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Existence and uniqueness theorem for flow and heat transfer of a non-Newtonian fluid over a stretching sheet

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Abstract

Analysis is carried out to study the existence, uniqueness and behavior of exact solutions of the fourth order nonlinear coupled ordinary differential equations arising in the flow and heat transfer of a viscoelastic, electrically conducting fluid past a continuously stretching sheet. The ranges of the parametric values are obtained for which the system has a unique pair of solutions, a double pair of solutions and infinitely many solutions.

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References

  • Andersson, H.I., 1992. MHD flow of a viscoelastic fluid past a stretching surface. Acta Mechanica, 95(1–4):227–230. [doi:10.1007/BF01170814]

    Article  MathSciNet  MATH  Google Scholar 

  • Chen, C.K., Char, M.I., 1988. Heat transfer of a continuous stretching surface with suction or blowing. J. Math. Anal. and Appl., 135(2):568–580. [doi:10.1016/0022-247X(88)90172-2]

    Article  MathSciNet  MATH  Google Scholar 

  • Cortell, R., 2006a. A note on flow and heat transfer of a viscoelastic fluid over a stretching sheet. Int. J. Non-Linear Mech., 41(1):78–85. [doi:10.1016/j.ijnonlinmec.2005.04.008]

    Article  MATH  Google Scholar 

  • Cortell, R, 2006b. Flow and heat transfer of an electrically conducting fluid of second grade over a stretching sheet subject to suction and to a transverse magnetic field. Int. J. Heat and Mass Trans., 49(11–12):1851–1856. [doi:10.1016/j.ijheatmasstransfer.2005.11.013]

    Article  MATH  Google Scholar 

  • Dunn, J.E., Fosdick, R.L., 1974. Thermodynamics, stability and boundedness of fluids of complexity 2 and fluids of second grade. Arch. Ratl. Mech. Anal., 56(3):191–252. [doi:10.1007/BF00280970]

    Article  MathSciNet  MATH  Google Scholar 

  • Dunn, J.E., Rajagopal, K.R., 1995. Fluids of differential type: Critical review and thermodynamic analysis. Int. J. Engng. Sci., 33(5):689–729. [doi:10.1016/0020-7225(94)00078-X]

    Article  MathSciNet  MATH  Google Scholar 

  • Fosdick, R.L., Rajagopal, K.R., 1979. Anomalous features in the model of ’second order fluids’. Arch. Ratl. Mech. Anal., 70(2):145–152. [doi:10.1007/BF00250351]

    Article  MathSciNet  MATH  Google Scholar 

  • Fox, V.G., Ericksen, L.E., Fan, L.T., 1969. The laminar boundary layer on a moving continuous flat sheet immersed in a non-Newtonian fluid. American Inst. Chem. Engng. J., 15:327–333.

    Article  Google Scholar 

  • Gupta, P.S., Gupta, A.S., 1977. Heat and mass transfer on a stretching sheet with suction or blowing. Canadian J. Chem. Engng., 55:744–746.

    Article  Google Scholar 

  • Hayat, T., Sajid, M., 2007. Analytic solution for axisymmetric flow and heat transfer of a second grade fluid past a stretching sheet. Int. J. Heat and Mass Trans., 50(1–2):75–84. [doi:10.1016/j.ijheatmasstransfer.2006.06.045]

    Article  MathSciNet  MATH  Google Scholar 

  • Hayat, T., Khan, M., Siddiqui, A.M., Asgar, S., 2004a. Transient flow of a second grade fluid. Int. J. Non-Linear Mech., 39(10):1621–1633. [doi:10.1016/j.ijnonlinmec2002.12.001]

    Article  MATH  Google Scholar 

  • Hayat, T., Hutter, K., Nadeem, S., Asgar, S., 2004b. Unsteady hydromagnetic rotating flow of a conducting second grade fluid. Zeitschrift fr angewandte Mathematik und Physik, 55(4):626–641. [doi:10.1007/s00033-004-1129-0]

    Article  MathSciNet  MATH  Google Scholar 

  • Hayat, T., Abbas, Z., Sajid, M., 2006. Series solution for the upper convected Maxwell fluid over a porous stretching plate. Physics Letter A, 358(5–6):396–403. [doi:10.1016/j.physleta.2006.04.117]

    Article  MATH  Google Scholar 

  • Khan, S.K., Sanjayanand, E., 2005. Viscoelastic boundary layer flow and heat transfer over an exponentially stretching sheet. Int. J. Heat and Mass Trans., 48(8):1534–1542. [doi:10.1016/j.ijheatmasstransfer.2004.10.032]

    Article  MATH  Google Scholar 

  • Kichenassamy, S., Olver, P., 1992. Existence and non-existence of solitary wave solutions to higher order model evaluation equations. SIAM J. Math. Anal., 23(5):1141–1166. [doi:10.1137/0523064]

    Article  MathSciNet  MATH  Google Scholar 

  • Liu, I.C., 2004. Flow and heat transfer of an electrically conducting fluid of second grade over a stretching sheet subject to a transverse magnetic field. Int. J. Heat and Mass Trans., 47(19–20):4427–4437. [doi:10.1016/j.ijheatmasstransfer.2004.03.029]

    Article  MATH  Google Scholar 

  • McCormack, P.D., Crane, L., 1973. Physics of Fluid Dynamics, Academic Press, New York.

    MATH  Google Scholar 

  • Rajagopal, K.R., Na, Y.T., Gupta, A.S., 1984. Flow of a viscoelastic fluid over a stretching sheet. Rheologica Acta, 23(2):213–215. [doi:10.1007/BF01332078]

    Article  Google Scholar 

  • Rivlin, R.S., Ericksen, J.L., 1955. Stress deformation relation for isotropic material. J. Ratl. Mech. Anal., 4:323–425.

    MathSciNet  Google Scholar 

  • Sakiadis, B.C., 1961. Boundary layer behavior on continuous solid surfaces. American Inst. Chem. Engng. J., 7:26–28.

    Article  Google Scholar 

  • Vajravelu, K., Soewono, E., 1996. Fourth order non-linear systems arising in combined free and forced convection flow of a second-order fluid. Int. J. Non-Linear Mech., 31(2):129–137. [doi:10.1016/0020-7462(95)00058-5]

    Article  MathSciNet  MATH  Google Scholar 

  • Vajravelu, K., Rollins, D., 2004. Hydromagnetic flow of a second grade fluid over a stretching sheet. Appl. Math. and Comp., 148(3):783–791. [doi:10.1016/S0096-3003(02)00942-6]

    Article  MathSciNet  MATH  Google Scholar 

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Sahoo, B., Sharma, H.G. Existence and uniqueness theorem for flow and heat transfer of a non-Newtonian fluid over a stretching sheet. J. Zhejiang Univ. - Sci. A 8, 766–771 (2007). https://doi.org/10.1631/jzus.2007.A0766

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  • DOI: https://doi.org/10.1631/jzus.2007.A0766

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