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The purpose of this paper is to implement the numerical analysis based on finite volume method to compare the effects of stress-jump (SJ) and stress-continuity (SC) conditions on flow structure around and through a porous circular cylinder.

In this study, a steady flow of a viscous, incompressible fluid around and through a porous circular cylinder of diameter “D,” using Darcy-Brinkman-Forchheimer’s equation in the porous region, is discussed. The SJ condition proposed by Ochoa-Tapia and Whitaker is applied at the porous-fluid interface and compared with the traditional interfacial condition based on the SC condition in fluid and porous media. Equations with the relevant boundary conditions are numerically solved using a finite volume approach. In this study, Reynolds and Darcy numbers are varied within the ranges of 1 < Re < 40 and 10-7 < Da < 10-2, respectively, and the porosities are e=0.45, 0.7 and 0.95.

Results show that the SJ condition leads to a much smaller boundary layer within porous medium near the interface as compared to the SC condition. Two interfacial conditions yield similar results with decrease in porosity.

There is no published research in the literature about the effects of important parameters, such as Porosity and Darcy numbers on different fluid-porous interface conditions for a porous cylinder and comparison the effects of SJ and SC conditions on flow structure around and through a porous circular cylinder.

The lattice Boltzmann simulation of fluid flow in partial porous geometries with curved porous-fluid interfaces has not been investigated yet. It is mainly because of the lack of a method in the lattice Boltzmann framework to model the hydrodynamic compatibility conditions at curved porous-fluid interfaces, which is required for the two-domain approach. Therefore, the purpose of this study is to develop such a method.

This research extends the non-equilibrium extrapolation lattice Boltzmann method for satisfying no-slip conditions at curved solid boundaries, to model hydrodynamic compatibility conditions at curved porous-fluid interfaces.

The proposed method is tested against the results available from conventional numerical methods via the problem of fluid flow through and around a porous circular cylinder in crossflow. As such, streamlines, geometrical characteristics of recirculating wakes and drag coefficient are validated for different Reynolds (5 ≤ Re ≤ 40) and Darcy (10⁻⁵ ≤ Da ≤ 5 × 10⁻¹) numbers. It is also shown that without applying any compatibility conditions at the interface, the predicted flow structure is not satisfactory, even for a very fine mesh. This result highlights the importance of the two-domain approach for lattice Boltzmann simulation of the fluid flow in partial porous geometries with curved porous-fluid interfaces.

No research is found in the literature for applying the hydrodynamic compatibility conditions at curved porous-fluid interfaces in the lattice Boltzmann framework.

The purpose of this paper is to investigate the unsteady flow past through a permeable diamond-shaped cylinder and to study the effects of the aspect ratios and Darcy numbers of the cylinder.

The lattice Boltzmann method with D2Q9 lattice model was used to simulate the unsteady flow through permeable diamond-shaped cylinders. The present numerical method is validated against the available data.

The key findings are that increasing the permeability enhances the suppression of vortex shedding, and that the Strouhal number is directly proportion to the Darcy number, Reynolds number and the aspect ratio of the porous cylinder.

The present study considers unsteady laminar flow past through single permeable diamond-shaped cylinder. According to the authors’ knowledge, very few studies have been found in this field. The present findings are novel and original, which in turn can attract wide attention and citations.

The purpose of this paper is to analyze two different approaches (Models A and B) for an adiabatic boundary condition at the wall of a channel filled with a porous medium. The analytical solutions for the velocity distribution, the fluid and solid phase temperature distributions are derived and compared with numerical solutions. The phenomenon of heat flux bifurcation for Model A is demonstrated. The effects of pertinent parameter C on the applicability of the Models A and B are discussed. Analytical solutions for the overall Nusselt number and the heat flux distribution at the channel wall are derived and the influence of pertinent parameters Da and k on the overall Nusselt number and the heat flux distribution is discussed.

Two approaches (Models A and B) for an adiabatic boundary condition in porous media under local thermal non-equilibrium (LTNE) conditions are analyzed in this work. The analysis is applied to a microchannel which is modeled as a porous medium.

The phenomenon of heat flux bifurcation at the wall for Model A is demonstrated. The effect of pertinent parameter C on the applicability of each model is discussed. Model A is applicable when C is relatively large and Model B is applicable when C is small. The heat flux distribution is obtained and the influence of Da and k is discussed. For Model A, ϕ_Afin increases and ϕ_Asub, ϕ_Acover decrease as Da decreases and k is held constant, ϕ_Asub increases and ϕ_Afin, ϕ_Acover decrease as k increases while Da is held constant; for Model B, ϕ_Bfin increases and ϕ_Bsub decreases either as Da decreases or k decreases. The overall Nusselt number is also obtained and the effect of Da and k is discussed: Nu increases as either Da or k decrease for both models. The overall Nusselt number for Model A is larger than that for Model B when Da is large, the overall Nusselt numbers for Models A and B are equivalent when Da is small.

