• Kyungpook Mathematical Journal
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• v.61 no.2
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• pp.323-351
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• 2021

The present paper addresses magnetohydrodynamic pulsating flow and heat transfer of two immiscible, incompressible, and conducting couple stress fluids between two permeable beds. The flow between the permeable beds is assumed to be governed by Stokes' [28] couple stress fluid flow equations, whereas the dynamics of permeable beds is determined by Darcy's law. In this study, matching conditions were used at the fluid-fluid interface, whereas the B-J slip boundary condition was employed at the fluid-porous interface. The governing equations were solved analytically, and the expressions for velocity, temperature, mass flux, skin friction, and rate of heat transfer were obtained. The analytical expressions were numerically evaluated, and the results are presented through graphs and tables.

• Journal of applied mathematics & informatics
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• v.10 no.1_2
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• pp.175-191
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• 2002

The equations of a polar fluid of hydromagnetic fluctuating through a porous medium axe cast into matrix form using the state space and Laplace transform techniques the resulting formulation is applied to a variety of problems. The solution to a problem of an electrically conducting polar fluid in the presence of a transverse magnetic field and to a problem for the flow between two parallel fixed plates is obtained. The inversion of the Laplace transforms is carried out using a numerical approach. Numerical results for the velocity, angular velocity distribution and the induced magnetic field are given and illustrated graphically for each problems.

• Journal of applied mathematics & informatics
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• v.37 no.5_6
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• pp.507-519
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• 2019

The ground for this paper is to examine the generalized Stokes' first and second issues for an incompressible couple pressure liquid under isothermal conditions. Exact solutions for each problem are acquired by using the Laplace transform (LT) with respect to the time variable t and the sine Fourier transform (FT) with respect to the y-variable. Further, a comparison is given of the obtained results and the results of Devakar and Lyengar [1] and by using the four inverse Laplace transform algorithms (Stehfest's, Tzou's, Talbot, Fourier series) in the space time domain utilizing a numerical methodology. Moreover, velocity profiles are plotted and considered for various occasions and distinctive estimations of couple stress parameters. At the end, the outcomes are exhibited by graphs and in tabular forms.

• Transactions of the Korean Society of Mechanical Engineers B
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• v.23 no.8
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• pp.969-977
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• 1999

A similarity solution of a steady laminar flow of micropolar fluids past wedges has been studied. The similarity variables found by Falkner and Skan are employed to reduce the streamwise-dependence in the coupled nonlinear boundary layer equations. Numerical solutions of the equations are then obtained using the fourth-order Runge-Kutta method and the distribution of velocity, micro-rotation, shear and couple stress across the boundary layer are obtained. These results are compared with the corresponding flow problems for Newtonian fluid past wedges with various wedge angles. Numerical results show that, keeping ${\beta}$ constant, the skin friction coefficient is lower for a micropolar fluid, as compared to a Newtonian fluid. For the case of constant material parameter K, however, the velocity distribution for a micropolar fluid is higher than that of a Newtonian fluid.

• Journal of Mechanical Science and Technology
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• v.18 no.3
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• pp.491-498
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• 2004

An analysis of the plane Couette flow between two parallel plates of a viscous, incompressible, micropolar fluid is presented. Especially, the effects of non-zero values of the micro-gyration boundary condition coefficient and pressure gradient on the flow fields are studied. Numerical results show that the micro polar parameter was found to have much more of an impact on the flow behaviors. It is also observed that the micro-gyration boundary condition coefficient influenced on the coefficients of skin friction and couple stress due to its different effect on the surface stress.

• Proceedings of the KSME Conference
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• 2001.06e
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• pp.196-201
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• 2001

In this paper, we have described the microchannel fluid behavior in a slot between rotating curvilinear surfaces of revolution using micropolar fluid theory. ]n order to solve this problem, we have used boundary layer equations and applied non-zero values of the microrotation vector on the wall. The results are compared with the corresponding flow problems for Newtonian fluid. Results show that both the velocity distribution and the microrotation component distribution for a micropolar fluid are lower than that of a Newtonian fluid.

