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**Heat and mass transfer for Sorét and Dufour’s effect on mixed convection boundary layer flow over a stretching vertical surface in a porous medium filled with a viscoelastic fluid.**
*(English)*
Zbl 1221.80005

Summary: A mathematical model is analyzed in order to study the heat and mass transfer characteristics in mixed convection boundary layer flow about a linearly stretching vertical surface in a porous medium filled with a viscoelastic fluid, by taking into account the diffusion-thermo (Dufour) and thermal-diffusion (Soret) effects. The governing partial differential equations are transformed into a set of coupled ordinary differential equations, which are solved analytically using the homotopy analysis method (HAM) to determine the convergent series expressions of velocity, temperature and concentration. The physical interpretation to these expressions is assigned through graphs and a table for the wall shear stress \(f''(0)\), Nusselt number \(-\theta'(0)\) and Sherwood number \(-\phi'(0)\). Results show that the fields are influenced appreciably by the effects of the governing parameters: mixed convection parameter \(\lambda\), Lewis number Le, Prandtl number Pr, viscoelastic parameter \(K\), concentration buoyancy parameter \(N\), porosity parameter \(\gamma\), Dufour number \(D_f\) and Soret number Sr. It was evident for some kinds of mixtures such as light and medium molecular weights, that the Soret and Dufour effects should be considered as well.

### MSC:

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

35C10 | Series solutions to PDEs |

65M99 | Numerical methods for partial differential equations, initial value and time-dependent initial-boundary value problems |

76D10 | Boundary-layer theory, separation and reattachment, higher-order effects |

76R10 | Free convection |

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\textit{T. Hayat} et al., Commun. Nonlinear Sci. Numer. Simul. 15, No. 5, 1183--1196 (2010; Zbl 1221.80005)

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