Flow Of Incompressible Micropolar Fluid Research Articles

Numerical analysis of thermal characteristics for micropolar fluid flux close to an isothermal vertical plate inward porous region

The merit of this manuscript is to examine numerically a heated vertical plate with uniform temperature subjected to a steady, viscous, incompressible micro-polar fluid flow that is situated inside a saturated porous medium with permeability and porosity. Similarity variables have been applied to convert coupled of constrained partial differential equations that describe physical problem into coupled of constrained nonlinear ordinary differential equations, which in turn allows for the reliable numerical solution of the problems. Finite difference and shooting methods coupled with Runge-Kutta scheme have been implemented by Matlab function bvp4c to solve equations numerically. The graphical findings showed the impact of emerging dimensionless physical parameters for micro- polar liquid on non-dimensional velocity, temperature, and micro-rotation distributions. The latest findings exhibit a high degree of agreement with the findings from earlier research. Elevating parameter values drive to an increase in the velocity profile values, but a decrease in the temperature distribution values. The benchmarks parameters of this research are modified vortex viscosity and micro-inertia density. The high porosity in the range of 0.7–0.9 is considered the noteworthy limitation of the current study. Furthermore, increasing the material's physical characteristics cause the micro-rotation vorticity profile's curvature to flip.

Stabilized Gauge Uzawa scheme for an incompressible micropolar fluid flow

In this paper, a second order Gauge Uzawa scheme for the governing equations of an incompressible micropolar fluid flow is introduced and analyzed. The derivation of this scheme is obtained using the second order backward difference approximation. Later, the unconditional stability of the GUM scheme for the micropolar equations will be shown. Then, an a priori error estimate is established to prove the convergence. Finally, we present some numerical simulations that confirm the theoretical results.

Homotopy Simulation of Dissipative Micropolar Flow and Heat Transfer from a Two-Dimensional Body with Heat Sink Effect

Non-Newtonian flow from a wedge constitutes a fundamental problem in chemical<br /> engineering systems and is relevant to processing of polymers, coating systems, etc. Motivated by such applications, the homotopy analysis method (HAM) was employed to<br /> obtain semi-analytical solutions for thermal convection boundary layer flow of incompressible micropolar fluid from a two-dimensional body (wedge). Viscous dissipation<br /> and heat sink effects were included. The non-dimensional boundary value problem<br /> emerges as a system of nonlinear coupled ordinary differential equations, by virtue of<br /> suitable coordinate transformations. The so-called Falkner-Skan flow cases are elaborated. Validation of the HAM solutions was achieved with earlier simpler models, as well as with a Nakamura finite difference method for the general model. The micropolar model employed simulates certain polymeric solutions quite accurately, and features rotary motions of micro-elements. Primary and secondary shear stress, wall couple stress, Nusselt number, microrotation velocity, and temperature were computed for the effect of<br /> vortex viscosity parameter (micropolar rheological), Eckert number (viscous dissipation),<br /> Falkner-Skan (pressure gradient) parameter, micro-inertia density, and heat sink parameter. The special cases of Blasius and stagnation flow were also addressed. It was observed from the study that the temperature and thermal boundary layer thickness are both suppressed with increasing wedge parameter and wall heat sink effect, which is beneficial to temperature regulation in polymer coating dynamics. Further, strong reverse spin was generated in the microrotation with increasing vortex viscosity, which resulted in<br /> increase in angular momentum boundary layer thickness. Also, both primary and secondary skin friction components were reduced with increasing wedge parameter. Nusselt number was also enhanced substantially with greater wedge parameter.

Flow of Micropolar Fluid Between Two Parallel Plates with Different Periodic Suction and Injection

The unsteady stokes flow of incompressible micropolar fluid between two porous plates is considered. The lower plate is subjected to periodic suction and different periodic injection is applied at the upper plate. Stream function for the flow is obtained and the variation of velocity function f  & g with  is shown graphically. The effects of the dimensionless parameters p, frequency parameter pt , micropolarity parameter pl and the microrotation parameter pj on the velocity functions f  and microrotation velocity function g are discussed and shown through the graphs.

On the MHD flow and heat transfer of a micropolar fluid in a rectangular duct under the effects of the induced magnetic field and slip boundary conditions

The heat and mass transfer due to the steady laminar and incompressible micropolar fluid flow through a rectangular duct with the slip flow and convective boundary conditions are numerically calculated. The fluid moves under an external magnetic field applied on a plane perpendicular to the axis of the duct. The governing nonlinear partial differential equations of momentum, microrotation, induction, and the energy are solved simultaneously by the finite difference method. The effect of various numbers and parameters such as Reynolds, magnetic Reynolds, Hartmann, coupling, Brinkman numbers, the slip flow and convective parameters are presented in graphs. Some comparisons with previous works are included.

