• Journal of Mechanical Science and Technology
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• v.16 no.7
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• pp.959-965
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• 2002

Effective hydraulic conductivity of a statistically anisotropic heterogeneous medium is obtained for steady two-dimensional flows employing stochastic analysis. Flow equations are solved up to second order and the effective conductivity is obtained in a semi-analytic form depending only on the spatial correlation function and the anisotropy ratio of the hydraulic conductivity field, hence becoming a true intrinsic property independent of the flow field. Results are obtained using a statistically anisotropic Gaussian correlation function where the anisotropy is defined as the ratio of integral scales normal and parallel to the mean flow direction. Second order results indicate that the effective conductivity of an anisotropic medium is greater than that of an isotropic one when the anisotropy ratio is less than one and vice versa. It is also found that the effective conductivity has upper and lower bounds of the arithmetic and the harmonic mean conductivities.

• Journal of applied mathematics & informatics
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• v.26 no.1_2
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• pp.161-176
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• 2008

The effect of variable viscosity on MHD mixed convection Hiemenz flow over a thermally stratified porous wedge plate has been studied in the presence of suction or injection. The wall of the wedge is embedded in a uniform Darcian porous medium in order to allow for possible fluid wall suction or injection and has a power-law variation of the wall temperature. An approximate numerical solution for the steady laminar boundary-layer flow over a wall of the wedge in the presence of thermal diffusion has been obtained by solving the governing equations using numerical technique. The fluid is assumed to be viscous and incompressible. Numerical calculations are carried out for different values of dimensionless parameters and an analysis of the results obtained shows that the flow field is influenced appreciably by the magnetic effect, variable viscosity, thermal stratification and suction / injection at wall surface. Effects of these major parameters on the transport behaviors are investigated methodically and typical results are illustrated to reveal the tendency of the solutions. Comparisons with previously published works are performed and excellent agreement between the results is obtained.

• Journal of computational fluids engineering
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• v.21 no.4
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• pp.19-27
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• 2016

The flow analyses through a porous hydraulic fractures is among the most important tasks in recently developed shale reservoirs but is rendered difficult by non-Darcy effects and geometric changes in the hydraulic fractures during production. In this study, several Computational Fluid Dynamics(CFD) models of hydraulic fractures, with a simple shape such as that of parallel plates, filled with proppants were built. Direct Numerical Simulation(DNS) analyses were then carried out to examine the flow loss characteristics of the fractures. The hydraulic diameters for the simulation models were calculated using the DNS results, and then they were compared with the results from Kozeny's definition of hydraulic diameter which is most widely used in the flow analysis field. Also, the characteristic parameters based on both hydraulic diameters were estimated for the investigation of the flow loss variation features. Consequently, it was checked in this study that the hydraulic diameter based on Kozeny's definition is not accordant to the results from the DNS analyses, and the case using the CFD results exhibits f Re robustness like general pipe flows, whereas the other case using Kozeny's definition doesn't. Ultimately, it is expected that discoveries reported in this study would help further porous flow analyses such as hydraulic fracture flows.

• 한국전산유체공학회:학술대회논문집
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• 2004.03a
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• pp.183-189
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• 2004

The flow and the heat transfer about the cross-flow fin-tube heat exchanger in an out-door unit of a heat pump system has been numerically Investigated. Using the general purpose analysis code, FLUENT, the Navier-Stokes equations and the energy equation are solved for the three dimensional computation domain that encompasses multiple rows of the fin-tube. The temperature on the fin and tube surface is assumed constant but compensated later through the fin efficiency when predicting the heat-transfer rate. The contact resistance is also taken into consideration. The flow and temperature fields for a wide range of inlet velocity and fin-tube arrangements are examined and the results are presented in the paper. The details of the flow are very well captured and the heat transfer rate for a range of inlet velocity is in excellent agreement with the measured data. The flow solution provides the effective permeability and the inertial resistance factor of the heat exchanger if the exchanger were to be approximated by the porous medium. This information is essential in carrying out the global flow field calculation which, in turn, provides the inlet velocity lot the microscopic temperature-field calculation of the heat exchanger unit.

