• Transactions of the Korean Society of Mechanical Engineers B
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• v.24 no.12
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• pp.1635-1643
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• 2000

The present work investigates a heat transfer phenomenon at the interface between a porous medium and an impermeable wall. In an effort to appropriately describe the heat transfer phenomenon at the interface, the heat transfer at the interface between the microchannel heat sink, which is an ideally organized porous medium, and the finite-thickness substrate is examined. From the examination, it is clarified that the he heat flux distribution at the interface is not uniform for the impermeable wall with finite thickness. On the other hand, the first approach, based on the energy balance for the representative elementary volume in the porous medium, is physically reason able. When the first approach is applied to the thermal boundary condition, and additional boundary condition based on the local thermal equilibrium assumption at the interface is used. This additional boundary condition is applicable except for the very th in impermeable wall. Hence, for practical situations, the first approach in combination with the local thermal equilibrium assumption at the interface is suggested as an appropriate thermal boundary condition. In order to confirm our suggestion, convective flows both in a microchannel heat sink and in a sintered porous channel subject to a constant heat flux condition are analyzed. The analytically obtained thermal resistance of the microchannel heat sink and the numerically obtained overall Nusselt number for the sintered porous channel are shown to be in close agreement with available experimental results when our suggestion for the thermal boundary conditions is applied.

• Proceedings of the KSME Conference
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• 2007.05b
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• pp.2261-2266
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• 2007

In this study, the numerical analysis to estimate condensation heat and mass transfer of the condenser was carried out using the PMA (porous medium approach). In the PMA, the details of tube bundle in the condenser are replaced by the porous medium, and the flow resistance term is added in the momentum equation. In this regard, the PMA is quite helpful for the study of tube bundle in the large condenser. The pressure loss through tube bundle can be compensated by viscous and inertial momentum sink terms, which was validated numerically. Value of the pressure drop was compared to that of Butterworth correlation. Three dimensional analysis of condensation for McAllister condenser with the PMA was conducted using Fluent 6.2 and UDFs (use-defined functions). The result of condensation rate was analogous to previous results (experimental and numerical data).

• 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.

• Proceedings of the KSME Conference
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• 2000.04b
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• pp.57-64
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• 2000

The present work investigates the heat transfer characteristics for laminar fully developed forced convection in an internally finned tube with axially uniform heat flux and peripherally uniform temperature through analytical models of convection in a porous medium. Using the Brinkman-extended Darcy flow model and the two equation model fur heat transfer, analytical solutions fur fluid flow and heat transfer are obtained and compared with the exact solution for fluid flow and the numerical solutions for conjugate heat transfer to validate the porous medium approach. Using the analytical solutions, parameters of engineering importance are identified and their effects on fluid flow and heat transfer are studied. Also, the expression fur total thermal resistance is derived from the analytical solutions and minimized in order to optimize the thermal performance of the internally finned tubes.

• Interaction and multiscale mechanics
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• v.1 no.1
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• pp.83-101
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• 2008

A derivation is given of two-scale models that are able to describe deformation and flow in a fluid-saturated and progressively fracturing porous medium. From the micromechanics of the flow in the cavity, identities are derived that couple the local momentum and the mass balances to the governing equations for a fluid-saturated porous medium, which are assumed to hold on the macroscopic scale. By exploiting the partition-of-unity property of the finite element shape functions, the position and direction of the fractures are independent from the underlying discretization. The finite element equations are derived for this two-scale approach and integrated over time. The resulting discrete equations are nonlinear due to the cohesive crack model and the nonlinearity of the coupling terms. A consistent linearization is given for use within a Newton-Raphson iterative procedure. Finally, examples are given to show the versatility and the efficiency of the approach.

