**Muhammad Ramzan 1,2, Asma Liaquet 1, Seifedine Kadry 3, Sungil Yu 4, Yunyoung Nam 5,\* and Dianchen Lu <sup>6</sup>**


Received: 1 November 2019; Accepted: 9 December 2019; Published: 11 December 2019

**Abstract:** The present research examines the impact of second-order slip with thermal and solutal stratification coatings on three-dimensional (3D) Williamson nanofluid flow past a bidirectional stretched surface and envisages it analytically. The novelty of the analysis is strengthened by Cattaneo–Christov (CC) heat flux accompanying varying thermal conductivity. The appropriate set of transformations is implemented to get a differential equation system with high nonlinearity. The structure is addressed via the homotopy analysis technique. The authenticity of the presented model is verified by creating a comparison with the limited published results and finding harmony between the two. The impacts of miscellaneous arising parameters are deliberated through graphical structures. Some useful tabulated values of arising parameters versus physical quantities are also discussed here. It is observed that velocity components exhibit an opposite trend with respect to the stretching ratio parameter. Moreover, the Brownian motion parameter shows the opposite behavior versus temperature and concentration distributions.

**Keywords:** coatings; second order slip; double stratification; Cattaneo–Christov heat flux; variable thermal conductivity; Williamson nanofluid
