*Article* **On the Analysis of the Non-Newtonian Fluid Flow Past a Stretching/Shrinking Permeable Surface with Heat and Mass Transfer**

**Shahid Khan 1, Mahmoud M. Selim 2,3, Aziz Khan 4, Asad Ullah 5, Thabet Abdeljawad 4,6,7,\*, Ikramullah 8, Muhammad Ayaz <sup>9</sup> and Wali Khan Mashwani <sup>1</sup>**


**Abstract:** The 3D Carreau fluid flow through a porous and stretching (shrinking) sheet is examined analytically by taking into account the effects of mass transfer, thermal radiation, and Hall current. The model equations, which consist of coupled partial differential equations (PDEs), are simplified to ordinary differential equations (ODEs) through appropriate similarity relations. The analytical procedure of HAM (homotopy analysis method) is employed to solve the coupled set of ODEs. The functional dependence of the hydromagnetic 3D Carreau fluid flow on the pertinent parameters are displayed through various plots. It is found that the x-component of velocity gradient (*f* (*η*)) enhances with the higher values of the Hall and shrinking parameters (*m*, ), while it reduces with magnetic parameter and Weissenberg number (*M*, *We*). The y-component of fluid velocity (*g*(*η*)) rises with the augmenting values of *m* and *M*, while it drops with the augmenting viscous nature of the Carreau fluid associated with the varying Weissenberg number. The fluid temperature *θ*(*η*) enhances with the increasing values of radiation parameter (*Rd*) and Dufour number (*Du*), while it drops with the rising Prandtl number (*Pr*). The concentration field (*φ*(*η*)) augments with the rising Soret number (*Sr*) while drops with the augmenting Schmidt number (*Sc*). The variation of the skin friction coefficients (*Cf x* and *Cf z*), Nusselt number (*Nux*) and Sherwood number (*Shx*) with changing values of these governing parameters are described through different tables. The present and previous published results agreement validates the applied analytical procedure.

**Keywords:** thermal radiations; magnetic field; Carreau fluid; stretching/shrinking surface; Hall effect; nonlinear radiations; HAM
