Analysis of the Momentum Transport Boundary Conditions at a Fluid-Porous Interface

2016 ◽  
Author(s):  
Hao Chen ◽  
Jiabing Wang ◽  
Kun Yang
Keyword(s):  
Composite System ◽  
Fluid Layer ◽  
Velocity Slip ◽  
Interface Condition ◽  
Free Fluid ◽  
Slip Coefficient ◽  
Porous Composite ◽  
Stress Jump ◽  
Flow Type ◽  
The Impact

The porous composite system is consists of porous medium and free fluid layer, which has extensive industrial applications. The study method for the flow field in the porous composite system includes the microscopic, mesoscopic and macroscopic approaches. When the two-domain approach is adopted, which is one of the macroscopic methods, the momentum transport boundary conditions at the interface between porous medium and free fluid layer is essential to analyze the flow field in the system. When Darcy equation is adopted to describe the flow in porous region, the Beavers-Joseph (BJ) interface condition can be used. When Darcy-Brinkman equation is adopted to describe the flow in porous region, the stress-jump (Ochoa-Tapia & Whitaker: OTW) interface condition can be used. To utilize these interface conditions, the velocity slip coefficient used in the BJ interface condition and the stress-jump coefficient used in the OTW interface condition should be specified. In this paper, a brush configuration is approximately treated as the equivalent porous media in the composite system. A numerical simulation method is used to obtain the microscopic solution for the flow in the system based on the Navier-Stokes equation applied in whole system, and an analytical method is used to obtain the corresponding macroscopic solution based on the two-domain approach. By comparing the microscopic and macroscopic solutions, the velocity slip coefficient and the stress-jump coefficient are determined since they can be treated as adjustable parameters. The influence of different flow types, including Poiseuille flow, Couette flow, and free boundary flow, are investigated. Also the impact of free fluid layer thickness and porous structure on the velocity slip coefficient and the stress-jump coefficient are discussed. The results indicate that, the velocity slip coefficient and the stress-jump coefficient are not only the parameters which depend on the porous structure, but also depend on the thickness of free fluid layer and flow type. When the thickness of free fluid layer is lower than a certain value, the impact of free fluid layer thickness on the velocity slip coefficient and the stress-jump coefficient is much obvious. In addition, when the thickness of free fluid layer is small, these coefficients are found to be dependent on the flow type. However, when the thickness of free fluid layer is large, the stress jump coefficient is independent of the thickness of free fluid layer and the flow type. Thus the stress jump coefficient obtained for a specific case can be used to predict velocity for different flow types and different thickness of free fluid layers.

Islamic Law and Society

1990 ◽  
Vol 7 (2) ◽  
pp. 177-191
Author(s):  
Louay M. Safi
Keyword(s):  
Composite System ◽  
Islamic Law ◽  
Legal Theory ◽  
Fifth Century ◽  
Muslim Community ◽  
Social Growth ◽  
The Social ◽  
Collective Experience ◽  
Law And Morality ◽  
The Impact

Shari'ah (Islamic law) has been the dominant moral and legal code ofMuslim societies for the gnxter part of their history. During the early centuriesof Islam, Shari'ah hcilitated the social growth and develojment of the Muslims,growth that culminaa in the establishment of a vast emph and an outstandmgcivilization. By the close of the fifth century of Islam, however, Shari'ahbegan to lose its role as the guiding force that inspired Muslim creativityand ingenuity and that nurtured the growing spirit of the Muslim community(Ummah). Consequently, the Ummah entered a period of stagnation thatgradually gave way to intellectual decline and social decadence. Regrettably,this painful trend continues to be more or less 'part of the individualconsciousness and collective experience of Muslims.This paper attempts to trace the development of the principles of Islamicjurisprudence, and to assess the impact of Shari'ah on society. It argues thatthe law ceased to grow by the sixth century of Islam as a result of thedevelopment of classical legal theory; more specifically, law was put on hold,as it were, after the doctrine of the infallibility of ijma' (juristic consensus)was articulated. The rigid principles of classical theory, it is contended, havebeen primarily induced by the hulty epistemology employed.by sixth-centuryjurists.Shari'ah, or Islamic law, is a comprehensive system encompassing thewhole field of human experience. It is not simply a legal system, but rathera composite system of law and morality. That is, Islamic law aspires to regulateall aspects of human activities, not only those that may entail legalconsequences. Hence, all actions and relationships are evaluated in accordancewith a scale of five moral standards.According to Shari'ah, an act may be classified as obligatory (wajib),recommended (mandub), permissible (mubah), reprehensible (makruh), orprohibited (haram). These five categories reflect the varying levels of moral ...

