Effect of chemical reaction in a third grade fluid in porous medium analyzed by unsteady magnetohydrodynamic couette

An analysis was carried out on unsteady magnetohydrodynamic (MHD) Couette third grade fluid in a porous medium in the presence of chemical reaction parameter. The Darcy’s law and Fick’s law of diffusion were introduced to stimulate the porosity and chemical reaction in the problem. The resulting flow problem was investigated and model of the problem in form of partial differential equations were obtained. He-Laplace method was used to obtain the solution of the equations and expressions for the velocity field, temperature and concentration distribution were given for each case. Graphical results for various interesting parameters were analyzed and presented.Keywords: Plane Couette; Magnetohydrodynamic; Porous Medium; Chemical Reaction Paramete

COUETTE FLOW PROBLEM FOR AN UNSTEADY MHD THIRD-GRADE FLUID WITH HALL CURRENTS

ABSTRACT: In this work, we analyze Coutte flow problem for an unsteady mangneto-hydrodynamic (MHD) third-grade fluid in the presence of a pressure gradient and Hall currnts. Existing literature on the topic shows that the effecs of Hall current on Coutte flow of an unsteady MHD third-grade fluid with a prssure gradient has not yet been investigated. The arising non-linear problem is solved by the homotopy analysis method (HAM) and the convergence of the obtained complex series solution is carefully analyzed. The effects of pressure number, Hartmann number and Hall parameter on unsteady velocity are discussed via analysis of plots. ABSTRAK: Kajian dijalan untuk menganalisa masalah aliran Coutte bagi bendalir MHD gred ketiga dan arus Hall. Bagi topik ini kesan arus Hall terhadap aliran Couette dalam bendalir MHD gred ketiga tak mantap dengan kecerunan tekanan, belum pernah dikaji selidik.  Masalah tak linear berbangkit diselesaikan dengan kaedah analisis homotopi (HAM) dan ketumpuan solusi rangkaian kompleks dianalisa dengan teliti. Kesan nilai tekanan, nombor Hartmann dan parameter Hall terhadap halaju tak mantap diperbincangkan melalui plot yang dianalisis. KEYWORDS: Cuette; flow; hall currents; unsteady; third-grade fluid; HAM

Anomalous diffusion in rotating Casson fluid through a porous medium

This paper investigates the space-fractional anomalous diffusion in unsteady Casson fluid through a porous medium, based on an uncoupled continuous time random walk. The influences of binary chemical reaction and activation energy between two horizontal rotating parallel plates are taken into account. The governing equations of motion are reduced to a set of nonlinear differential equations by time derivatives discretization and generalized transformation, which are solved by bvp4c and implicit finite difference method (IFDM). Stability and convergence of IFDM are proved and some numerical comparisons to the previous study are presented with excellent agreement. The effects of involved physical parameters such as fractional derivative parameter, rotation parameter and time parameter are presented and analyzed through graphs. Results indicate that the increase of fractional derivative parameter triggers concentration increase near the lower plate, while it causes a reduction near the upper plate. It is worth mentioning that the decrease of heat transfer rate on the plate is observed with the higher time parameter.</p

The Effect of Variable Magnetic Field on Viscous Fluid between 3-D Rotatory Vertical Squeezing Plates: A Computational Investigation

In this paper, the 3-D squeezing flow of viscous incompressible fluid between two parallel plates rotating at the same rate is investigated. The flow is observed under the influence of the varying magnetic field. The flow phenomena are modeled by utilizing the basic governing equations, i.e., equation of continuity, coupled Navier Stokes, and Magnetic Field equations. Using appropriate similarity transformations, the resultant partial differential equations are then transformed into a system of ordinary differential equations. The computational technique is developed via the Homotopy Analysis Method (HAM) to obtain the solution of transformed systems of ordinary differential equations. The influence of several engineering fluid parameters, such as squeeze Reynolds number, magnetic field strength parameter, and magnetic Reynolds number, on velocity and magnetic field components, are observed from different graphs. It has been investigated that by increasing the squeeze Reynolds number, fluid velocity in the y and z directions will be increased as well. On the magnetic field component along the y-axis, an increasing influence of squeezing Reynolds number is also noticed. Similarly, raising the magnetic Reynolds number increases the velocity along the y-axis, whereas the inverse relationship is found for magnetic field components. Furthermore, for each flow phenomenon, an error analysis is also presented.The work of U.F.-G. was supported by the government of the Basque Country for the ELKARTEK21/10 KK-2021/00014 and ELKARTEK20/78 KK-2020/00114 research programs, respectively

Hall Current and Ion-Slip Effects on the Entropy Generation of Couple Stress Fluid with Velocity Slip and Temperature Jump

