**Asad Ullah 1,2,\*, Ebraheem O. Alzahrani 3, Zahir Shah 1, Muhammad Ayaz <sup>1</sup> and Saeed Islam <sup>1</sup>**


Received: 22 November 2018; Accepted: 27 December 2018; Published: 30 December 2018

**Abstract:** The current investigation is carried out on the thin film flow of Reiner-Philippoff fluid of boundary-layer type. We have analyzed the flow of thin films of Reiner-Philippoff fluid in the changeable heat transmission and radiation over a time-dependent stretching sheet in 2D. The time-dependent governing equations of Reiner-Philippoff fluid model are simplified with the help of transformation of similarity variables. To investigate the behavior of the Reiner-Philippoff fluid with variable stretching surface for different physical effects, we considered thermophoresis and Brownian motion parameters in the flow. The Homotopy Analysis Method is implemented in the reduced model to achieve a solution of the original problem. A numerical convergence of the implemented method is also analyzed. The behavior of temperature, velocity, and concentration profiles have been investigated with the variation of skin friction, Nusselt number, and Sherwood number. A comparative graphical survey is presented for the velocity gradient, under different parameters. An analytical analysis is presented for the time-dependent parameter over thin film flow. The results we obtained are better than the previously available results. For the survey, the physical representation of the embedded parameters, like, *β* depends on the stretching parameter *ζ*, and the Reiner-Philippoff fluid parameter are discussed in detail and plotted graphically. Prandtl number *Pr*, Brownian motion parameter *Nb*, thermophoretic number *Nt*, and Schmidt number *Sc* are presented by graphs and discussed in detail.

**Keywords:** Reiner-Phillipoff fluid; thin film; time-dependent; thermal radiation; homotopy analysis method (HAM)
