*Article* **Impact of Thermal Radiation and Heat Source**/**Sinkon MHD Time-Dependent Thin-Film Flow of Oldroyed-B, Maxwell, and Je**ff**ry Fluids over a Stretching Surface**

#### **Abdul Samad Khan 1,\*, Yufeng Nie 1 and Zahir Shah 2**


Received: 1 March 2019; Accepted: 27 March 2019; Published: 2 April 2019

**Abstract:** In this study paper, we examined the magnetohydrodynamic (MHD) flow of three combined fluids, Maxwell, Jeffry, and Oldroyed- B fluids, with variable heat transmission under the influence of thermal radiation embedded in a permeable medium over a time-dependent stretching sheet. The fluid flow of liquid films was assumed in two dimensions. The fundamental leading equations were changed to a set of differential nonlinear and coupled equations. For this conversion, suitable similarity variables were used. An optimal tactic was used to acquire the solution of the modeled problems. The convergence of the technique has been shown numerically. The obtained analytical and numerical consequences are associated graphically and tabulated. An excellent agreemen<sup>t</sup> was obtained between the homotropy analysis method (HAM) and numerical methods. The variation of the skin friction and Nusslet number and their influence on the temperature and concentration profiles were scrutinized. The influence of the thermal radiation, unsteadiness effect, and MHD were the main focus of this study. Furthermore, for conception to be physically demonstrated, the entrenched parameters are discussed graphically in detail along with their effect on liquid film flow.

**Keywords:** Jeffrey, Maxwell, Oldroyed-B fluids; unsteady stretching surface; magnetic field; homotropy analysis method (HAM)