In this work, analytical study of Hall current and Ion-slip effects on the rate of entropy generation of couple stress fluid is considered. The obtained partial differential equations governing the flow are reduced to ordinary differential equations by similarity variables, semi-analytical solution of the dimensionless nonlinear coupled differential equations for velocity, temperature, entropy generation and Bejan number are constructed using Differential Transform Technique. Effects of Hall current, Ion-slip, couples stress and magnetic parameters are presented and discussed graphically. From the results it is observed that Hall current and rotation parameters enhance secondary velocity, fluid temperature and entropy generation. In addition rarefaction and Hartman number reduce fluid temperature and entropy generation

Effects of Hall Current and Rotation on Unsteady MHD Couette Flow in the Presence of an Inclined Magnetic Field

Unsteady hydromagnetic Couette flow of a viscous incompressible electrically conducting fluid in a rotating system in the presence of an inclined magnetic field taking Hall current into account is studied. Fluid flow within the channel is induced due to impulsive movement of the lower plate of the channel. Exact solution of the governing equations is obtained by Laplace transform technique. The expression for the shear stress at the moving plate is also derived. Asymptotic behavior of the solution is analyzed for small and large values of time t to highlight (i) the transient approach to the final steady state flow and (ii) the effects of Hall current, magnetic field, rotation and angle of inclination of magnetic field on the flow-field. It is found that Hall current and rotation tend to accelerate fluid velocity in both the primary and secondary flow directions. Magnetic field has retarding influence on the fluid velocity in both the primary and secondary flow directions. Angle of inclination of magnetic field has accelerating influence on the fluid velocity in both the primary and secondary flow directions

Entropy Generation of MHD Poiseuille Flow with Hall and Joule Heating Effects

In this article investigation has been conducted on the effects of Hall parameter, rotation parameter and Joule heating on the entropy generation of fully developed electrically conducting Poiseuille flow. The coupled system of ordinary differential equations for the flow are obtained, non-dimensionalised and solutions are constructed by Adomian decomposition technique. The effects of Hall current, Ion-slip, Joule heating and magnetic parameters on the velocity, temperature, entropy generation and Bejan number are explained and shown graphically. The results indicate that fluid entropy generation is induced by increase in Hall current, rotation and Joule heating parameters. Furthermore Bejan number is accelerated by Hall current, rotation, Magnetic and Joule heating parameters which signifies that heat transfer irreversibility dominates entropy generation

Effects of Rotation and Magnetic Field on Unsteady Couette Flow in a Porous Channel

Unsteady hydromagnetic Couette flow of a viscous incompressible electrically conducting fluid in a rotating system in the presence of a uniform transverse magnetic field is studied. The plates of the channel are considered porous and fluid flow within the channel is induced due to the impulsive movement of the upper plate of the channel. General solution of the governing equations is obtained which is valid for every value of time t. For small values of time t, the solution of the governing equations is obtained by Laplace transform technique. The expression for the shear stress at the stationary plate due to the primary and secondary flows is obtained in both the cases. It is found that the solution obtained by Laplace transform technique converges more rapidly than the general solution when time t is very small. Magnetic field retards the fluid flow in both the primary and secondary flow directions. Rotation retards primary flow whereas it accelerates secondary flow. There exists incipient flow reversal near the stationary plate on increasing rotation parameter K2. Suction accelerates primary flow whereas it retards secondary flow. Injection retards both the primary and secondary flows

Entropy Generation of Unsteady MHD Couette Flow through Vertical Microchannel with Hall and Ion Slip Effects

In this work, the entropy generation of unsteady hydromagnetic Couette flow through vertical microchannel has been considered, the effects of Hall current and Ion-slip are also examined. One of the plates moves with uniform velocity in the direction of the fluid flow while the other plate is stationary. The partial differential equations governing the flow are obtained and transformed to ordinary differential equations. The obtained solutions for the velocity and energy equations via differential transform technique are used to calculate the entropy generation and Bejan number. The results are presented through plots and discussed. It is noticed that primary velocity decreases with increase in Hall current, ionslip and magnetic field parameters whereas it increases as rarefaction parameter, wall-ambient temperature difference ratio, Brinkman number and Grashof number increase in values. Also secondary velocity receives a boost with increase in Hall current, Ion-slip, rarefaction parameters, wall-ambient temperature difference ratio, Brinkman and Grashof numbers. Furthermore, entropy generation is minimised as Hall current, Ion-slip and rarefaction parameters increase

Effects of Hall Current on Unsteady MHD Couette Flow of Class-II in a Rotating System

Unsteady hydromagnetic Couette flow of class-II of a viscous incompressible electrically conducting fluid in a rotating system with Hall effects in the presence of a uniform transverse magnetic field is studied. Both the fluid and plates of the channel are assumed to be at rest when time and fluid flow within the channel is induced due to non-torsional oscillations of the upper plate in its own plane with a velocity about a non-zero uniform velocity at time . Exact solution of the governing equations is obtained by Laplace transform technique. Asymptotic behavior of the solution is analyzed for small and large values of rotation parameter and magnetic parameter when time t>>1. The numerical values of the fluid velocity are depicted graphically whereas that of shear stress at the plates are presented in tabular form for various values of Hall current parameter , rotation parameter , magnetic parameter and frequency parameter