Proper representation of the energy equation and the boundary conditions for heat transfer in porous media is very important. There are two different models for representing energy transfer in porous media: local thermal equilibrium (LTE) and LTNE. Although LTE model is more convenient to use, the LTE assumption is not valid when a substantial temperature difference exists between the solid and fluid phases.

Fluid flow and convective heat transfer in porous media have many important applications such as thermal energy storage, nuclear waste repository, electronic cooling, geothermal energy extraction, petroleum processing and heat transfer enhancement.

This work has important fundamental implications.

In this work the microchannel is modeled as an equivalent porous medium. The analytical solutions for the velocity distribution, the fluid and solid phase temperature distributions are obtained and compared with numerical solutions. The first type of heat flux bifurcation phenomenon, which indicates that the direction of the temperature gradient for the fluid and solid phases is different at the channel wall, occurs when Model A is utilized. The effect of pertinent parameter C on the applicability of the models is also discussed. The analytical solutions for the overall Nusselt number and the heat flux distribution at the channel wall are derived, and the effects of pertinent parameters Da and k on the overall Nusselt number and the heat flux distribution are discussed.

This paper aims to provide a limited, but selective bibliography on modelling heat and mass transfer in composite fluid‐porous domains.

Since the pioneer study by Beavers and Joseph, the problem of interface continuity and/or jump conditions at a fluid‐porous interface has been of interest to the fluid mechanics and heat and mass transfer community. The paper is concerned both with numerical simulations of heat and fluid flow in such systems, and with the linear stability problems.

The one‐ and two‐domain formulations are equivalent. Using the Darcy‐Brinkman extension instead of the Darcy model reduces the number of ad hoc parameters in this configuration.

The problem of double diffusive convection has still to be solved and analyzed.

The discussion on the interface conditions is of great relevance to many industrial and practical situations.

The important question of the macroscopic formulation of the problem is tackled in the paper.

The purpose of this paper is to use a computational technique to simulate the flow in a two-dimensional (2D) wind tunnel where the effect of the solid walls facing the model has been addressed using a porous geometry so that interference arriving at the solid walls are duly damped and a flow suction procedure has been adopted at the side wall to minimize the span-wise effect of the growing side wall boundary layer.

A CFD procedure based on discretization of the Navier–Stokes equations has been used to model the flow in a rectangular volume with appropriate treatment for solid walls of the confined volume in which the model is placed. The rectangular volume was configured by stacking O-Grid sections in a span-wise direction using geometric growth from the wall. A porous wall condition has been adapted to counter the wall interference signatures and a separate suction procedure has been implemented for reducing the side wall boundary layer effects.

It has been shown that through such corrective measures, the flow in a wind tunnel can be adequately simulated using computational modeling. Computed results were compared against experimental measurements obtained from IAR (Institute for Aerospace, Canada) and NAL (National Aeronautical Laboratory, Japan) to show that indeed appropriate corrective means may be adapted to reduce the interference effects.

The solutions seemed to converge a lot better using relatively coarser grids which placed the shock locations closer to the experimental values. The finer grids were more stiff to converge and resulted in reversed flow with the two equation k-w model in the region where the intention was to draw out the fluid to thin down the boundary layer. The one equation Spalart–Allmaras model gave better result when porosity and wall suction routines were implemented.

This method could be used by industry to point check the results against certain demanding flow conditions and then used for more routine parametric studies at other conditions. The method would prove to be efficient and economical during early design stages of a configuration.

The method makes use of an O-grid to represent the confined test section and its dual treatment of wall interference and blockage effects through simultaneous application of porosity and boundary layer suction is believed to be quite original.

It is well known that the mixed convection process is the combined effect of the presence of both the forced and the free convection processes. In several applications such as environmental chambers, IC engines, etc. the forced convection is brought in by multiple suction/injection (S/I) effect. Study of mixed convection in a vertical square fluid saturated porous cavity with multiple S/I effect greatly contributes to such an understanding. So far, not much research work has reported in this direction. Hence, the purpose of this paper is to investigate such a mixed convection process in a fluid saturated vertical porous square cavity.

In this study, the authors numerically solved the couple partial differential equations governing the mixed convection process in a fluid saturated vertical square porous cavity by finite element method. The study is parametric in nature wherein the authors cover a large range of values for different parameters arising the mathematical model governing the problem under consideration.

