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HEAT TRANSFER OVER A STRETCHING POROUS SHEET SUBJECTED TO POWER LAW HEAT FLUX IN PRESENCE OF HEAT SOURCE

ABSTRACT
In the present investigation the boundary layer steady flow and heat transfer of a viscous incompressible fluid due to a stretching porous sheet in presence of heat source are studied. The equations of motion and heat transfer are reduced to non-linear ordinary differential equations and the exact solutions are obtained in the form of confluent hypergeometric function (Kummer’s Function) for prescribed heat flux, when the wall is at prescribed second order power law heat flux or the prescribed heat flux at the stretching porous wall varies as the square of the distance from the origin. The effects of the various parameters entering into the problem on the temperature distribution and recovery temperature are discussed.
KEYWORDS
PAPER SUBMITTED: 2010-03-31
PAPER REVISED: 2010-09-21
PAPER ACCEPTED: 2010-08-12
DOI REFERENCE: https://doi.org/10.2298/TSCI100331074K
CITATION EXPORT: view in browser or download as text file
THERMAL SCIENCE YEAR 2011, VOLUME 15, ISSUE Supplement 2, PAGES [S187 - S194]
REFERENCES
  1. Sakiadis, B.C., Boundary layer behavior on continuous solid surface, American Institute of Chemical Engineers Journal, 7 (1961), 1, pp. 26-28
  2. Erickson, L.E., Fan, L.T., Fox, V.G., Heat and mass transfer of a moving continuous flat plate with suction or injection, Ind. Engng. Chem. Fundam., 5 (1966), 1, pp. 19-25
  3. Gupta P.S., Gupta A.S., Heat and mass transfer on a stretching sheet with suction or blowing, Canad. J. of Chem. Eng., 55 (1977), 6, pp.744-746
  4. Crane, L.J., Flow past a stretching plate, ZAMP, 21 (1970), 4, pp. 645-647
  5. Mc Cormack, P.D., Crane, L.J., Physical Fluid Dynamics Academic Press, New York, USA, 1973
  6. McLeod, J.B., Rajagopal, K.R., On the uniqueness of flow of a Navier- Stokes fluid due to a stretching boundary, Arch. Rational Mech. Anal., 98 (1987), 4, pp. 385-393
  7. Troy, W.C., Overman II, E.A., Ermentrout, G.B., Keener, J.P., Uniqueness of flow of a second order fluid past a stretching surface, Q. Appl. Math., 44 (1987), 4, pp. 753-755
  8. Danberg, J.E., Fansler, K.S., Non similar solution for the flow in the boundary layer past a stretched wall, Q Appl Math, 34 (1976), pp. 305-311
  9. Vleggaar, J., Laminar boundary-layer behavior on continuous accelerating surfaces, Chem. Eng. Sci., 32 (1977), 12, pp. 1517-1525
  10. Soundalgekar, V.M., Murty, T.V.R., Heat transfer past a continuous moving plate with variable temperature, Warme-und Stoffubertragung, 14 (1980), 2, pp. 91-93
  11. Carragher, P., Crane, L., Heat transfer on continuous stretching sheet, ZAMM, 62 (1982), 10, pp. 564-565
  12. Grubka, L.T., Bobba, K.M., Heat transfer characteristics of a continuous stretching surface with variable temperature, J Heat Transfer, 107 (1985), pp. 248-250
  13. Dutta, B.K., Heat transfer from a stretching sheet in a viscous flow with suction or blowing, ZAMM, 68 (1988), 6, pp. 231-236
  14. Chen, C.K., Char, M.I., Heat transfer of a continuous stretching surface with suction or blowing, J. Math. Anal. Appl., 135 (1988), 2, pp. 568-580
  15. Afzal, N., Varshney, I.S., The cooling of low heat resistance stretching sheet moving through a fluid, Wirme- und Stoffiibertrag, 14 (1980), 4, pp. 289-293
  16. Kuiken, H.K., On the boundary layer in fluid mechanics that decay algebraically along stretches on wall that are not vanishingly small, I. M. A. J. Appl. Math., 27 (1981), 4, pp. 387-405
  17. Banks, W.H.H., Similarity solutions of the boundary layer equations for stretching wall, J. Mec. Theo. Appl., 2 (1983), 3, pp. 375-392
  18. Banks, W.H.H., Zaturska, M.B., Eigen solutions in boundary-layer flow adjacent to a stretching wall, I. M. A. J. Appl. Math., 36 (1986), 3, pp. 263-273
  19. Chakrabarti, A., Gupta, A.S., Hydromagnetic flow and heat transfer over a stretching sheet, Q Appl Math, 37 (1979), pp. 73-78
  20. Chiam, T.C., Hydromagnetic flow over a surface stretching with a power law velocity, Int. J. Engng. Sci., 33 (1995), 3, pp. 429-435
  21. Abo-Eldahab, E.M., Salem, A. M., Hall effect on MHD free convection flow of a non Newtonian power law fluid at a stretching surface, Int. Comm. Heat Mass Transfer, 31 (2004), 3, pp. 343-354
  22. Kechil, S.A., Hashim, I., Series solution for unsteady boundary-layer flows due to impulsively stretching plate, Chinese Physics Letters, 24 (2007), 1, pp. 139-142
  23. Liao S.J., Series solutions of unsteady boundary-layer flows over a stretching flat plate, Studies in Applied Mathematics, 117 (2006), 3, pp. 239-263
  24. Vajravelu, K., Hadjinicolaou, A., Heat transfer in a viscous fluid over a stretching sheet with viscous dissipation and internal heat generation, Int Comm Heat Mass Transf, 20 (1993), pp. 417-430
  25. Abel, M.S., Khan, S.K., Prasad, K.V., Convective heat and mass transfer in a visco-elastic fluid flow through a porous medium over a stretching sheet, Int J Numer Meth Heat Fluid Flow, 11 (2001), pp. 779-792
  26. Bhargava, R., Kumar, L., Takhar, H.S., Finite element solution of mixed convection micropolar flow driven by a porous stretching sheet, Int J Engng Sci, 41 (2003), pp. 2161-2178
  27. Rashad, A.M., Radiative effect on heat transfer from a stretching surface in a porous medium, Int. J. of Appl. Math. and Mech., 3 (2007), 4, pp.14-23
  28. Shafie, S., Amin, N., Pop, I., Unsteady boundary layer due to a stretching sheet in a porous medium using Brinkman equation model, Int J Heat and Technol, 24 (2006), pp. 111-117.
  29. Veena, P.H., Pravin, V.K., Shahjahan, S.M., Hippargi, V.B., Non-similar solutions for heat and mass transfer flow in an electrically conducting visco-elastic fluid over a stretching sheet embedded in a porous medium, International Journal of Modern Mathematics, 2 (2007), pp. 9-26.
  30. Sharma, P.R., Singh, G., Effects of ohmic heating and viscous dissipation on steady MHD flow near a stagnation point on an isothermal stretching sheet, Thermal Science, 13 (2009), pp. 5-12.
  31. Abdullah, I.A., Analytic solution of heat and mass transfer over a permeable stretching plate affected by chemical reaction, internal heating, dufour-soret effect and Hall Effect, Thermal Science, 13 (2009), pp.183-197.
  32. Kumar, H., Radiative heat transfer with hydromagnetic flow and viscous dissipation over a stretching surface in the presence of variable heat flux, Thermal Science, 13 (2009), pp. 163-169.
  33. Erdelyi, A., Higher Transcendental Functions, Vol. 1, Mc Graw-Hill Inc., New York, USA, 1953

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