• Journal of applied mathematics & informatics
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• v.41 no.5
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• pp.1085-1102
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• 2023

In this study the magneto hydrodynamic (MHD) micro polar fluid flow of a viscous incompressible fluid past a porous medium in the presence of chemical reaction is considered. This work is devoted to investigate the Soret effect and Electromagnetic radiation effect and analyze analytically. In the energy equation the applied magnetic field strength and in the concentration equation the Soret effect are incorporated. The basic PDE (partial differential equations) are reduced to ODE (ordinary differential equations) using non dimensional variables. Then the analytical solution of the dimensionless equations are found using perturbation technique. The features of the fluid flow parameters are analyzed, discussed and explained graphically. The graphical solutions are found using MATLAB R2019b. Skin friction coefficient at the wall, Couple stress coefficient at the plate and the local surface heat flux are also thoroughly examined. Overall, this study sheds light on the complex interplay between physical parameters in the behavior of MHD micro-polar fluid past a porous medium in the presence of chemical reaction.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.9 no.2
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• pp.45-53
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• 2005

This paper investigates the influence of thermal conductivity and variable viscosity on the problem of micropolar fluid in the presence of suction or injection. The fluid viscosity is assumed to vary as an exponential function of temperature and the thermal conductivity is assumed to vary as a linear function of temperature. The governing fundamental equations are approximated by a system of nonlinear ordinary differential equations and are solved numerically by using shooting method. Numerical results are presented for the distribution of velocity, microrotation and temperature profiles within the boundary layer. Results for the details of the velocity, angular velocity and temperature fields as well as the friction coefficient, couple stress and heat transfer rate have been presented.

• Geomechanics and Engineering
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• v.10 no.4
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• pp.423-436
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• 2016

Currently, there is a great interest in the coupling between multiphase fluid flow and geomechanical effects in hydrocarbon reservoirs and surrounding rocks. The ideal solution for this coupled problem is to introduce the geomechanical effects through the stress analysis solution and implement an algorithm, which assures that the equations governing the flow and stress analyses are obeyed in each time step. This paper deals with the implementation of a program (FORTRAN90 interface code), which was developed to couple conventional reservoir (ECLIPSE) and geomechanical (ABAQUS) simulators, using a partial coupling algorithm. The explicit coupled hydro-mechanical behavior of Iranian field during depletion and $CO_2$ injection is studied using the soils consolidation procedure available in ABAQUS. Time dependent reservoir pressure fields obtained from three dimensional compositional reservoir models were transferred into finite element reservoir geomechanical models in ABAQUS as multi-phase flow in deforming reservoirs cannot be performed within ABAQUS. The FEM analysis of the reservoir showed no sign of plastic strain under production and $CO_2$ injection scenarios in any part of the reservoir and the stress paths do not show a critical behavior.

• Structural Engineering and Mechanics
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• v.59 no.1
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• pp.37-57
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• 2016

Reservoir geomechanics can play an important role in hydrocarbon recovery mechanism. In $CO_2$-EOR process, reservoir geomechanics analysis is concerned with the simultaneous study of fluid flow and the mechanical response of the reservoir under $CO_2$ injection. Accurate prediction of geomechanical effects during $CO_2$ injection will assist in modeling the Carbon dioxide recovery process and making a better design of process and production equipment. This paper deals with the implementation of a program (FORTRAN 90 interface code), which was developed to couple conventional reservoir (ECLIPSE) and geomechanical (ABAQUS) simulators, using a partial coupling algorithm. A geomechanics reservoir partially coupled approach is presented that allows to iteratively take the impact of geomechanics into account in the fluid flow calculations and therefore performs a better prediction of the process. The proposed approach is illustrated on a realistic field case. The reservoir geomechanics coupled models show that in the case of lower maximum bottom hole injection pressure, the cumulative oil production is more than other scenarios. Moreover at the high injection pressures, the production rates will not change with the injection bottom hole pressure variations. Also the FEM analysis of the reservoir showed that at $CO_2$ injection pressure of 11000 Psi the plastic strain has been occurred in the some parts of the reservoir and the related stress path show a critical behavior.