**Rahmat Ellahi 1,2,\*, Ahmed Zeeshan 2, Farooq Hussain 2,3 and Tehseen Abbas <sup>4</sup>**


**Particles along Slippery Walls**

Received: 19 March 2019; Accepted: 29 April 2019; Published: 2 May 2019

**Abstract:** The present study is about the pressure-driven heated bi-phase flow in two slippery walls. The non-Newtonian couple stress fluid is suspended with spherically homogenous metallic particles. The magnetic susceptibility of Hafnium allures is taken into account. The rough surface of the wall is tackled by lubrication effects. The nonlinear coupled partial differential equations along with the associated boundary conditions are first reduced into a set of ordinary differential equations by using appropriate transformations and then numerical results were obtained by engaging the blend of Runge–Kutta and shooting techniques. The sway of physical quantities are examined graphically. An excellent agreement within graphical illustration and numerical results is achieved.

**Keywords:** heated bi-phase flow; couple stress fluid; lubrication effects; slippery walls; magnetohydrodynamics