• Journal of the Korean Society for Aeronautical & Space Sciences
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• v.34 no.9
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• pp.89-96
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• 2006

In this study, fluid flow and thermal characteristics in a catalyst bed for nitrous oxide catalytic decomposition which is introduced as a hybrid rocket ignition system for small satellites were theoretically considered. To analyze the thermal phenomena of the catalyst bed, a so-called porous medium approach has been opted for modeling the honeycomb geometry of the catalyst bed. Using a Brinkman-extended Darcy model for fluid flow and the one-equation model for heat transfer, the analytical solutions for both velocity and temperature distributions in the catalyst bed are obtained and compared with experimental data to validate the porous medium approach. Based on the analytical solutions, parameters of engineering importance are identified to be the porosity of the catalyst bed, effective volumetric ratio, the ratio of the radius of the catalyst bed to the radius of a pore, heat flux generated by a heater, and pumping power. Their effects on thermal phenomena of the catalyst bed are studied.

• Steel and Composite Structures
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• v.38 no.5
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• pp.523-531
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• 2021

The generalized thermoelastic analysis problem of a two-dimension porous medium with and without energy dissipation are obtained in the context of Green-Naghdi's (GNIII) model. The exact solutions are presented to obtain the studying fields due to the pulse heat flux that decay exponentially in the surface of porous media. By using Laplace and Fourier transform with the eigenvalues scheme, the physical quantities are analytically presented. The surface is shocked by thermal (pulse heat flux problems) and applying the traction free on its outer surfaces (mechanical boundary) through transport (diffusion) process of temperature to observe the analytical complete expression of the main physical fields. The change in volume fraction field, the variations of the displacement components, temperature and the components of stress are graphically presented. Suitable discussion and conclusions are presented.

• Geomechanics and Engineering
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• v.23 no.3
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• pp.217-225
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• 2020

In this paper, the thermoelastic interactions in a two-dimension porous body are studied. This problem is solved by using the Green and Lindsay (GL) generalized thermoelasticity model under fractional time derivative. The derived approaches are estimated. with numeral results which are applied to the porous mediums in simplifying geometrical. The bounding plane surface of the present half-space continuum is subjected to a pulse heat flux. We use the Laplace-Fourier transforms methods with the eigenvalues approach to solve the problem. The numerical solutions for the field functions are obtained numerically using the numerical Laplace inversion technique. The effects of the fractional parameter and the thermal relaxation times on the temperature field, the displacement field, the change in volume fraction field of voids distribution and the stress fields have been calculated and displayed graphically and the obtained results are discussed.

• 유체기계공업학회:학술대회논문집
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• 2003.12a
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• pp.115-120
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• 2003

In this work, a continuous-flow micro-PCR system is systematically designed. From the numerical simulation based on the finite volume method, adapting oneself to a new environmental temperature without an external temperature controller is shown to be possible and a cooler as well as a heater is shown to be necessary to obtain three individual temperature zones for polymerase chain reaction. In addition, appropriate geometry of a heat sink for the cooler is determined by using a compact modeling method, the porous medium approach.

• Proceedings of the Korean Radioactive Waste Society Conference
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• 2005.06a
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• pp.231-238
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• 2005

On the basis of flow resistance theory the conceptual model and related mathematical descriptions is proposed for resistance modeling of groundwater flow in CPM(continuum Porous medium), DFN(discrete fracture network) and fractured-porous medium. The proposed model is developed on the basis of finite volume method assuming steady-state, constant density groundwater flow. The basic approach of the method is to evaluate inter-block flow resistance values for a staggered grid arrangement, i.e. fluxes are stored at cell walls and scalars at cell centers. The balance of forces, i.e. the Darcy law, is utilized for each control volume centered around the point where the velocity component is stored. The transmissivity (or permeability) at the interface is assumed to be the harmonic average of neighboring blocks. Flow resistance theory was utilized to relate the fluxes between the grid blocks with residual pressures. The flow within porous medium is described by three dimensional equations and that within an individual fracture is described by a two dimensional equivalent of the flow equations for a porous medium. Newly proposed models would contribute to develop flow simulation techniques with various matrix characteristics.