**Non-Newtonian Magnetohydrodynamics (MHD) andHeatTransferwithNonlinear**

#### **Jing Zhu \*, Yaxin Xu and Xiang Han**

 **Flow**

School of Mathematics and Physics, University of Science and Technology Beijing, Beijing 100080, China; S20180748@xs.ustb.edu.cn (Y.X.); S20170736@xs.ustb.edu.cn (X.H.)

**\*** Correspondence: zhujing@ustb.edu.cn; Tel.: +86-1368-121-2703

**Temperature**

Received: 29 August 2019; Accepted: 28 November 2019; Published: 6 December 2019

 **Jump**

**Abstract:** The velocity and thermal slip impacts on the magnetohydrodynamics (MHD) nanofluid flow and heat transfer through a stretched thin sheet are discussed in the paper. The no slip condition is substituted for a new slip condition consisting of higher-order slip and constitutive equation. Similarity transformation and Lie point symmetry are adopted to convert the derived governed equations to ordinary differential equations. An approximate analytical solution is gained through the homotopy analysis method. The impacts of velocity slip, temperature jump, and other physical parameters on flow and heat transfer are illustrated. Results indicate that the first-order slip and nonlinear slip parameters reduce the velocity boundary layer thickness and Nusselt number, whereas the effect on shear stress is converse. The temperature jump parameter causes a rise in the temperature, but a decline in the Nusselt number. With the increase of the order, we can ge<sup>t</sup> that the error reaches 10−<sup>6</sup> from residual error curve. In addition, the velocity contours and the change of skin friction coefficient are computed through Ansys Fluent.

**Keywords:** velocity-slip; temperature-jump; homotopy analysis method; nanofluids; power-law fluids
