Abstract
In the present investigation we have analyzed the boundary layer flow of a Jeffrey fluid over an exponentially stretching surface. The effects of thermal radiation are carried out for two cases of heat transfer analysis known as (1) Prescribed exponential order surface temperature (PEST) and (2) Prescribed exponential order heat flux (PEHF). The highly nonlinear coupled partial differential equations of Jeffrey fluid flow along with the energy equation are simplified by using similarity transformation techniques based on boundary layer assumptions. The reduced similarity equations are then solved analytically by the homotopy analysis method (HAM). The convergence of the HAM series solution is obtained by plotting \(\hbar\)-curves for velocity and temperature. The effects of physical parameters on the velocity and temperature profiles are examined by plotting graphs.
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References
Liu, C.: 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 Mass Transfer 47, 4427–4437 (2004)
Abel, S., Veena, P.H., Rajagopal, K., Pravin, V.K.: Non-Newtonian magnetohydrodynamic flow over a stretching surface with heat and mass transfer. Int. J. Non-Linear Mech. 39, 1067–1078 (2004)
Khan, S.K., Abel, M.S., Sonth, R.M.: Viscoelastic MHD flow, heat and mass transfer over a porous stretching sheet with dissipation of energy and stress work. Int. J. Heat Mass Transfer 40, 47–57 (2003)
Cortell, R.: Effects of viscous dissipation and work done by deformation on the MHD flow and heat transfer of a viscoelastic fluid over a stretching sheet. Phys. Lett. A 357, 298–305 (2006)
Liu, C., Anderson, H.I.: Heat transfer in a liquid film on an unsteady stretching sheet. Int. J. Therm. Sci. 47, 766–772 (2008)
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. Int. J. Heat Mass Transfer 50, 991–996 (2007)
Nadeem, S., Hussain, A., Malik, M.Y., Hayat, T.: Series solutions for the stagnation flow of a second-grade fluid over a shrinking sheet. Appl. Math. Mech.-Engl. Ed. 30, 1255–1262 (2009)
Abbas, Z., Hayat, T.: Radiation effects on MHD flow in a porous medium. Int. J. Heat Mass Transfer 51, 1024–1033 (2008)
Nadeem, S., Hussain, A.: Stagnation flow of a Jeffrey fluid over a shrinking sheet. Z. N. A 65a, 1–9 (2010)
Nadeem, S., Hussain, A.: MHD flow of a viscous fluid on a non linear porous shrinking sheet with HAM. Appl. Math. Mech.-Engl. Ed. 30, 1–10 (2009)
Nadeem, S., Abbasbandy, S., Hussain, M.: Series solutions of boundary layer flow of a Micropolar fluid near the stagnation point towards a shrinking sheet. Z. N. A, 64a, 575–582 (2009)
Nadeem, S., Awais, M.: Thin film flow of an unsteady shrinking sheet through porous medium with variable viscosity. Phys. Lett. A. 372, 4965–4972 (2008)
Sajid, M., Hayat, T.: Influence of thermal radiation on the boundary layer flow due to an exponentially stretching sheet. Int. Commun. Heat Mass Transf. 35, 347–356 (2008)
Sanjayanand, E., Khan, S.K.: On heat and mass transfer in a viscoelastic boundary layer flow over an exponentially stretching sheet. Int. J. Therm. Sci. 45, 819–828, (2006)
Khan, S.K., Sanjayanand, E.: Viscoelastic boundary layer flow and heat transfer over an exponential stretching sheet. Int. J. Heat Mass Transfer 48, 1534–1542 (2005)
Magyari, E., Keller, B.: Heat and mass transfer in the boundary layer on an exponentially stretching continuous surface. J. Phys. D: Appl. Phys. 32, 577–785 (1999)
Hayat, T., Sajid, M.: Homotopy analysis of MHD boundary layer flow of an upper-convected Maxwell fluid. Int. J. Eng. Sci. 45, 393–401 (2007)
Liao, S.J.: Beyond Perturbation: Introduction to Homotopy Analysis Method. Chapman & Hall/CRC, Boca Raton (2003)
Liao, S.J.: Notes on the Homotopy analysis method: some definitions and theorems. Comm. Nonlinear Sci. Numer. Simul. 14, 983–997 (2009)
Liao, S.J.: On the Homotopy analysis method for nonlinear problems. Appl. Math. Comput. 147, 499–513 (2004)
Liao, S.J.: Finding multiple solutions of nonlinear problems by means of the Homotopy analysis method. J. Hydrodynam. Ser. B 18, 54–56 (2006)
Nadeem, S., Ali, M.: Analytical solutions for pipe flow of a fourth grade fluid with Reynold and Vogel’s models of viscosities. Comm. Nonlinear Sci. Numer. Simul. 14, 2073–2090, (2009)
Nadeem, S., Hussain, A., Khan, M.: HAM solutions for boundary layer flow in the region of the stagnation point towards a stretching sheet. Comm. Nonlinear Sci. Numer. Simul. 15, 475–481 (2010)
Abbasbandy, S., Hayat, T.: Solution of the MHD Falkner–Skan flow by Homotopy analysis method. Comm. Nonlinear Sci. Numer. Simul. 14, 3591–3598 (2009)
Abbasbandy, S.: Homotopy analysis method for heat radiation equations. Int. Comm. Heat Mass Transfer 34, 380–387 (2007)
Abbasbandy, S.: The application of Homotopy analysis method to solve a generalized Hirota–Satsuma coupled KDV equation. Phys. Lett. A 361, 478–483 (2007)
Abbasbandy, S., Samadian, Z.F.: Soliton solutions for the fifth-order KDV equation with Homotopy analysis method. Nonlinear Dyn. 5, 183–187 (2008)
Bidin, B., Nazar, R.: Numerical solution of the boundary layer flow over an exponentially stretching sheet with thermal radiation. Eur. J. Sci. Res. 33, 710–717 (2009)
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Nadeem, S., Zaheer, S. & Fang, T. Effects of thermal radiation on the boundary layer flow of a Jeffrey fluid over an exponentially stretching surface. Numer Algor 57, 187–205 (2011). https://doi.org/10.1007/s11075-010-9423-8
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DOI: https://doi.org/10.1007/s11075-010-9423-8