Infinite Flat Plate With Slip Velocity[J]. Applied Mathematics and Mechanics, 2012, 33(5): 628-642. doi: 10.3879/j.issn.1000-0887.2012.05.010

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Variable Fluid Properties and Thermal Radiation Effects on the Flow and Heat Transfer in a Micropolar Fluid Film Past a Moving Permeable Infinite Flat Plate With Slip Velocity

doi: 10.3879/j.issn.1000-0887.2012.05.010

Department of Mathematics, Faculty of Science, Benha University 13518, Egypt

Received Date: 2011-01-04
Rev Recd Date: 2011-12-27
Publish Date: 2012-05-15

Abstract

Abstract

The influence of thermal radiation on the problem of mixed convection thin film flow and heat transfer of a micropolar fluid past a moving infinite vertical porous flat plate with slip velocity was dealt with. The fluid viscosity and the thermal conductivity were assumed to vary as a function of temperature. The equations governing the flow were solved numerically using the Chebyshev spectral method for some representative value of various parameters. Comparisons with previously published work were performed and found to be in an excellent agreement. The effects of various parameters on the velocity, the microrotation velocity and the temperature profiles as well as the skinfriction coefficient and the Nusselt number were plotted and discussed.
- micropolar fluid,
- thin film,
- slip velocity,
- variable fluid properties,
- thermal radiation,
- Chebyshev spectral method