The influence of multiple S/I effects on mixed convection is analyzed for a wide range of controlling parameters such as S/I flow velocities (a), S/I window size (D/H) and Rayleigh number (Ra). Both the flow and temperature fields are highly sensitive to magnitude of S/I velocity, S/I window slit size and “Ra”. While heat fluxes along the isothermal left vertical wall decrease with increasing S/I velocities they are formed to increase with increasing “(D/H)” and “Ra”. Nusselt numbers increase with increasing “Ra” and increasing size of S/I window slit size. Multi‐cellular circulation pattern and thermal boundary layers are seen to manifest in flow and temperature fields, respectively.

The study is based on 2D model, but the model is generic in nature; also it is fully numerical in nature. Due to lack of apt literature no experimental support is provided. The mathematical model used in the study is based on certain assumptions such as isotropic porous medium, fluid is viscous in nature and follows Newtonian laws and the porous structure is saturated with fluid, etc. Regarding future work, 3D modelling and simulation is in progress and attempts are also being made to collaborate with experimental groups on the problem under investigation.

The results from the work are relevant to the context of heat and fluid flow studies in IC engines, influence of mixed convection process on bacterial growth process in environmental chambers and cooling of electronic devices, etc.

The paper describes a mathematical model, especially the boundary treatment, for describing the influence of multiple S/I effects on mixed convection flow in a vertical square enclosure filled with a Darcian fluid saturated homogeneous porous medium. To understand the physics behind the mixed convection process in the proposed configuration, extensive numerical simulations have been carried out for the first time for different values of the important governing parameters arising from the model.

To consider simultaneous heat and mass transfer by mixed convection for a non‐Newtonian power‐law fluid from a permeable vertical plate embedded in a fluid‐saturated porous medium in the presence of suction or injection and heat generation or absorption effects.

The problem is formulated in terms of non‐similar equations. These equations are solved numerically by an efficient implicit, iterative, finite‐difference method.

It was found that as the buoyancy ratio was increased, both the local Nusselt and Sherwood numbers increased in the whole range of free and mixed convection regime while they remained constant for the forced‐convection regime. However, they decreased and then increased forming dips as the mixed‐convection parameter was increased from the free‐convection limit to the forced‐convection limit for both Newtonian and dilatant fluid situations.

The problem is limited to slow flow of non‐Newtonian power‐law fluids in porous media. Future research may consider inertia effects of porous media for relatively higher velocity flows.

A very useful source of information for researchers on the subject of non‐Newtonian fluids in porous media.

This paper illustrates simultaneous heat and mass transfer in porous media for power‐law fluids with heat generation or absorption effects.

Considers the motion of a viscous fluid within the narrow gap under a floating disk above an infinite porous plate. The flow is caused by a uniform blowing from the porous surface. If we ignore edge effects, after scaling the variables, an expression for the vertical component of the velocity is found with two particularities in the sense of an asymptotic expansion and for a self‐similar solution. We obtain an expression for the pressure distribution under the disk. Then, with this solution, Navier‐Stokes equations are reduced into one non‐linear equation of the fourth order with two points boundary conditions. First, we used a development of this equation by Newton’s method. The purpose of this paper is to show that the numerical scheme of quasilinearization gives rapid convergence to solution of this boundary layer problem. The vertical force balance gives the prediction for the height of the disk floating above the porous surface when the mass of the disk is known. Without any previous hypothesis, “TRIO”, a general computer code for thermal and fluid flow analysis developed at the CEA (Commissariat à l’Energie Atomique), confirms our main hypothesis and all our results. These two numerical solutions are well in keeping with the analytical and experimental solutions of Hinch and Lemaitre in 1994.

This chapter explores the multiplicity, formation, and porosity of organizational boundaries in new, fluid forms of production. Conceptualizing them as “partial organizations,” we argue that both the intentional design of organizational elements (such as membership, hierarchy, rules, monitoring, and sanctioning) as well as unintended adjustments of “unorganized” aspects drive boundary formation and impact boundary porosity. In addition, we contend that structuring dynamics will create specific trajectories for boundaries over time. Empirically, we further our theoretical framework on the basis of an in-depth case study of the Apache open-source software community during its formative years (1995–2002). We find that both the salience and formalization of boundaries increase over time. However, different conceptions of boundaries (such as efficiency, competence, power, and identity) become salient at different points in time. While design and adjustment drive boundary formation with regard to all boundary conceptions in our empirical case, porosity develops differently for each of them. We also demonstrate that the formalization of boundaries does not necessarily reduce boundary porosity, but actually may increase it.