scholarly journals MHD Flow of the Micropolar Fluid between Eccentrically Rotating Disks

2014 ◽  
Vol 2014 ◽  
pp. 1-7 ◽  
Author(s):  
Neetu Srivastava
Keyword(s):  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Micropolar Fluid ◽  
Flow Characteristic ◽  
Flow Characteristics ◽  
Mhd Flow ◽  
Analytical Investigation ◽  
Strong Interactions ◽  
Rotating Disks ◽  
Incompressible Micropolar Fluid

This analytical investigation examines the magnetohydrodynamic flow problem of an incompressible micropolar fluid between the two eccentrically placed disks. Employing suitable transformations, the flow governing partial differential equations is reduced to ordinary differential equations. An exact solution representing the different flow characteristic of micropolar fluid has been derived by solving the ordinary differential equations. Analysis of the flow characteristics of the micropolar fluid has been done graphically by varying the Reynolds number and the Hartmann number. This analysis has been carried out for the weak and strong interactions.

scholarly journals Unsteady viscous MHD flow over a permeable curved stretching/shrinking sheet

2016 ◽  
Vol 26 (8) ◽  
pp. 2370-2392 ◽  
Author(s):  
Ioan Pop ◽  
Siti Suzilliana Putri Mohamed Isa ◽  
Norihan M. Arifin ◽  
Roslinda Nazar ◽  
Norfifah Bachok ◽  
...  
Keyword(s):  
Magnetic Field ◽  
Boundary Layer ◽  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Nonlinear Partial Differential Equations ◽  
Flow Characteristics ◽  
Mhd Flow ◽  
Integration Scheme ◽  
Shrinking Sheet ◽  
Content Type

Purpose The purpose of this paper is to theoretically study the problem of the unsteady boundary layer flow past a permeable curved stretching/shrinking surface in the presence of a uniform magnetic field. The governing nonlinear partial differential equations are converted into ordinary differential equations by similarity transformation, which are then solved numerically. Design/methodology/approach The transformed system of ordinary differential equations was solved using a fourth-order Runge-Kutta integration scheme. Results for the reduced skin friction coefficient and velocity profiles are presented through graphs and tables for several sets of values of the governing parameters. The effects of these parameters on the flow characteristics are thoroughly examined. Findings Results show that for the both cases of stretching and shrinking surfaces, multiple solutions exist for a certain range of the curvature, mass suction, unsteadiness, stretching/shrinking parameters and magnetic field parameter. Originality/value The paper describes how multiple (dual) solutions for the flow reversals are obtained. It is shown that the solutions exist up to a critical value of the shrinking parameter, beyond which the boundary layer separates from the surface and the solution based upon the boundary layer approximations is not possible.

Numerical Solution for Boundary Layer Flow of a Dusty Micropolar Fluid Due to a Stretching Sheet with Constant Wall Temperature

2021 ◽  
Vol 87 (1) ◽  
pp. 30-40
Author(s):  
Anisah Dasman ◽  
Abdul Rahman Mohd Kasim ◽  
Iskandar Waini ◽  
Najiyah Safwa Khashi’ie
Keyword(s):  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Wall Temperature ◽  
Micropolar Fluid ◽  
Stretching Sheet ◽  
Numerical Solutions ◽  
Numerical Study ◽  
Particle Interaction ◽  
Dust Particles ◽  
Constant Wall Temperature

This paper aims to present the numerical study of a dusty micropolar fluid due to a stretching sheet with constant wall temperature. Using the suitable similarity transformation, the governing partial differential equations for two-phase flows of the fluid and the dust particles are reduced to the form of ordinary differential equations. The ordinary differential equations are then numerically analysed using the bvp4c function in the Matlab software. The validity of present numerical results was checked by comparing them with the previous study. The results graphically show the numerical solutions of velocity, temperature and microrotation distributions for several values of the material parameter K, fluid-particle interaction parameter and Prandtl number for both fluid and dust phase. The effect of microrotation is investigated and analysed as well. It is found that the distributions are significantly influenced by the investigated parameters for both phases.

