**Thin Film Flow of Couple Stress Magneto-Hydrodynamics Nanofluid with Convective Heat over an Inclined Exponentially Rotating Stretched Surface**

**Asifa Tassaddiq 1,\*, Ibni Amin 2, Meshal Shutaywi 3, Zahir Shah 4, Farhad Ali 5, Saeed Islam 2,6,7,\* and Asad Ullah <sup>8</sup>**


Received: 20 February 2020; Accepted: 30 March 2020; Published: 1 April 2020

**Abstract:** In this article a couple stress magneto-hydrodynamic (MHD) nanofluid thin film flow over an exponential stretching sheet with joule heating and viscous dissipation is considered. Similarity transformations were used to obtain a non-linear coupled system of ordinary differential equations (ODEs) from a system of constitutive partial differential equations (PDEs). The system of ordinary differential equations of couple stress magneto-hydrodynamic (MHD) nanofluid flow was solved using the well-known Homotopy Analysis Method (HAM). Nusselt and Sherwood numbers were demonstrated in dimensionless forms. At zero Prandtl number the velocity profile was analytically described. Furthermore, the impact of different parameters over different state variables are presented with the help of graphs. Dimensionless numbers like magnetic parameter *M*, Brownian motion parameter *Nb*, Prandtl number Pr, thermophoretic parameter *Nt*, Schmidt number *Sc*, and rotation parameter *S* were analyzed over the velocity, temperature, and concentration profiles. It was observed that the magnetic parameter *M* increases the axial, radial, drainage, and induced profiles. It was also apparent that *Nu* reduces with greater values of Pr. On increasing values of the Brownian motion parameter the concentration profile declines, while the thermophoresis parameter increases.

**Keywords:** MHD; nanofluid; stretching surface; rotating fluid; Homotopy Analysis Method (HAM)