Analysis of Entropy Generation Due to Micropolar Fluid Flow in a Rectangular Duct Subjected to Slip and Convective Boundary Conditions

The entropy generation due to steady, incompressible micropolar fluid flow in a rectangular duct with slip and convective boundary conditions (CBCs) is calculated. An external uniform magnetic field is applied which is directed arbitrarily in a plane perpendicular to the flow direction. The governing partial differential equations of momentum, angular momentum, and energy are solved numerically using finite-difference method. The obtained velocity, microrotation, and temperature distributions are then used to evaluate the entropy generation and Bejan number. The effects of various parameters on the entropy generation and Bejan number are discussed through graphs.

Stokes’ Second Problem for a Micropolar Fluid with Slip

In this paper is presented the model of an incompressible micropolar fluid flow with slip using the initial and boundary conditions when the wall velocity is considered depending on the frequency of the vibration. Regarding the boundary conditions of the velocity at the wall, we remark that there is a discontinuity of the velocity at the fluid-wall interface. The solutions for velocity and microrotation with the given conditions are obtained using the method of numerical inversion of Laplace transform.

The effects of slip condition and multiple stenoses on micropolar fluid flow through a channel of non-uniform cross-section

In this paper, steady incompressible micropolar fluid flow through a non-uniform channel with multiple stenoses is considered. Assuming the stenoses to be mild and using the slip boundary condition, the equations governing the flow of the proposed model are solved, and closed-form expressions for the flow characteristics (resistance to flow and wall shear stress) are derived. The effects of different parameters on these flow characteristics are analyzed. It is observed that both the resistance to the flow and the wall shear stress increase with the heights of the stenoses and the slip parameter; but decrease with the Darcy number. Furthermore, the effects of the wall exponent parameter, the cross-viscosity coefficient and the micropolar parameter on the flow characteristics are discussed.

Effect of Magnetic Field on Entropy Generation Due to Micropolar Fluid Flow in a Rectangular Duct

The entropy generation due to heat transfer, fluid friction and magnetic field has been calculated for the steady, incompressible micropolar fluid flow in a rectangular duct with constant wall temperatures. An external uniform magnetic field is applied which is directed arbitrarily in a plane perpendicular to the flow direction. The governing partial differential equations of momentum, angular momentum and energy are solved numerically using Finite difference method. The obtained velocity, microrotation and temperature distributions are then used to evaluate the entropy generation and Bejan number. Finally the graphs are presented to show the influence of various physical parameters on entropy generation rate and Bejan number.

Investigation of micropolar fluid flow in a helical pipe via asymptotic analysis

In this paper we study the flow of incompressible micropolar fluid through a pipe with helical shape. Pipe’s thickness and the helix step are considered as the small parameter ε. Using asymptotic analysis with respect to ε, the asymptotic approximation is built showing explicitly the effects of fluid microstructure and pipe’s distortion on the velocity distribution. The error estimate for the approximation is proved rigorously justifying the obtained model.

On the micropolar flow in a circular pipe: the effects of the viscosity coefficients

This paper considers the stationary flow of incompressible micropolar fluid through a thin cylindrical pipe governed by the pressure drop between pipe's ends. Its goal is to investigate the influence of the viscosity coefficients on the effective flow. Depending on the magnitude of viscosity coefficients with respect to the pipe's thickness, it derives different asymptotic models and discusses their properties.

Creeping flow of micropolar fluid past a porous sphere

The creeping flow of incompressible micropolar fluid past a porous sphere with permeability k is studied assuming uniform flow far away from the body. The stream function is determined by matching the solutions of Stokes equations for the flow outside the sphere with that of the Brinkman equations inside the porous sphere. The drag force experienced by the sphere is determined. The variation of drag and the streamline pattern for different values of the permeability parameter ( η), the coupling number ( N) and the micropolar parameter ( m) is studied numerically. It is observed that the drag on the porous sphere, when the fluid is micropolar is more than that of the Newtonian fluid case. The flow pattern depends on the permeability k as in the case of Newtonian fluid and on the coupling number ( N) but not on the micropolar parameter ( m).

