**Impact of Nonlinear Thermal Radiation on the Time-Dependent Flow of Non-Newtonian Nanoliquid over a Permeable Shrinking Surface**

#### **A. Zaib 1, Umair Khan 2, Ilyas Khan 3,\*, El-Sayed M. Sherif 4,5, Kottakkaran Sooppy Nisar 6 and Asiful H. Seikh 4**


Received: 5 December 2019; Accepted: 9 January 2020; Published: 28 January 2020

**Abstract:** Symmetry and fluid dynamics either advances the state-of-the-art of mathematical methods and extends the limitations of existing methodologies to new contributions in fluid. Physical scenario is modelled in terms of di fferential equations as mathematical models in fluid mechanics to address current challenges. In this work a physical problem to examine the unsteady flow of a third-grade non-Newtonian liquid induced through a permeable shrinking surface containing nanoliquid is considered. The model of Buongiorno is utilized comprising the thermophoresis and Brownian e ffects through nonlinear thermal radiation and convective condition. Based on the flow symmetry, suitable similarity transformations are employed to alter the partial di fferential equations into nonlinear ordinary di fferential equations and then these ordinary di fferential equations are numerically executed via three-stage Lobatto IIIa formula. The flow symmetry is discussed for interesting physical parameters and thus this work is concluded. More exactly, the impacts of pertinent constraints on the concentration, temperature and velocity profiles along together drag force, Sherwood and Nusselt numbers are explained through the aid of the tables and plots. The outcomes reveal that the dual nature of solutions is gained for a specific amount of suction and flow in the decelerating form *A* < 0. However, the unique result is obtained for flow in accelerating form *A* ≥ 0. In addition, the non-linear parameter declines the liquid velocity and augments the concentration and temperature fields in the first result, whereas the contrary behavior is scrutinized in the second result.

**Keywords:** Buongiorno model; unsteady flow; nanoliquid; special third-grade liquid; non-linear thermal radiation