scholarly journals Analytical Solution to the MHD Flow of Micropolar Fluid Over a Linear Stretching Sheet

2015 ◽  
Vol 20 (2) ◽  
pp. 397-406 ◽  
Author(s):  
P.G. Siddheshwar ◽  
U.S. Mahabaleshwar
Keyword(s):  
Numerical Methods ◽  
Analytical Solution ◽  
Differential Equations ◽  
Boundary Conditions ◽  
Micropolar Fluid ◽  
Stretching Sheet ◽  
Perturbation Technique ◽  
Mhd Flow ◽  
Regular Perturbation ◽  
Linear Differential

Abstract The flow due to a linear stretching sheet in a fluid with suspended particles, modeled as a micropolar fluid, is considered. All reported works on the problem use numerical methods of solution or a regular perturbation technique. An analytical solution is presented in the paper for the coupled non-linear differential equations with inhomogeneous boundary conditions.

scholarly journals Mixed Convective Flow and Heat Transfer of a Dual Stratified Micropolar Fluid Induced by a Permeable Stretching/Shrinking Sheet

Entropy ◽  
2019 ◽  
Vol 21 (12) ◽  
pp. 1162 ◽  
Author(s):  
Najiyah Safwa Khashi’ie ◽  
Norihan Md Arifin ◽  
Roslinda Nazar ◽  
Ezad Hafidz Hafidzuddin ◽  
Nadihah Wahi ◽  
...  
Keyword(s):  
Heat Transfer ◽  
Differential Equations ◽  
Micropolar Fluid ◽  
Convective Flow ◽  
Mhd Flow ◽  
Similarity Solutions ◽  
Surface Velocity ◽  
Shrinking Sheet ◽  
Transfer Characteristics ◽  
Flow And Heat Transfer

The present study accentuates the magnetohydrodynamics (MHD) flow and heat transfer characteristics of a dual stratified micropolar fluid over a permeable stretching/shrinking sheet. Thermal and solutal buoyancy forces are also included to incorporate with the stratification effect. Similarity, transformation is applied to reduce the governing model (partial differential equations) into a set of nonlinear ordinary differential equations (ODEs) due to its complexity. Using bvp4c solver in the MATLAB software, numerical results for some limiting cases are in favorable agreement with the earlier published results. Both assisting and opposing buoyancy flows have dual similarity solutions within specific range of suction and stretching/shrinking parameters, whereas only a distinctive solution is observed for pure forced convective flow. The micropolar fluid shows a disparate pattern of flow, heat and mass transfer characteristics between stretching and shrinking cases. Unlike the shrinking flow, the surface velocity gradient, local Nusselt and Sherwood numbers for stretching flow intensify with the increment of the material parameter. The result from stability analysis reveals that the first solution is the real solution, whereas the second solution is virtual.

scholarly journals MHD Flow of a Micropolar Fluid past a Stretched Permeable Surface with Heat Generation or Absorption

2009 ◽  
Vol 14 (1) ◽  
pp. 27-40 ◽  
Author(s):  
M.-E. M. Khedr ◽  
A. J. Chamkha ◽  
M. Bayomi
Keyword(s):  
Differential Equations ◽  
Heat Generation ◽  
Micropolar Fluid ◽  
Radiation Effects ◽  
Mhd Flow ◽  
Skin Friction Coefficient ◽  
Permeable Surface ◽  
Physical Parameters ◽  
Special Cases ◽  
Heat Generation Or Absorption

This work considers steady, laminar, MHD flow of a micropolar fluid past a stretched semi-infinite, vertical and permeable surface in the presence of temperature dependent heat generation or absorption, magnetic field and thermal radiation effects. A set of similarity parameters is employed to convert the governing partial differential equations into ordinary differential equations. The obtained self-similar equations are solved numerically by an efficient implicit, iterative, finite-difference method. The obtained results are checked against previously published work for special cases of the problem in order to access the accuarcy of the numerical method and found to be in excellent agreement. A parametric study illustrating the influence of the various physical parameters on the skin friction coefficient, microrotaion coefficient or wall couple stress as well as the wall heat transfer coefficient or Nusselt number is conducted. The obtained results are presented graphically and in tabular form and the physical aspects of the problem are discussed.