Unsteady stokes flow of micropolar fluid between two parallel porous plates

In this paper, we consider the unsteady flow of incompressible micropolar fluid between two parallel porous plates when there is a periodic suction at the lower plate and injection at the upper plate. Stream function for the flow is obtained and the effects of microrotation parameter and frequency parameter on skin friction at the lower and upper plates are numerically studied.

Three-dimensional micropolar flow near saddle and nodal points of attachment

The steady viscous and incompressible micropolar fluid flow in the immediate neighbourhood of Saddle and Nodal points of attachment is examined. The governing equations of motion have been shown to be reducible to simultaneous ordinary third-order differential equations which contain a parameter C which is determined by the main stream flow. The numerical solutions of these equations have been computed by numerical techniques which are suitable for boundary value problems. The results have been calculated for the range −1 ≤ C ≤ 50. The accuracy of the results is checked very carefully by comparing the results on different grid sizes. The results are presented both in tabular and graphical forms.

Finite element solution of flow and heat transfer of a micropolar fluid over a stretching sheet

A steady, incompressible micropolar fluid flow and heat transfer over a stretching sheet has been analysed. The resulting system of non-linear ordinary coupled differential equations is solved by finite element method using variational Ritz model. Numerical results obtained for velocity, microrotation and temperature distributions are shown graphically.

Stagnation point micropolar fluid flow between porous discs with uniform blowing

The axially symmetric laminar incompressible micropolar fluid flow resulting from uniform blowing through two parallel discs has been investigated. The governing equations of momentum and angular momentum have been solved using shooting technique employing the method of adjoints. In comparison to the Newtonian fluid, the radial velocity decreases near the stagnation point while a contrary is observed near the plate with increase in micropolar effects in the fluid.

The rectilinear oscillations of an elliptic cylinder in incompressible micropolar fluid

The paper is a study of the flow of incompressible micropolar fluid arising from the harmonic oscillation of an elliplic cylinder parallel to either of the principal axes of its cross section. The stream function as well as the velocity and microrotation vectors are obtained and expressed in infinite series form involving Mathieu functions and functions allied to them. The drag on the cylinder is evaluated and the effect of variations of the polarity and frequency parameters on the drag as revealed by numerical studies is shown through figures.

The slow stationary flow of incompressible micropolar fluid past a spheroid

The paper examines the slow stationary flow of incompressible micropolar fluid past a spheroid (prolate and oblate) adopting the Stokesian approximation, so that the inertial terms in the momentum equation and the bilinear terms in the balance of first stress moments are neglected. The flow over the space outside the body is analyzed and the velocity, microrotation, stress and couple stress are obtained analytically in infinite series form. The drag on the body is determined and it is observed that there is no couple exerted on the body. Numerical studies are undertaken to see the variation of the drag with respect to the geometric as well as the physical flow parameters. These have been presented in the form of figures. Micropolarity of the fluid has an augmenting effect on the drag. In an Appendix, an alternative method of determining the drag is indicated.

The rectilinear oscillations of a spheroid in a micropolar fluid

The paper examines the oscillatory flow of incompressible micropolar fluid arising from the harmonic oscillation of a spheroid rectilinearly along its axis of symmetry under the assumption of small amplitude of oscillation. The velocity and microrotation are obtained and the drag experienced by the spheroid is determined. The drag parameters K and K' are numerically evaluated.

Existence of periodic solutions of the equations of incompressible micropolar fluid flow

The equations of incompressible micropolar fluid flow are a coupled system of vector differential equations involving the two basic vectors, viz. the velocity q̄ and the microrotation v̄ of the fluid elements. Let D = D ( t) be a bounded region in space, and let a flow velocity and a microrotation be prescribed at each point of the boundary of D( t). Assume that D( t) as well as the assigned velocity and microrotation vectors depend periodically on the time t and that the condition (2 μ+ k) j−4 a ⩽ 0 is satisfied (equation (25) in the text). Further assumptions are that (i) to every continuous initial distribution of the flow fields over D, there corresponds a solution of the field equations for all time t ⩾ 0 satisfying the prescribed boundary conditions; (ii) there is one solution for which the Reynolds numbers Re, Rm satisfy the condition Re 2 + Rm 2 < 80 and this solution is equicontinuous in x ̄ = (x,y,z) for all t. Then there exists a unique, stable, periodic solution of the micropolar flow equations in D( t) taking the prescribed values on the boundary. The proof of the theorem rests on a formula describing the rate of decay of the kinetic energy of the difference of two micropolar flows in the domain subject to the same boundary conditions.