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**Flow and heat transfer of a non-Newtonian fluid past a stretching sheet with partial slip.**
*(English)*
Zbl 1221.76021

Summary: The entrained flow and heat transfer of a non-Newtonian third grade fluid due to a linearly stretching surface with partial slip is considered. The partial slip is controlled by a dimensionless slip factor, which varies between zero (total adhesion) and infinity (full slip). Suitable similarity transformations are used to reduce the resulting highly nonlinear partial differential equations into ordinary differential equations. The issue of paucity of boundary conditions is addressed and an effective second order numerical scheme has been adopted to solve the obtained differential equations even without augmenting any extra boundary conditions. The important finding in this communication is the combined effects of the partial slip and the third grade fluid parameter on the velocity, skin-friction coefficient and the temperature field. It is interesting to find that the slip and the third grade fluid parameter have opposite effects on the velocity and the thermal boundary layers.

### Keywords:

third grade fluid; partial slip; heat transfer; finite difference method; shooting method; broyden’s method
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\textit{B. Sahoo}, Commun. Nonlinear Sci. Numer. Simul. 15, No. 3, 602--615 (2010; Zbl 1221.76021)

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### References:

[1] | Sakiadis, B.C., Boundary-layer behavior on continuous solid surfaces: I. boundary-layer equations for two-dimensional and axisymmetric flow, Aiche j, 7, 26-28, (1961) |

[2] | Blasius, H., Grenzschichten in flüssigkeiten mit kleiner reibung, Z math physik, 56, 1-37, (1908) · JFM 39.0803.02 |

[3] | Cortell, R., Numerical solutions of the classical Blasius flat-plate problem, Appl math comput, 170, 706-710, (2005) · Zbl 1077.76023 |

[4] | Erickson, L.E.; Fan, L.T.; Fox, V.G., Heat and mass transfer on a moving continuous flat plate with suction or injection, Ind eng chem fund, 5, 19-25, (1969) |

[5] | Crane, L.J., Flow past a stretching sheet, Z angew math phys (ZAMP), 21, 645-647, (1970) |

[6] | Mcleod, J.B.; Rajagopal, K.R., On the uniqueness of flow of a navier – stokes fluid due to a stretching boundary, Arch ration mech anal, 98, 386-393, (1987) · Zbl 0631.76021 |

[7] | Gupta, P.S.; Gupta, A.S., Heat and mass transfer on a stretching sheet with suction or blowing, Can J chem eng, 55, 744-746, (1977) |

[8] | 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) · Zbl 1221.76233 |

[9] | Vajravelu, K.; Cannon, J.R., Fluid flow over a nonlinearly stretching sheet, Appl math comput, 181, 609-618, (2006) · Zbl 1143.76024 |

[10] | Cortell, R., Effects of viscous dissipation and radiation on the thermal boundary layer over a nonlinearly stretching sheet, Phys lett A, 372, 631-636, (2008) · Zbl 1217.76028 |

[11] | Wang, C.Y., The three-dimensional flow due to a stretching flat surface, Phys fluids, 27, 1915-1917, (1984) · Zbl 0545.76033 |

[12] | Ariel, P.D., On computation of the three-dimensional flow past a stretching sheet, Appl math comput, 188, 1244-1250, (2007) · Zbl 1114.76056 |

[13] | Rajagopal, K.R.; Na, T.Y.; Gupta, A.S., Flow of a viscoelastic fluid over a stretching sheet, Rheol acta, 23, 213-215, (1984) |

[14] | Andersson, H.I., MHD flow of a viscoelastic fluid past a stretching sheet, Acta mech, 95, 227-230, (1992) · Zbl 0753.76192 |

[15] | Ariel, P.D., MHD flow of a viscoelastic fluid past a stretching sheet with suction, Acta mech, 105, 49-56, (1994) · Zbl 0814.76086 |

[16] | Liu, I.-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 trans, 47, 4427-4437, (2004) · Zbl 1111.76336 |

[17] | Sahoo, B.; Sharma, H.G., Existence and uniqueness theorem for flow and heat transfer of a non-Newtonian fluid over a stretching sheet, J zhej univ sci A, 8, 766-771, (2007) · Zbl 1144.80347 |

[18] | Cortell, R., A note on flow and heat transfer of a viscoelastic fluid over a stretching sheet, Int J nonlinear mech, 41, 78-85, (2006) · Zbl 1160.80302 |

[19] | Man, C.S., Nonsteady channel flow of ice as a modified second-order fluid with power-law viscosity, Arch ration mech anal, 119, 35-57, (1992) · Zbl 0757.76001 |

[20] | Truesdell, C.; Noll, W., The nonlinear field theories of mechanics, (2004), Springer · Zbl 0779.73004 |

[21] | Dunn, J.E.; Rajagopal, K.R., Fluids of differential type: critical review and thermodynamic analysis, Int J eng sci, 33, 689-729, (1995) · Zbl 0899.76062 |

