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**Mixed convection in the stagnation-point flow of a Maxwell fluid towards a vertical stretching surface.**
*(English)*
Zbl 1196.35160

Summary: In the present analysis, we study the steady mixed convection boundary layer flow of an incompressible Maxwell fluid near the two-dimensional stagnation-point flow over a vertical stretching surface. It is assumed that the stretching velocity and the surface temperature vary linearly with the distance from the stagnation-point. The governing nonlinear partial differential equations have been reduced to the coupled nonlinear ordinary differential equations by the similarity transformations. Analytical and numerical solutions of the derived system of equations are developed. The homotopy analysis method (HAM) and finite difference scheme are employed in constructing the analytical and numerical solutions, respectively. Comparison between the analytical and numerical solutions is given and found to be in excellent agreement. Both cases of assisting and opposing flows are considered. The influence of the various interesting parameters on the flow and heat transfer is analyzed and discussed through graphs in detail. The values of the local Nusselt number for different physical parameters are also tabulated. Comparison of the present results with known numerical results of viscous fluid is shown and a good agreement is observed.

### MSC:

35Q35 | PDEs in connection with fluid mechanics |

76A10 | Viscoelastic fluids |

74F10 | Fluid-solid interactions (including aero- and hydro-elasticity, porosity, etc.) |

35A24 | Methods of ordinary differential equations applied to PDEs |

76M20 | Finite difference methods applied to problems in fluid mechanics |

80A20 | Heat and mass transfer, heat flow (MSC2010) |

35B30 | Dependence of solutions to PDEs on initial and/or boundary data and/or on parameters of PDEs |

### Keywords:

stagnation-point flow; Maxwell fluid; heat transfer; stretching sheet; HAM solution; numerical solution
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\textit{Z. Abbas} et al., Nonlinear Anal., Real World Appl. 11, No. 4, 3218--3228 (2010; Zbl 1196.35160)

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