Boundary layer flow of a dusty fluid over a permeable shrinking surface

Abstract

Purpose The purpose of this paper is to numerically study the boundary layer problem for the case of two-dimensional flow of dusty fluid over a shrinking surface in the presence of the fluid suction at the surface. Design/methodology/approach The governing equations of the problem are reduced to the system of ordinary differential equations using the similarity transformation and then solved using the bvp4c method in the Matlab software. Findings The effects of the drag coefficient parameter L, the fluid–particle interaction parameter δ, the suction parameter s and the particle loading parameter ω on the flow of the permeable shrinking sheet are investigated. It is found that the aforementioned parameters have different effects in the shrinking sheet flow. This study has also succeeded in discovering the second solution, and through the stability analysis, it is suggested that the solution is unstable and not physically realizable in practice. Practical implications The current findings add to a growing body of literature on the boundary layer problem in the dusty fluid. The dusty fluid is significant in various practical applications such as in the transporting suspended powdered materials through pipes, propulsion and combustion in rockets, the flow of blood in arteries, wastewater treatment and as corrosive particles in engine oil flow. Originality/value Even though the dusty fluid problem has been extensively studied in the flow of the stretching sheet, limited findings can be found over a shrinking flow. In fact, this is the first study to discover the second solution in the dusty fluid problem.

Numerical Computation of Dusty Hybrid Nanofluid Flow and Heat Transfer over a Deformable Sheet with Slip Effect

“…Next, a new time-dependent, dimensionless variable had to be introduced. Hence, we have (Hamid et al [15]):…”

“…Due to the occurrence of nonuniqueness in the present research, the stability analysis was performed by referring to the work of Merkin [60], Weidman et al [61] and Harris et al [62]. These analyses have been implemented by other researchers too (see, for example, the work of Hamid et al [15], Anuar et al [27,28], Waini et al [43] and Khashi'ie et al [45]). Some important steps were implemented to identify the stability of solutions, i.e., (i) considering an unsteady governing equation; (ii) introducing new dimensionless time variables and similarity variables; (iii) implementing linear eigenvalue equations, and (iv) relaxing the boundary conditions.…”

“…An exact analytical solution of magnetohydrodynamic (MHD) dusty fluid caused by a stretching sheet was studied by Jalil et al [14]. Unlike in previous research, Hamid et al [15] explored the permeable shrinking surface in a dusty fluid and observed the occurrence of dual solutions. Gireesha et al [16] numerically studied the nonlinear thermal radiation and hall current impact on a dusty fluid in a heated stretching sheet, while Abbas et al [17] examined dusty fluid flow in a porous medium and took the impact of slip and MHD into consideration.…”

Jeffrey Fluid Embedded with Dust Particles over a Shrinking Sheet: A Numerical Investigation

“…Nonetheless, there is limited existing study into the two-phase flow that accounts for shrinking surface. In recent years, Hamid et al, [19] carried out stability analysis on dusty fluid while Santhosh and Raju [20] took into account the unsteady flow of dusty Carreau-Casson fluids over shrinking sheet. Very recently the investigation related to the non-Newtonian dusty fluid over a stretching sheet has been continued by Dasman et al, [21], Arifin et al, [22] and Aljabali et al, [23].…”

Numerical Simulation of 3D Condensation Nanofluid Film Flow with Carbon Nanotubes on an Inclined Rotating Disk

“…Sandeep et al [6] performed radiative flow and heat transfer analysis of a dusty nanofluid with electrically conducting dust particles (Cu, CuO); they studied how increased heat transfer promoted particle interactions. Pop et al [7] performed a two-dimensional boundary layer flow analysis of dusty fluids over a shrinking surface. Boundary layer approximation was utilized to formulate the problem, and the solution was obtained using the bvp4c MATLAB function.…”