Numerical solutions for unsteady boundary layer flow of a dusty fluid past a permeable stretching/shrinking surface with particulate viscous effect

Abstract

Purpose This present aims to present the numerical study of the unsteady stretching/shrinking flow of a fluid-particle suspension in the presence of the constant suction and dust particle slip on the surface. Design/methodology/approach The governing partial differential equations for the two phases flows of the fluid and the dust particles are reduced to the pertinent ordinary differential equations using a similarity transformation. The numerical results are obtained using the bvp4c function in the Matlab software. Findings The results revealed that in the decelerating shrinking flow, the wall skin friction is higher in the dusty fluid when compared to the clean fluid. In addition, the effect of the fluid-particle interaction parameter to the fluid-phase can be seen more clearly in the shrinking flow. Other non-dimensional physical parameters such as the unsteadiness parameter, the mass suction parameter, the viscosity ratio parameter, the particle slip parameter and the particle loading parameter are also considered and presented in figures. Further, the second solution is discovered in this problem and the solution expanded with higher unsteadiness and suction values. Hence, the stability analysis is performed, and it is confirmed that the second solution is unstable. Practical implications In practice, the flow conditions are commonly varying with time; thus, the study of the unsteady flow is very crucial and useful. The problem of unsteady flow of a dusty fluid has a wide range of possible applications such as in the centrifugal separation of particles, sedimentation and underground disposable of radioactive waste materials. Originality/value Even though the problem of dusty fluid has been broadly investigated, limited discoveries can be found over an unsteady shrinking flow. Indeed, this paper managed to obtain the second (dual) solutions, and stability analysis is performed. Furthermore, the authors also considered the artificial particle-phase viscosity, which is an important term to study the particle-particle and particle-wall interactions. With the addition of this term, the effects of the particle slip and suction parameters can be investigated. Very few studies in the dusty fluid embedded this parameter in their problems.

Dusty hybrid nanofluid flow over a shrinking sheet with magnetic field effects

“…However, the effect is more pronounced on the dust phase velocity. Physically, the increase in β v tends to increase the interphase drag force between the phases (Hamid et al , 2018). Consequently, the momentum boundary layer thickness decreases which imply an increase in the fluid velocity.…”

“…Both fluid-particle phases are assumed to behave as interacting continua. Besides, the interaction between the solid particles and the fluid is described by the Stokes linear drag force, and other possible interactions such as the virtual force, the shear lift force, and the spin-lift force are ignored (Hamid et al , 2017, 2018). Considering these physical assumptions, along with the boundary layer approximations, the governing equations for the flow of the dusty hybrid nanofluid together with the boundary conditions are given as follows (Siddiqa et al , 2015; Jalil et al , 2017; Radhika et al , 2020):…”

“…Based on equation (8), the analysis is initiated by using the new dimensionless variables given as follows (Hamid et al , 2017, 2018): …”

“…Moreover, it is worth mentioning that the dusty fluid flow over a shrinking sheet was considered by Hamid et al (2017) for the first time. Then, a similar problem has been extended by themselves by considering the unsteady flow which can be found in Hamid et al (2018). They managed to discover the dual solutions for the problem and concluded that one of the solutions is stable through the temporal stability analysis.…”

Impact of heat generation/absorption on the unsteady magnetohydrodynamic stagnation point flow and heat transfer of nanofluids

“…Referring to Weidman et al (2006), the stability of the solutions can be ascertained by identifying the initial growth or decay of the system. This can be done by perturbing the basic flow f = f 0 (h ), g = g 0 (h ) and u = u 0 (h ) with the following time-dependent solution form (Hamid et al, 2018;Jusoh et al, 2019):…”