Department of Mathematics
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Item Stokes Flow Through a Membrane Built up by Nonhomogeneous Porous Cylindrical Particles(Elsevier, 2019-12) Tiwari, AshishThis work deals with the creeping flow of an incompressible viscous fluid through a membrane. It is assumed that the membrane is composed of nonhomogeneous porous cylindrical particles with radially varying permeability enclosing a cavity. The flow within the nonhomogeneous porous medium is governed by the Darcy equation. The flow inside the cavity and outside the nonhomogeneous porous region is governed by the Stokes equations. An analytical solution of the problem is obtained by using the cell model technique. Exact expressions for the drag force acting on the membrane and hydrodynamic permeability of the membrane are derived. The influence of radially varying permeability on flow parameters is considered. The effects of various parameters of the problem on hydrodynamic permeability of the membrane are discussed for four models. Some previous results for hydrodynamic permeability are verified as special limiting casesItem Creeping flow of micropolar fluid through a swarm of cylindrical cells with porous layer (membrane)(Elsevier, 2019-11) Tiwari, AshishThe flow of micropolar fluid through a membrane modeled as a swarm of solid cylindrical particles with porous layer using the cell model technique is considered. The flow is directed perpendicular to the axis of the cylinders. Boundary value problem involves traditional conditions of velocities and stresses continuity, no-stress and no-couple stress/no-spin condition on hypothetical cell surface. The problem is solved analytically and the influence of micropolar and porous medium parameters on hydrodynamic permeability of a membrane is investigated.Item Creeping flow of micropolar fluid parallel to the axis of cylindrical cells with porous layer(Elsevier, 2019-08) Tiwari, AshishThe present paper considers the flow of micropolar fluid through a membrane modeled as a swarm of solid cylindrical particles with porous layer using the cell model technique. Traditional boundary conditions on hypothetical cell surface were added with an additional condition: the no spin condition / no couple stress condition. Expressions for velocity and microrotation vector components have been obtained analytically. Effect of various parameters such as particle volume fraction, permeability parameter, micropolarity number etc. on hydrodynamic permeability of membrane has been discussedItem Creeping flow of Jeffrey fluid through a swarm of porous cylindrical particles: Brinkman–Forchheimer model(Elsevier, 2021-12) Tiwari, AshishThe majority of the previous studies analyzed the flow of fluids with constant viscosity through membranes composed of porous cylindrical particles using the particle-in-cell approach with the Brinkman equation governing the flow through porous media. However, a slight variation in temperature affects the viscosity of the fluids and hence affects the filtration process of fluids through membranes. The motivation of this problem came from the fact that viscosity is concentration dependent due to presence of impurities and contaminants in the fluids and hence can be taken as function of position or temperature. The present work is a theoretical attempt to investigate the impact of temperature-dependent viscosity on the creeping flow of Jeffrey fluid through membrane consisting of the aggregates of the porous cylindrical particles. The flow pattern of the Jeffrey fluid is taken along the axial direction of the cylindrical particles, and the cell model approach is utilized to formulate the governing equations driven by a constant pressure gradient. The flow regime is divided into two-layer form, one is inside the porous cylindrical particle enclosing a solid core, which is governed by the Brinkman–Forchheimer equation, and another one is outside of the porous cylindrical particle, which is governed by the Stokes equation. Being a nonlinear equation, an analytical solution of the Brinkman–Forchheimer equation is intractable. To overcome this difficulty, the regular and singular perturbation methods have been employed to solve the Brinkman–Forchheimer equation under the assumption of temperature-dependent viscosity for small and large permeability of the porous medium, respectively; however, an analytical approach is utilized to solve the Stokes equation.