A note on some solutions of micropolar fluid in a channel with permeable walls

2018 ◽  
Vol 14 (1) ◽  
pp. 91-101 ◽  
Author(s):  
Jawad Raza ◽  
Azizah M. Rohni ◽  
Zurni Omar
Keyword(s):  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Micropolar Fluid ◽  
Design Methodology ◽  
Shooting Method ◽  
Similarity Transformation ◽  
Physical Parameters ◽  
Content Type ◽  
Single Solution ◽  
Permeable Walls

Purpose The purpose of this paper is to investigate different branches of the solution of micropolar fluid in a channel with permeable walls. Moreover, the intention of the study is to examine the effect of different physical parameters on fluid flow. Design/methodology/approach The mathematical modeling is performed on the basis of law of conservation of mass, momentum and angular momentum. The governing partial differential equations were transformed into ordinary differential equations by applying suitable similarity transformation. Afterwards, the set of nonlinear ordinary differential equations was solved numerically by a shooting method. Findings The study reveals that various branches of the solution of the proposed problem exist only in the case of strong suction. Originality/value The investigation of new branches of the solution of non-Newtonian micropolar fluid is relatively difficult as far as the single solution is concern. This study explores the new branches of the solution of a micropolar fluid in a channel with suction/injection. Simultaneous effect of suction Reynolds number and vortex viscosity parameter on velocity and micro-rotation profile is examined for different branches of solution in order to make the analysis more interesting.

MHD FLOW OF AN EYRING-POWELL FLUID WITH THE EFFECT OF THERMAL RADIATION, JOULE HEATING AND VISCOUS DISSIPATION

2020 ◽  
Vol 9 (11) ◽  
pp. 9259-9271
Author(s):  
K.R. Babu ◽  
G. Narender ◽  
K. Govardhan
Keyword(s):  
Differential Equations ◽  
Thermal Radiation ◽  
Ordinary Differential Equations ◽  
Viscous Dissipation ◽  
Joule Heating ◽  
Mhd Flow ◽  
Physical Parameters ◽  
Shooting Technique ◽  
Similarity Transformations ◽  
The Magnetic Field

A two-dimensional stream of an magnetohydrodynamics (MHD) Eyring-Powell fluid on a stretching surface in the presence of thermal radiation, viscous dissipation and the Joule heating is analyzed. The flow model in the form of the Partial Differential Equations (PDEs) is transformed into a system of non-linear and coupled Ordinary Differential Equations (ODEs) by implementing appropriate similarity transformations. The resulting ordinary differential equations are solved numerically by the shooting technique with Adams-Moulton Method of fourth order. The numerical solution obtained for the velocity and temperature profiles has been presented through graphs for different choice of the physical parameters. The magnetic field is found to have a direct relation with the temperature profile and an inverse with the velocity profile. Increasing the thermal radiation, the temperature tends to rise.

Effect of temperature on the MHD stagnation-point flow past an isothermal plate for a Boussinesquian Newtonian and micropolar fluid

2018 ◽  
Vol 28 (6) ◽  
pp. 1315-1334 ◽  
Author(s):  
Alessandra Borrelli ◽  
Giulia Giantesio ◽  
Maria Cristina Patria
Keyword(s):  
Magnetic Field ◽  
External Magnetic Field ◽  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Stagnation Point ◽  
Micropolar Fluid ◽  
Stagnation Point Flow ◽  
Content Type ◽  
Environment Temperature ◽  
Uniform External Magnetic Field