A Fracture Mechanics Based Parametric Study of the Copper-to-Copper Direct Thermo-Compression Bonded Interface Using Finite Element Method

2013 ◽  
Author(s):  
Ah-Young Park ◽  
Satish Chaparala ◽  
Seungbae Park
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Parametric Study ◽  
Initial Crack ◽  
Bonding Interface ◽  
Interface Condition ◽  
Large Temperature ◽  
Bonded Interface ◽  
The Impact ◽  
Element Method

Through-silicon via (TSV) technology is expected to overcome the limitations of I/O density and helps in enhancing system performance of conventional flip chip packages. One of the challenges for producing reliable TSV packages is the stacking and joining of thin wafers or dies. In the case of the conventional solder interconnections, many reliability issues arise at the interface between solder and copper bump. As an alternative solution, Cu-Cu direct thermo-compression bonding (CuDB) is a possible option to enable three-dimension (3D) package integration. CuDB has several advantages over the solder based micro bump joining, such as reduction in soldering process steps, enabling higher interconnect density, enhanced thermal conductivity and decreased concerns about intermetallic compounds (IMC) formation. Critical issue of CuDB is bonding interface condition. After the bonding process, Cu-Cu direct bonding interface is obtained. However, several researchers have reported small voids at the bonded interface. These defects can act as an initial crack which may lead to eventual fracture of the interface. The fracture could happen due to the thermal expansion coefficient (CTE) mismatch between the substrate and the chip during the postbonding process, board level reflow or thermal cycling with large temperature changes. In this study, a quantitative assessment of the energy release rate has been made at the CuDB interface during temperature change finite element method (FEM). A parametric study is conducted to analyze the impact of the initial crack location and the material properties of surrounding materials. Finally, design recommendations are provided to minimize the probability of interfacial delamination in CuDB.

Ferro-nanofluid squeeze film lubrication with heat transfer

2021 ◽  
pp. 135065012110276
Author(s):  
Manimegalai Kavarthalai ◽  
Vimala Ponnuswamy
Keyword(s):  
Heat Transfer ◽  
Heat Transfer Rate ◽  
Contact Time ◽  
Transfer Rate ◽  
Fluid Layer ◽  
Darcy Law ◽  
Squeeze Film ◽  
Mean Temperature ◽  
Special Cases ◽  
The Impact

A theoretical study of a squeezing ferro-nanofluid flow including thermal effects is carried out with application to bearings and articular cartilages. A representational geometry of the thin layer of a ferro-nanofluid squeezed between a flat rigid disk and a thin porous bed is considered. The flow behaviours and heat transfer in the fluid and porous regions are investigated. The mathematical problem is formulated based on the Neuringer–Rosensweig model for ferro-nanofluids in the fluid region including an external magnetic field, Darcy law for the porous region and Beavers–Joseph slip condition at the fluid–porous interface. The expressions for velocity, fluid film thickness, contact time, fluid flux, streamlines, pathlines, mean temperature and heat transfer rate in the fluid and porous regions are obtained by using a perturbation method. An asymptotic solution for the fluid layer thickness is also presented. The problem is also solved by a numerical method and the results by asymptotic analysis, perturbation and numerical methods are obtained assuming a constant force squeezing state and are compared. It is shown that the results obtained by all the methods agree well with each other. The effects of various parameters such as Darcy number, Beavers–Joseph constant and magnetization parameter on the flow behaviours, contact time, mean temperature and heat transfer rate are investigated. The novel results showing the impact of using ferro-nanofluids in the two applications under consideration are presented. The results under special cases are further compared with the existing results in the literature and are found to agree well.