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References

[1]	Sakiadis B C. Boundary layer behavior on continuous solid surface—Ⅱ: the boundary layer on a continuous flat surface[J]. AIChE J, 1961, 7(2): 221-225.
[2]	Tsou F K, Sparrow E M, Goldstein K J. Flow and heat transfer in the boundary layer on a continuous moving surface[J]. Int J Heat Mass Transfer, 1967, 10(2): 219-235.
[3]	Erickson L E, Fan L T, Fox V G. Heat and mass transfer on a moving continuous flat plate with suction or blowing[J]. Ind Engng Chem Fund, 1966, 5: 19-25.
[4]	Griffin J F, Thorne J L. On the thermal boundary layer growth on continuous moving belts[J]. AIChE J, 1967, 13(6): 1210-1211.
[5]	Moutsoglou A, Chen T S. Buoyancy effects in boundary layers on inclined continuous moving sheets[J]. J Heat Transfer, 1980, 102(2):171-173.
[6]	Jeng D R, Chang T C A, DeWitt K J. Momentum and heat transfer on a continuous moving surface[J]. J Heat Transfer, 1986,108(3): 532-537.
[7]	Takhar H S, Chamkha A J, Nath G. Effect of buoyancy forces on the flow and heat transfer over a continuous moving vertical or inclined surface[J]. Int J Thermal Sci, 2001, 40(9): 825-833.
[8]	Mahmoud M A A. Variable viscosity effects on hydromagnetic boundary layer flow along a continuously moving vertical plate in the presence of radiation[J]. Appl Math Sci, 2007, 1(17): 799-814.
[9]	Mahmoud M A A, Megahed A M. On steady hydromagnetic boundary-layer flow of a non-Newtonian power-law fluid over a continuously moving surface with suction[J]. Chem Eng Comm, 2007, 194(11): 1457-1469.
[10]	Mahmoud M A A, Megahed A M. Effects of viscous dissipation and heat generation (absorption) in a thermal boundary layer of a non-Newtonian fluid over a continuously moving permeable flat plate[J]. J Applied Mechanics and Technical Physics, 2009, 50(5): 819-825.
[11]	Bar-Cohen A, Sherwood G, Hodes M, Solbreken G L. Gas-assisted evaporative cooling of high density electronic modules[J]. IEEE Trans CPMT, Part A, 1995, 18(3): 502-509.
[12]	Chun K R, Seban R A. Heat transfer to evaporating liquid films[J]. ASME J Heat Transfer, 1971, 93: 391-396.
[13]	Killion J D, Garimella S. Simulation of pendant droplets and falling films in horizontal tube absorbers[J]. ASME J Heat Transfer, 2004, 126(6): 1003-1013.
[14]	Rabani E, Rechman D R, Gelssler P L, Brus L E. Drying mediated self assembly of nano-particles[J]. Nature, 2003, 426: 271-274.
[15]	Calvert P, Ink-jet printing for materials and devices[J]. Chem Mater, 2001, 13(10): 3299-3305.
[16]	Wang C. Liquid film on an unsteady stretching surface[J]. Quarterly of Applied Mathematics, 1990, 48: 601-610.
[17]	Andersson H I, Aarseth J B, Dandapat B S. Heat transfer in a liquid film on an unsteady stretching surface[J]. Int J Heat and Mass Transfer, 2000, 43(1): 69-74.
[18]	Dandapat B S, Santra B, Andersson H I. Thermocapillarity in a liquid film on an unsteady stretching surface[J]. Int J Heat Mass Transfer, 2003, 46(16): 3009-3015.
[19]	Chen C H. Effect of viscous dissipation on heat transfer in a non-Newtonian liquid film over an unsteady stretching sheet[J]. J Non-Newtonian Fluid Mech, 2006, 135(2/3): 128-135.
[20]	Wang C, Pop I. Analysis of the flow of a power-law fluid film on an unsteady stretching surface by means of homotopy analysis method[J]. J Non-Newtonian Fluid Mech, 2006, 138(2/3): 161-172.
[21]	Abbas Z, Hayat T, Sajid M, Asghar S. Unsteady flow of a second grade fluid film over an unsteady stretching sheet[J]. Mathematical and Computer Modelling, 2008, 48: 518-526.
[22]	Abel M S, Mahesha N, Tawade J. Heat transfer in a liquid film over an unsteady stretching surface with viscous dissipation in presence of external magnetic field[J]. Applied Mathematical Modelling, 2009, 33(8): 3430-3441.
[23]	Santra B, Dandapat B S. Unsteady thin-film flow over a heated stretching sheet[J]. Int J Heat Mass Transfer, 2009, 52(7/8): 1965-1970.
[24]	Noor N F M, Abdulaziz O, Hashim I. MHD flow and heat transfer in a thin liquid film on an unsteady stretching sheet by the homotopy analysis method[J]. Int J Numer Meth Fluids, 2010, 63: 357-373.
[25]	Siddiqui A M, Mahmood R, Ghori Q K. Homotopy perturbation method for thin film flow of a third grade fluid down an inclined plane[J]. Chaos, Solitons and Fractals, 2008, 35(1): 140-147.
[26]	Eringen A C. Theory of micropolar fluids[J]. J Math Mech, 1966, 16: 1-18.
[27]	Eringen A C. Theory of thermomicropolar fluids[J]. J Math Appl, 1972, 38: 480-495.
[28]	Armin T, Turk M A, Sylvester N D. Microcontinuum fluid mechanics a review[J]. Int J Engng Sci, 1973, 11(8): 905-915.
[29]	Armin T, Turk M A, Sylvester N D. Application of microcontinuum fluid mechanics[J]. Int J Engng Sci, 1974, 12(4): 273-279.
[30]	Lukaszewicz G. Micropolar Fluids: Theory and Application[M]. Basel: Birkhuser, 1999.
[31]	Eringen A C. Microcontinuum Field Theories—Ⅱ: Fluent Media[M]. New York: Springer, 2001.
[32]	乔德哈瑞 R C, 吉哈 A K.化学反应对竖直平板边界磁流体动力学微极流体滑流的影响[J]. 应用数学和力学，2008, 29(9): 1069-1082.(Chaudhary R C, Jha A K. Effects of chemical reactions on MHD micropolar fluid past a vertical plate in slip-flow regime[J]. Applied Mathematics and Mechanics（English Edition）, 2008, 29(9): 1179-1194.)
[33]	Hayat T, Sajid M, Ali N. On exact solutions for thin film flows of a micropolar fluid[J]. Communications in Nonlinear Science and Numerical Simulation, 2009, 14(2): 451-461.
[34]	Dandapat B S, Santra B, Vajravelu K. The effects of variable fluid properties and thermocapillarity on the flow of a thin film on an unsteady stretching sheet[J]. Int J Heat Mass Transfer, 2007, 50(5/6): 991-996.
[35]	Nadeem S, Faraz N. Thin film flow of a second grade fluid over a stretching/shrinking sheet with variable temperature-dependent viscosity[J]. Chinese Phys Lett, 2010, 27(3): 034704.
[36]	Makinde O D. Laminar falling liquid film with variable viscosity along an inclined heated plate[J]. Applied Mathematics and Computation, 2006, 175(1): 80-88.
[37]	Mahmoud M A A, Megahed A M. MHD flow and heat transfer in a non-Newtonian liquid film over an unsteady stretching sheet with variable fluid properties[J]. Can J Phy, 2009, 87(10): 1065-1071.
[38]	Hayat T, Javed T, Abbas Z. Slip flow and heat transfer of a second grade fluid past a stretching sheet through a porous space[J]. Int J Heat Mass Transfer, 2008, 51(17/18): 4528-4534.
[39]	Asghar S, Gulzar M M, Ayub M. Effects of partial slip on flow of a third grade fluid[J]. Acta Mech Sin, 2006, 22(5): 393-396.
[40]	Mahmoud M A A. Slip effects on flow and heat transfer of a non-Newtonian fluid on a stretching surface with thermal radiation[J]. Int J Chem React Engng, 2008, 6(1): A92.
[41]	Sajid M, Awais M, Nadeem S, Hayat T. The influence of slip condition on thin film flow of a fourth grade fluid by the homotopy analysis method[J]. Computers and Mathematics With Applications, 2008, 56(8): 2019-2026.
[42]	祖额科 J, 阿么德 S. 流经有热源多孔平板并伴有化学反应的传热传质混合对流MHD流动[J]. 应用数学和力学，2010, 31(10): 1160-1171.(Zueco J, Ahmed S. Combined heat and mass transfer by mixed convection MHD flow along a porous plate with chemical reaction in presence of heat source[J]. Applied Mathematics and Mechanics（English Edition）, 2010, 31(10): 1217-1230.)
[43]	Chandrakala P. Radiation effects on flow past an impulsively started vertical oscillating plate with uniform heat flux[J]. Int J Dynamics of Fluids, 2011, 7(1): 1-8.
[44]	Jena S K, Mathur M N. Similarity solution for laminar free convection flow of thermo-micropolar fluid past a non-isothermal vertical flat plate[J]. Int J Engng Sci, 1981, 19(11): 1431-1439.
[45]	Peddieson J, M