**Dianchen Lu 1, Sumayya Mumtaz 2, Umer Farooq 1,2 and Adeel Ahmad 2,\***


Received: 11 February 2019; Accepted: 16 March 2019; Published: 25 March 2019

**Abstract:** This article investigates the unsteady flow and heat transfer analyses of a viscous-based nanofluid over a moving surface emerging from a moving slot. This new form of boundary layer flow resembles with the boundary layer flow over a stretching/shrinking surface depending on the motion of the moving slot. The governing partial differential equations are transformed to correct similar form using the Blasius–Rayleigh–Stokes variable. The transformed equations are solved numerically. Existence of dual solutions is observed for a certain range of moving slot parameter. The range of dual solution is strongly influenced by Brownian and thermophoretic diffusion of nanoparticles.

**Keywords:** unsteady flow and heat transfer; nanofluid; Blasius–Rayleigh–Stokes variable; dual solutions; numerical solution; correlation expressions