A Novel Methodology for Thermal Analysis of a Composite System Consisting of a Porous Medium and an Adjacent Fluid Layer

2005 ◽  
Vol 127 (6) ◽  
pp. 648-656 ◽  
Author(s):  
Jung Yim Min ◽  
Sung Jin Kim
Keyword(s):  
Porous Medium ◽  
Analytical Solutions ◽  
Composite System ◽  
Numerical Solutions ◽  
Fluid Layer ◽  
Darcy Number ◽  
Jump Conditions ◽  
Interfacial Conditions ◽  
Innovative Methodology ◽  
Flux Jump

An innovative methodology is presented for the purpose of analyzing fluid flow and heat transfer in a porous–fluid composite system, where the porous medium is assumed to have a periodic structure, i.e., solid and fluid phases repeat themselves in a regular pattern. With the present method, analytical solutions for the velocity and temperature distributions are obtained when the distributions in the adjacent fluid layer are allowed to vary in the directions both parallel and perpendicular to the interface between the porous medium and the adjacent fluid layer. The analytical solutions are validated by comparing them with the corresponding numerical solutions for the case of the ideal composite channel, and with existing experimental data. The present analytical solutions have a distinctive advantage in that they do not involve any unknown coefficients resulting from the previous interfacial conditions. Moreover, by comparing interfacial conditions derived from the present study with the stress- and flux-jump conditions developed by previous investigators, the unknown coefficients included in the stress- and flux-jump conditions are analytically determined and are shown to depend on the porosity, the Darcy number and the pore diameter.

Natural Convection in a Cavity Partially Filled with a Vertical Porous Medium

2011 ◽  
Vol 321 ◽  
pp. 15-18 ◽  
Author(s):  
Fang Liu ◽  
Bao Ming Chen
Keyword(s):  
Heat Transfer ◽  
Finite Element Method ◽  
Boundary Condition ◽  
Porous Medium ◽  
Nusselt Number ◽  
Free Fluid ◽  
Stress Jump ◽  
Convection And Heat Transfer ◽  
Flow And Heat Transfer ◽  
Stress Jump Boundary Condition

The shear stress jump boundary condition that must be imposed at an interface between a porous medium and a free fluid in an enclosure is investigated. Two-domain approach is founded and finite element method is used to solve the problem. Three stress jump coefficients 0, 1, -1 are analyzed for different Rayleigh number, permeability and thickness of porous layer. Variation of Maximum stream function and Nusselt number show stronger convection and heat transfer when the stress jump coefficient is positive. There is little distinctive in flow and heat transfer when the value of coefficient is equal to 0 and -1.

Creeping Flow Relative to a Porous Spherical Shell

2000 ◽  
Vol 16 (3) ◽  
pp. 137-143
Author(s):  
Ming-Da Chen ◽  
Wang-Long Li
Keyword(s):  
Spherical Shell ◽  
Stokes Equations ◽  
Creeping Flow ◽  
Free Fluid ◽  
Fluid Interfaces ◽  
Stress Jump ◽  
The Core ◽  
Porous Spherical Shell ◽  
Darcy Equations ◽  
Shell Region

ABSTRACTIn this study, the problem of creeping flow relative to an isolated porous spherical shell has been examined. The Brinkman-extended Darcy equations and the Stokes' equations are utilized to model the flow in the porous region (shell region) and free fluid region (inside the core and outside the shell), respectively. The stress jump boundary conditions at the porous media/free fluid interfaces are included and the exact solution has been found. The drag experienced by the porous shell has been discussed for various jump parameters and shell thickness.

scholarly journals Navier slip and suction/injection effects on oscillatory flow of nanofluid with fluid-particle interaction in a channel

2021 ◽  
Vol 321 ◽  
pp. 04002
Author(s):  
Jafar Hasnain ◽  
Mariam Sheikh ◽  
Zaheer Abbas
Keyword(s):  
Oscillatory Flow ◽  
Flow Problem ◽  
Transmission Rate ◽  
Fluid Velocity ◽  
Particle Interaction ◽  
Velocity Slip ◽  
Transverse Magnetic ◽  
Navier Slip ◽  
Basic Equations ◽  
The Impact

In this paper, the slip and porosity effects on the channel walls are studied for the oscillatory flow of heat-absorbing/generating dusty nanofluid flowing through a porous medium. The channel is vertical and exposed to the transverse magnetic field and thermal radiation. The base fluid is water with silver as nanoparticles. The basic equations of the flow problem, which appeared to be dimensional, are remodelled in the dimension-less form with the help of non-dimensional variables. The obtained equations are solved analytically using the variable separable method. The graphs are presented to show the impact of these parameters on the flow fields, skin friction, heat transmission rate and discussed in detail. Results reveal that the flow velocities of fluid and particles for suction are greater than in the case of injection. The fluid velocity upsurges with the improved values of the velocity slip parameter.

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