Unsteady Micropolar Fluid Research Articles

Viscous dissipation and Joule heating effects on the unsteady micropolar fluid flow past a horizontal surface of revolution

This study aims to investigate the Joule effect, thermal radiation, and Coriolis effects in unsteady magnetohydrodynamics (MHD) micropolar flow over a 3-D unstable sheet. A magnetic field is typically applied to the surface; additionally, it is assumed that the fluid is conducting electricity. Other micro-rotations are also considered. The physical issue is resolved with the help of the fundamental equations, and the issue's complexity is reduced with the use of similarity variables. In the present approach, the homotopy analysis method (HAM) is employed. The heat, skin's friction factor, temperature, micro movements, and velocity associated with the emerging parameters and transfer rates are considered. The boundary layer thickness is increased as the parameter of vorticity increases. When the magnitude of the magnetic field increases, the skin friction coefficient decreases. The state variables are approximated up to six decimal places numerically. The numerical values of −f″(0) and −θ′(0) are computed to higher decimal places and compared with the available literature to validate the results. The outcomes obtained are compared with the available literature; the results here are corroborated, and the performance of the HAM is demonstrated.

Mathematical Study of unsteady micropolar fluid flow due to non-linear stretched sheet in the presence of magnetic field

The goal of this research is to check irregularity in heat generation, chemical reaction and thermal radiation effect an unsteady micropolar fluid flow. With the help of suitable similarity variables, the group of governing system of PDE and their associative boundary conditions are converted into the family of ODE and then solved using the HAM. The effect of various and important dimensionless parameters on the momentum, micro-rotation, energy and concentration equations have been discussed with graphical representation as well as tabular forms. It is observed that buoyancy force parameter, mixed convection parameter and permeability parameter enhance the velocity distribution while micropolar reduces the velocity profile. The temperature profiles are boosted for time and space dependent heat generation and absorption parameter respectively but reverse trend is observed for Prandtl number and unsteadiness parameter. Skin-friction factor, mass transfer rate and heat transfer rate have been listed and displayed in tables.

Micropolar Fluid Flow Along with an Inclined Riga Plate Through a Porous Medium

This study presents the one-dimensional unsteady micropolar fluid flow set in a porous medium along with an inclined infinite Riga plate. This Riga plate is created an electric and magnetic field, where a transverse Lorentz force is generated that contributes a flow along with the plate. The explicit finite difference method is used to find the solution of the non-dimensional form of the governing equations and estimated results are analyzed in terms of Microrotation parameter, Suction parameter, thermal Grashof number, mass Grashof number, Permeability parameter, Hartmann number, Dufour number, Soret number, Schmidt number. Also, the effects of the pertinent parameters on the local and average shear stress, Nusselt number, and Sherwood number are reported numerically as well as graphically.

Micropolar fluid flow in a thick domain with multiscale oscillating roughness and friction boundary conditions

We consider an unsteady micropolar fluid flow in a two-dimensional domain Ωε. The velocity field is assumed to satisfy a fluid-solid friction interface condition on a part of the boundary while the micro-rotation field satisfies non-homogeneous Dirichlet boundary conditions. The problem is thus described by a non-linear coupled variational parabolic system for the fluid velocity vϵ, the pressure pϵ and the angular micro-rotation field Zϵ. The thickness and the roughness of the fluid domain are described by multiple separated scales of periodic oscillations, i.e. Ωε={(z1,z2):0<z1<L,0<z2<εmhε(z1)} with hε(z1)=h(z1,z1ε,z1ε2,⋯,z1εm), 0<ε<<1, and m≥2. Existence, uniqueness and uniform estimates of the solution (vϵ,pϵ,Zϵ) are stated. Then we study the asymptotic behaviour of the flow as ε tends to zero by using the multiple scale convergence method for reiterated homogenization. The assumption m≥2 raises several technical difficulties in the limit process and leads to non-standard divergence free conditions for the limit velocity. We derive the limit problem which is totally decoupled for the limit velocity and pressure (v0,p0) on the one hand and the limit micro-rotation field Z0 on the other hand. More precisely (v0,p0) is solution of a variational elliptic inequality and Z0 solves an elliptic partial differential equation, where the time variable appears as a parameter. Moreover we prove that v0,p0 and Z0 are uniquely determined by auxiliary well-posed problems.

