**Abdullah Dawar 1, Zahir Shah 2, Poom Kumam 3,4,5,\*, Waris Khan <sup>6</sup> and Saeed Islam <sup>7</sup>**


Received: 5 June 2019; Accepted: 9 July 2019; Published: 17 July 2019

**Abstract:** The aim of this research work is to increase our understanding of the exhaustion of energy in engineering and industrial fields. The study of nanofluids provides extraordinary thermal conductivity and an increased heat transmission coefficient compared to conventional fluids. These specific sorts of nanofluids are important for the succeeding generation of flow and heat transfer fluids. Therefore, the investigation of revolutionary new nanofluids has been taken up by researchers and engineers all over the world. In this article, the study of the thin layer flow of Darcy-Forchheimer nanofluid over a nonlinear radially extending disc is presented. The disc is considered as porous. The impacts of thermal radiation, magnetic field, and heat source/sink are especially focused on. The magnetic field, positive integer, porosity parameter, coefficient of inertia, and fluid layer thickness reduce the velocity profile. The Prandtl number and fluid layer thickness reduce the temperature profile. The heat source/sink, Eckert number, and thermal radiation increase the temperature profile. The suggested model is solved analytically by the homotopy analysis method (HAM). The analytical and numerical techniques are compared through graphs and tables, and have shown good agreement. The influences of embedded parameters on the flow problem are revealed through graphs and tables.

**Keywords:** Darcy-Forchheimer nanofluid; nonlinear extending disc; variable thin layer; HAM and numerical method