[22] | Andersson, H.I.; Kumaran, V., On sheet-driven motion of power-law fluids, Int J nonlinear mech, 41, 1228-1234, (2006) · Zbl 1160.76302 |

[23] | Aksoy, Y.; Pakdemirli, M.; Khalique, C.M., Boundary layer equations and stretching sheet solutions for the modified second grade fluid, Int J eng sci, 45, 829-841, (2007) · Zbl 1213.76060 |

[24] | Sajid, M.; Hayat, T.; Asghar, S., Non-similar analytic solution for MHD flow and heat transfer in a third-order fluid over a stretching sheet, Int J heat mass trans, 50, 1723-1736, (2006) · Zbl 1140.76042 |

[25] | Sajid, M.; Hayat, T., Non-similar series solution for boundary layer flow of a third order fluid over a stretching sheet, Appl math comput, 189, 1576-1585, (2007) · Zbl 1120.76004 |

[26] | Sajid, M.; Hayat, T.; Asghar, S., Non-similar solution for the axisymmetric flow of a third-grade fluid over a radially stretching sheet, Acta mech, 189, 193-205, (2007) · Zbl 1117.76006 |

[27] | Sahoo, B., Hiemenz flow and heat transfer of a non-Newtonian fluid, Comm nonlinear sci num sim, 14, 811-826, (2009) |

[28] | Navier, C.L.M.H., Sur LES lois du mouvement des fluides, Mem acad R sci inst fr, 6, 389-440, (1827) |

[29] | Rao, I.J.; Rajagopal, K.R., The effect of the slip boundary condition on the flow of fluids in a channel, Acta mech, 135, 113-126, (1999) · Zbl 0936.76013 |

[30] | Wang, C.Y., Flow due to a stretching boundary with partial slip-an exact solution of the navier – stokes equation, Chem eng sci, 57, 3745-3747, (2002) |

[31] | Andersson, H.I., Slip flow past a stretching surface, Acta mech, 158, 121-125, (2002) · Zbl 1013.76020 |

[32] | Ariel, P.D., Axisymmetric flow due to a stretching sheet with partial slip, Comput math appl, 54, 1169-1183, (2007) · Zbl 1138.76030 |

[33] | Wang, C.Y., Analysis of viscous flow due to a stretching sheet with surface slip and suction, Nonlinear anal real world appl, 10, 375-380, (2009) · Zbl 1154.76330 |

[34] | Ariel, P.D.; Hayat, T.; Asghar, S., The flow of an elastico-viscous fluid past a stretching sheet with partial slip, Acta mech, 187, 29-35, (2006) · Zbl 1103.76010 |

[35] | Hayat, T.; Javed, T.; Abbas, Z., Slip flow and heat transfer of a second grade fluid past a stretching sheet through a porous space, Int J heat mass trans, 51, 4528-4534, (2008) · Zbl 1144.80316 |

[36] | Rivlin, R.S.; Ericksen, J.L., Stress deformation relation for isotropic materials, J ration mech anal, 4, 323-425, (1955) · Zbl 0064.42004 |

[37] | Fosdick, R.L.; Rajagopal, K.R., Thermodynamics and stability of fluids of third grade, Proc R soc lond, ser A, 369, 351-377, (1980) · Zbl 0441.76002 |

[38] | Pakdemirli, M., The boundary layer equations of third grade fluids, Int J nonlinear mech, 27, 785-793, (1992) · Zbl 0764.76004 |

[39] | Ariel, P.D., A hybrid method for computing the flow of viscoelastic fluids, Int J num meth fluids, 14, 757-774, (1992) · Zbl 0753.76111 |

[40] | Liao, S.J., Beyond perturbation: introduction to homotopy analysis method, (2003), Chapman & Hall/CRC Press Boca Raton |

[41] | Sahoo, B.; Sharma, H.G., MHD flow and heat transfer from a continuous surface in a uniform free stream of a non-Newtonian fluid, Appl math mech, 28, 1467-1477, (2007) · Zbl 1231.34015 |

[42] | Sahoo, B.; Sharma, H.G., Effects of partial slip on the steady von karman flow and heat transfer of a non-Newtonian fluid, Bull braz math soc, 38, 595-609, (2007) · Zbl 1133.76003 |

[43] | Sahoo, B., Effects of partial slip, viscous dissipation and joule heating on von karman flow and heat transfer of an electrically conducting non-Newtonian fluid, Comm nonlinear sci num sim, 14, 2982-2998, (2009) |

[44] | Broyden, C.G., A class of methods for solving nonlinear simultaneous equations, Math comput, 19, 577-593, (1965) · Zbl 0131.13905 |

[45] | Broyden, C.G., On the discovery of the good Broyden method, Math program ser B, 87, 209-213, (2000) · Zbl 0970.90002 |

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