Squeezing flow analysis of MHD micropolar fluid on radial and angular velocity: A semianalytical approach

AbstractSqueezing flow of an unsteady micropolar fluid between two parallel disks has been analyzed in the current study. Transverse magnetic field and flow through the porous medium are also considered and discussed. Similarity transformation is adopted to formulate the governing equations that turn complex PDEs into nonlinear ODEs. These transformed equations are handled semianalytically by using the Adomian decomposition method (ADM). For computational purposes, various characterizing parameters are used and their behaviors are presented via plotting. Computations for the physical quantities of interest are obtained and shown in tables. The conformity of the present solution is obtained in comparison to an earlier study in a particular case and found to be in good agreement.

Magnetohydrodynamic micropolar fluid flow in presence of nanoparticles through porous plate: A numerical study

This study numerically investigates Magnetohydrodynamic (MHD) convective and chemically reactive unsteady micropolar fluid flow with nanoparticles through the vertical porous plate with mass diffusion, thermal radiation, radiation absorption and heat source. A flow model is established by employing the well-known boundary layer approximations. To obtain the non-similar equation, the boundary layer governing equations including continuity, momentum, energy and concentration balance were nondimensionalised by usual transformation. A non-similar approach is applied to the flow model. To optimize the parametric values, the stability and convergence analysis (SCA) have been analysed for the Prandtl number (Pr) and Lewis number (Le). It is observed that with initial boundary conditions, U =V =T = C= 0 and for Delta tau = 0.005, Delta X = 0.20 and Delta Y = 0.25, the system converged at Prandtl number, P-r >= 0.356 and Lewis number, L-e >= 0.16. The coupled non-linear partial differential equations are solved by explicit finite difference method (EFDM) and the numerical results have been calculated by Compaq Visual FORTRAN 6.6a. Evaluation of the thermal and momentum boundary layer thickness with isotherms and streamlines analysis of boundary layer flows have been shown for the thermal radiation parameter (R). The effects of various parameters entering the problem on velocity, angular velocity, temperature and concentration are shown graphically.

English

English

English

English

Bivariate spectral quasi-linearisation exploration of heat transfer in the boundary layer flow of micropolar fluid with strongly concentrated particles over a surface at absolute zero due to impulsive

The problem of unsteady micropolar fluid flow over a surface in which the heat energy falls at a lower limit of thermodynamic temperature scale due to impulsive is investigated. In this article, a new spectral method (BSQLM) for solving the partial differential equation is shown to unravel the heat transfer within the boundary layer. Some fluid layers at the free stream were given an impulsive motion in the horizontal direction. The thermal conductivity of the non-Newtonian fluid is assumed to be temperature dependent due to the influence of internal heat source; hence modified to suit the case of melting heat transfer following all the fundamental theories. The mathematical model was non-dimensionalised and parameterised using similarity transformation suitable to unravel the flow at short-time and long-time periods. Smooth transitions within the time frame 0 ≤ ξ ≤ 1 in the domain 0 ≤ η ≤ 1 are observed. The minimum temperature distribution is ascertained when the magnitude of Prandtl number is significantly large.

Effects of Variable Viscosity and Thermal Conductivity of Unsteady Micropolar Fluid under Mixed Convection in Presence of Uniform Magnetic Field on Stretching Surface

Effects of Variable Viscosity and Thermal Conductivity of Unsteady Micropolar Fluid under Mixed Convection in Presence of Uniform Magnetic Field on Stretching Surface

Unsteady Micropolar Fluid over a Permeable Curved Stretching Shrinking Surface

This work deals with the unsteady micropolar fluid over a permeable curved stretching and shrinking surface. Using similarity transformations, the governing boundary layer equations are transformed into the nonlinear ordinary (similarity) differential equations. The transformed equations are then solved numerically using the shooting method. The effects of the governing parameters on the skin friction and couple stress are illustrated graphically. The results reveal that dual solutions exist for stretching/shrinking surface as well as weak/strong concentration. A comparison with known results from the open literature has been done and it is shown to be in excellent agreement.

