processes Article On Fluid Flow Field Visualization in a Staggered Cavity: A Numerical Result Khalil Ur Rehman 1, *, Nabeela Kousar 1 , Waqar A. Khan 2 and Nosheen Fatima 1 1 Department of Mathematics, Air University, PAF Complex E-9, Islamabad 44000, Pakistan; nabeela@mail.au.edu.pk (N.K.); cheemanosheen911@gmail.com (N.F.) 2 Department of Mechanical Engineering, College of Engineering, Prince Mohammad Bin Fahd University, Al Khobar 31952, Saudi Arabia; wkhan@pmu.edu.sa * Correspondence: khalil.rehman@mail.au.edu.pk Received: 6 October 2019; Accepted: 22 October 2019; Published: 15 February 2020   Abstract: In this paper we have considered a staggered cavity. It is equipped with purely viscous fluid. The physical design is controlled through mathematical formulation in terms of both the equation of continuity and equation of momentum along with boundary constraints. To be more specific, the Navier-Stokes equations for two dimensional Newtonian fluid flow in staggered enclosure is formulated and solved by well trusted method named finite element method. The novelty is increased by considering the motion of upper and lower walls of staggered cavity case-wise namely, in first case we consider that the upper wall of staggered cavity is moving and rest of walls are kept at zero velocity. In second case we consider that the upper and bottom walls are moving in a parallel way. Lastly, the upper and bottom walls are considered in an antiparallel direction. In all cases the deep analysis is performed and results are proposed by means of contour plots. The velocity components are explained by line graphs as well. The kinetic energy examination is reported for all cases. It is trusted that the findings reported in present pagination well serve as a helping source for the upcoming studies towards fluid flow in an enclosure domains being involved in an industrial areas. Keywords: staggered cavity; Newtonian fluid model; Moving Walls; finite element method 1. Introduction The field of fluid mechanics deals with the flow of fluids and forces us to understand the underlying physics. To study the fluids flow one needs mathematical treatment as well as experimentations. Owing theoretical frame it is well consensus that to study the fluids flow field the simplest mathematical model is Navier-Stokes equations. The both compressible and incompressible flow fields can be studied by coupling the Navier-Stokes equation with stress tensors of concerned fluid models. In this direction, the simpler classical problem of viscous fluid model in two dimensional space was developed by Crane [1]. The analytical solution was proposed for this problem. Since then many investigations in similar manner were carried to inspect the flow field properties of both Newtonian and non-Newtonian fluid models like Devi et al. [2] studied flow due to stretched surface in three dimensional frame. An exact solution of Navier-Stokes equations subject to stretched surface was proposed by Smith [3]. Pop and Na [4] extended the study by considering time dependent flow field. The mathematical equations were developed by assuming that the viscous fluid flow is attain due to stretching sheet. Later, the developed partial differential equations were converted into ordinary differential equations and power series solution was exercised. The mathematical model for two dimensional stagnation point flow in the presence of heat transfer aspects was proposed by Chaim [5]. In this attempt it is assumed that the surface was stretched linearly. The numerical solution via shooting method was proposed in this paper. The electrically conducting fluid flow along with convective heat transfer Processes 2020, 8, 226; doi:10.3390/pr8020226 www.mdpi.com/journal/processes