Purpose This paper aims to analyze the steady two-dimensional stagnation-point flow of an electrically conducting Newtonian or micropolar fluid when the obstacle is uniformly heated. Design/methodology/approach The governing boundary layer equations are transformed into a system of ordinary differential equations using appropriate similarity transformations. Some analytical considerations about existence and uniqueness of the solution are obtained. The system is then solved numerically using the bvp4c function in MATLAB. Findings If the temperature of the obstacle Tw coincides with the environment temperature T0, then the motion reduces to the usual orthogonal stagnation-point flow; if Tw = T0, then it is necessary to include in the similarity function describing the velocity an oblique part due to the temperature. Also, the presence of a uniform external magnetic field orthogonal to the obstacle is examined. In all cases, the motion is reduced to a system of nonlinear ordinary differential equations with boundary conditions, whose solution is discussed numerically when the Prandtl and the Hartmann number varies. Originality/value The present results are original and new for the problem of magnetohydrodynamic mixed convection in the plane stagnation-point flow of a Newtonian or a micropolar fluid over a vertical flat plate. At infinity, the motion approaches the orthogonal stagnation-point flow of an inviscid fluid; the effect of an uniform external magnetic field is considered, and the obstacle has a uniform temperature.

Stokes’ first problem for MHD flow of Casson nanofluid

2017 ◽  
Vol 13 (1) ◽  
pp. 2-10
Author(s):  
Syed Tauseef Mohyud-din ◽  
Umar Khan ◽  
Naveed Ahmed ◽  
M.M. Rashidi
Keyword(s):  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Mhd Flow ◽  
Governing Equations ◽  
Content Type ◽  
Buongiorno’S Model ◽  
Linear Ordinary Differential Equations ◽  
Flux Condition ◽  
Non Linear ◽  
Flow Heat

Purpose The purpose of this paper is to present investigation of the flow, heat and mass transfer of a nanofluid over a suddenly moved flat plate using Buongiorno’s model. This study is different from some of the previous studies as the effects of Brownian motion and thermophoresis on nanoparticle fraction are passively controlled on the boundary rather than actively. Design/methodology/approach The partial differential equations governing the flow are reduced to a system of non-linear ordinary differential equations. Viable similarity transforms are used for this purpose. A well-known numerical scheme called Runge-Kutta-Fehlberg method coupled with shooting procedure has been used to find the solution of resulting system of equations. Discussions on the effects of different emerging parameters are provided using graphical aid. A table is also given that provides the results of different parameters on local Nusselt and Sherwood numbers. Findings A revised model for Stokes’ first problem in nanofluids is presented in this paper. This model considers a zero flux condition at the boundary. Governing equations after implementing the similarity transforms get converted into a system of non-linear ordinary differential equations. Numerical solution using RK-Fehlberg method is also carried out. Emerging parameters are analyzed graphically. Figures indicate a quite significant change in concentration profile due to zero flux condition at the wall. Originality/value This work can be extended for other problems involving nanofluids for the better understanding of different properties of nanofluids.

The analysis of the flow of a micropolar fluid between two orthogonally moving porous disks with counter rotating directions

Open Physics ◽  
2013 ◽  
Vol 11 (5) ◽  
Author(s):  
Yina Sun ◽  
Xinhui Si ◽  
Liancun Zheng ◽  
Yanan Shen ◽  
Xinxin Zhang
Keyword(s):  
Reynolds Number ◽  
Differential Equations ◽  
Micropolar Fluid ◽  
Flow Behavior ◽  
Angular Speed ◽  
Expansion Ratio ◽  
Physical Parameters ◽  
Analysis Method ◽  
Rotating Disks ◽  
Homotopy Analysis

AbstractThe present work investigates the unsteady, imcompressible flow of a micropolar fluid between two orthogonally moving porous coaxial disks. The lower and upper disks are rotating with the same angular speed in counter directions. The flows are driven by the contraction and the rotation of the disks. An extension of the Von Kármán type similarity transformation is proposed and is applied to reduce the governing partial differential equations (PDEs) to a set of non-linear coupled ordinary differential equations (ODEs) in dimensionless form. These differential equations with appropriate boundary conditions are responsible for the flow behavior between large but finite coaxial rotating disks. The analytical solutions are obtained by employing the homotopy analysis method. The effects of some various physical parameters like the expansion ratio, the rotational Reynolds number, the permeability Reynolds number, and micropolar parameters on the velocity fields are observed in graphs and discussed in detail.

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