Boundary Layer Analysis of Exothermic and Endothermic Kind of Chemical Reaction in the Flow of Non-Darcian Unsteady Micropolar Fluid along an Infinite Vertical Surface

The problem of unsteady non – Newtonian flow past a vertical porous surface in the presence of thermal radiation is investigated. Using the theory of boundary layer analysis, the flow of micropolar fluid in the presence of exothermic and endothermic kind of chemical reaction is considered. It is assumed that the relationship between the flow rate and the pressure drop as the fluid flows over a porous medium is non – linear. Using local similarity transformation, the governing partial differential equations of the physical model are reduced to ordinary differential equations. The corresponding boundary value problem is solved numerically using shooting method along with Runge-Kutta Gill method together with quadratic interpolation. It is found that increase in micro-rotation parameter increases the velocity while the micro- rotation decreases across the flow region. Maximum micro-rotation of tiny particles is guaranteed at higher values of suction parameter. Local heat transfer rate decreases with an increase in exothermic /endothermic parameter.

Exact Solution of Two-Dimensional Problem of Unsteady Micropolar Fluid in the Half-Plane Subject to a Uniform Magnetic Field When the Shear Stresses are Given on the Boundary

Exact Solution of Two-Dimensional Problem of Unsteady Micropolar Fluid in the Half-Plane Subject to a Uniform Magnetic Field When the Shear Stresses are Given on the Boundary

A general formula for the drag on a sphere placed in a creeping unsteady micropolar fluid flow

In the present work, we investigate the creeping unsteady motion of an infinite micropolar fluid flow past a fixed sphere. The technique of Laplace transform is used. The drag formula is obtained in the physical domain analytically by using the complex inversion formula of the Laplace transform. The well known formula of Basset for the drag on a sphere placed in an unsteady viscous fluid flow and that of Ramkissoon and Majumdar for steady motion in the case of micropolar fluids are recovered as special cases. The obtained formula is employed to calculate the drag force for some micropolar fluid flows. Numerical results are obtained and represented graphically.

PULSATILE FLOW AND HEAT TRANSFER OF A MAGNETO-MICROPOLAR FLUID THROUGH A STENOSED ARTERY UNDER THE INFLUENCE OF BODY ACCELERATION

With an aim to investigate the effect of externally imposed body acceleration and magnetic field on pulsatile flow of blood through an arterial segment having stenosis is under consideration in this article. The flow of blood is presented by an unsteady micropolar fluid, and the heat-transfer characteristics have been taken into account. The nonlinear equations that govern the flow are solved numerically using finite difference technique by employing a suitable coordinate transformation. The numerical results have been observed for axial and microrotation component of velocity, fluid acceleration, wall shear stress (WSS), flow resistance, temperature, and the volumetric flow rate. It thus turns out that the rate of heat transfer increases with the increase of Hartmann number H, while the WSS has a reducing effect on the Hartmann number H and an enhancing effect on the ratio of viscosity K as well as on the constriction height δ.

Effect of Magnetohydrodynamic on Thin Films of Unsteady Micropolar Fluid through a Porous Medium

In This paper, we deal with the study of the effect of magnetohydrodynamic on thin films of unsteady micropolar fluid through a porous medium. These Thin films are considered for three different geometries. The governing continuity, momentum and angular momentum equations are converted into a system of non-linear ordinary differential equations by means of similarity transformation. The resulting system of coupled non-linear ordinary differential equations is solved numerically by using shooting method. A representative set of numerical results in the three thin film flow problems for velocity and micro-rotation profiles are discussed and presented graphically. A comprehensive parametric study is carried out to show the effects of the micropolar fluid parameters, magnetic field parameter, permeability parameter and etc. on the obtained solutions.