• Journal of applied mathematics & informatics
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• v.42 no.3
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• pp.607-623
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• 2024

This article studies the effects of heat generation/absorption and thermal radiation on the unsteady magnetohydrodynamic (MHD) Casson fluid flow past a vertical plate through rotating porous medium with constant temperature and mass diffusion. It is assumed that the plate temperature and concentration level are raised uniformly. For finding the exact solution, a set of non-dimensional partial differential equations is solved analytically using the Laplace transform technique. The influence of various non-dimensional parameters on the velocity are discussed, including the effects of the magnetic parameter M, heat generation/absorption Q, thermal radiation parameter R, Prandtl number Pr, Schmidt number Sc, permeability of porous medium parameter, Casson fluid parameter γ, on velocity, temperature, and concentration profiles, which are discussed through several figures. It is found that velocity, temperature, and concentration profiles in the case of heat generation parameter Q, Casson fluid parameter γ, thermal Grashof number Gr, mass Grashof number Gc, Permeability Porous medium parameter K, and time t have retarding effects. It is also seen that the magnetic field M, Thermal Radiation parameter R, Prandtl field Pr, Schmidt number Sc have reverse effects on it.

• Transactions of the Korean Society of Mechanical Engineers B
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• v.22 no.5
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• pp.708-715
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• 1998

The shelter effect of a porous wind fence on a triangular prism was experimentally investigated in a circulating water channel. A porous fence of porosity .epsilon.=38.5% was installed in front of the prism model. The fence and prism model were embedded in a turbulent boundary layer. The instantaneous velocity fields around the fence and prism model were measured by using the instantaneous velocity fields around the fence and prism model were measured by using the 2-frame PTV(Particle Tracking Velocimetry) system. By installing the fence in front of the prism, the recirculation flow region decreases compared with that of no fence case. The porous fence also decreases the mean velocity, turbulent intensity and turbulent kinetic energy around the prism. Especially, at the top of the prism, the turbulent kinetic energy is about half of that without the fence.

• The KSFM Journal of Fluid Machinery
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• v.20 no.2
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• pp.11-16
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• 2017

The accurate prediction of leakage flow through the brush element of brush seal at the steam turbine is important to find optimum design parameters for increasing an efficiency. In this study, CFD analysis method using commercial software FLUENT is proposed to predict leakage through the brush element. Since the brush element has a complex three-dimensional shape with many bristle assemblies, it is difficult to analyze the flow field. Therefore, if the brush element is assumed to be porous medium region, the analysis time can be shortened. Two determination methods of resistance coefficients of the Darcian porous medium equation are suggested. By comparing the 2D and 3D CFD analysis results for the leakage of the brush element using the two resistance coefficient determination methods, the effectiveness of the analysis for the porous medium assumption is proved.

• 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.

• Transactions of the Korean Society of Automotive Engineers
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• v.15 no.1
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• pp.78-88
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• 2007

In the present study a detailed examination of various porous media models for predicting filtration efficiency and pressure drop of diesel particulate filter (DPF), such as sphere-in-cell and constricted tube models, are attempted. In order for demonstrating their validities of correct estimation on permeability, geometry of property configurations common in commercial cordierite DPFs are correlated to the porous media flow models, and validations of predicted filtration efficiencies due to the use of different unit collectors are made with experiments. The result shows that the porosity, pore size and permeability of cordierite DPF can be successfully correlated by Kuwabara flow field with correction factor of 0.6. The unit collector efficiency predicted by sphere-in-cell model agrees very well with measurements in accumulation mode, whereas that by constricted tube model with significant prediction error.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.11 no.1
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• pp.1-11
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• 2007

A linear stability analysis applied to a system consist of a horizontal fluid layer overlying a layer of a porous medium affected by a vertical magnetic field on both layers. Flow in porous medium is assumed to be governed by Darcy's law. The Beavers-Joseph condition is applied at the interface between the two layers. Numerical solutions are obtained for stationary convection case using the method of expansion of Chebyshev polynomials. It is found that the spectral method has a strong ability to solve the multilayered problem and that the magnetic field has a strong effect in his model.