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Natural convection with Soret effect in a binary fluid saturating a shallow horizontal porous layer is studied both numerically and analytically. The vertical walls of the enclosure are heated and cooled by uniform heat fluxes and a solutal gradient is imposed vertically. In the formulation of the problem, we use the Darcy model and the density variation is taken into account by the Boussinesq approximation. The governing parameters of the problem are the aspect ratio, A, the thermal Rayleigh number, R_T, the buoyancy ratio, N, the Lewis number, Le and the Soret coefficient, N_S. The analytical solution, based on the parallel flow approximation, is found to be in good agreement with a numerical solution of the full governing equations. In the presence of a vertical destabilizing concentration gradient, the existence of both natural and antinatural flows is demonstrated. When the vertical concentration gradient is stabilizing, multiple steady state solutions are possible in a range of buoyancy ratio, N, that depends strongly on the Soret coefficient, N_S.

The purpose of this paper is to study numerically the fluid flow and heat transfer in an inclined channel provided with heated porous blocks on its lower plate.

The Brinkman‐Forchheimer extended Darcy model with the Boussinesq approximation is adopted for the flow in the porous regions. The governing equations with the appropriate boundary conditions are solved by the control volume method. The effect of some pertinent parameters such as the buoyancy force intensity, the porous blocks shape and height, the porous medium permeability and the Reynolds number are analyzed for various inclination angles ranging from −90° to +90°.

The results reveal, essentially, that the inclination angle of the channel can alter substantially the fluid flow and heat transfer mechanisms, especially at high Richardson and Darcy numbers. In this case, the maximum and minimum global Nusselt numbers are reached for α=+90° and α=−90°, respectively.

The results obtained in this work are valid for an inclined channel with porous blocks attached on the heated parts of the lower plate, whereas the upper wall is thermally insulated.

The results obtained in this worky can be used in the thermal control of electronic components. The use of porous blocks mounted on the heat sources will increase the rate of heat removal in order to maintain the electronic components at an acceptable operating temperature.

The paper provides an interesting method to improve the cooling of electronic devices by use of a porous medium.

The purpose of this paper is to improve the volume-averaged models for free convection flow in porous media.

A pore scale simulation is conducted against which an independent volume-averaged solver is fine-tuned.

Micro and macro scale results can merge if proper choice of local thermal non-equilibrium and thermal dispersion models are selected. This depends on the range of Ra values investigated.

This is the first time a work like this is published in the literature.

Purpose – The purpose of this article is to investigate consumption discourses in contexts characterized by multiple cultures and intercultural contacts, as multicultural contacts and multiple migrations challenge existing consumer acculturation models based on a dualistic process of acculturation. This chapter explores empirically the character of cultural reflexivity and its expression in consumers’ discourses. Given that nostalgia is one prominent dimension of the migration conceptualization, we seek to understand how the role of nostalgia changes in contexts where consumers are decreasingly territorially embedded agents.

Methodology – The study rests on in-depth analysis of migrant narratives from two research phases. While the first phase encompasses in-depth interviews, the second one combines interviews and observations to provide a depiction of intercultural contact within the micro cosmos of a multicultural apartment.

Findings – The findings of this chapter illustrate how migrants develop different nostalgic discourses, to either (re-)appropriate the Expatriate as defined by James (1999), or to appropriate global consumptionscapes through nostalgia for the routine.

Research implications – On the basis of these findings, the article discusses cultural reflexivity in terms of naturalization and cultivation narratives (Wilk, 1999), proposing shifts between reflexive and routinized consumption practices as basis for consumers’ cultural reflexivity.

Originality/value of chapter – The contribution of this chapter is firstly a contextualized and empirically grounded definition of cultural reflexivity. Secondly, it demonstrates that migrants’ consumption discourses revolve more around disruptions of routines than around acculturation processes. Thirdly, the chapter illustrates the use of nostalgia for emotional valorization of cultures beyond classical home cultural authenticity discourses.

The purpose of this paper is to numerically study the double-diffusive natural convection within an eccentric horizontal cylindrical annulus filled with a Newtonian fluid. The annulus walls are maintained at uniform temperatures and concentrations so as to induce aiding thermal and mass buoyancy forces within the fluid. For that, this simulation span a moderate range of thermal Rayleigh number (100Ra_T100,000), Lewis (0.1Le10), buoyancy ratio (0N5) and Prandtl number (Pr=0.71) to examine their effects on flow motion and heat and mass transfers.

A finite volume method in conjunction with the successive under-relaxation algorithm has been developed to solve the bipolar equations. These are written in dimensionless form in terms of vorticity, stream function, temperature and concentration. Beforehand, the implemented computer code has been validated through already published findings in the literature. The isotherms, streamlines and iso-concentrations are exhibited for various values of Rayleigh and Lewis numbers, and buoyancy ratio. In addition, heat and mass transfer rates in the annulus are translated in terms of Nusslet and Sherwood numbers along the enclosure’s sides.

It is observed that, for the range of parameters considered here, the results show that the average Sherwood number increases with, while the average Nusselt number slightly dips as the Lewis number increases. It is also found that, under the convective mode, the local Nusselt number (or Sherwood) increases with the buoyancy ratio. Likewise, according to Lewis number’s value, the flow pattern is either symmetric and stable or asymmetric and random. Besides that, the heat transfer is transiting from a conductive mode to a convective mode with increasing the thermal Rayleigh number, and the flow structure and the rates of heat and mass transfer are significantly influenced by this parameter.

The range of the Rayleigh number considered here covers only the laminar case, with some constant parameters, namely the Prandtl number (Pr = 0.71), and the tilt angle (α=90°). The analysis here is only valid for steady, two-dimensional, laminar and aiding flow within an eccentric horizontal cylindrical annulus. This motivates further investigations involving other relevant parameters as N (opposite flows), Ra, Pr, Le, the eccentricity, the tilt angle, etc.

An original framework for handling the double-diffusive natural convection within annuli is available, based on the bipolar equations. In addition, the achievement of this work could help researchers design thermal systems supported by annulus passages. Applications of the results can be of value in various arrangements such as storage of liquefied gases, electronic cable cooling systems, nuclear reactors, underground disposal of nuclear wastes, manifolds of solar energy collectors, etc.

Given the geometry concerned, the bipolar coordinates have been used to set the inner and outer walls boundary conditions properly without interpolation. In addition, since studies on double-diffusive natural convection in annuli are lacking, the obtained results may be of interest to handle other configurations (e.g., elliptical-shaped speakers) with other boundary conditions.

The purpose of this paper is to conduct a numerical study of the effect of magnetic field on thermocapillary convection of a two layered system of Newtonian fluids, confined in a rectangular cavity. The flow within the cavity is subject to the horizontal temperature gradient. Attention is focused on how the heat transfer and flow properties are affected subject to the applied magnetic field, particularly in the lower layer. For this purpose, the fluid combinations of di‐Boron Trioxide (B₂O₃) over Gallium Arsenide GaAs (III‐V), and Silicon oil 10 cSt over Fluorinert FC 70 are considered in the present study.

The non‐linear two‐dimensional vorticity transport equations along with the energy equations are solved for the two liquid layers using the Alternate Direct Implicit method, whereas the elliptic partial differential equations of the stream function are solved using the Successive Over Relaxation method.

It was found that despite the significant reduction of flow in the two layers, the number of cells in the lower layer increases with the increase in Hartmann number Ha. However, the flow intensity decreases with the increase in Hartmann number. This decrease is more pronounced in the lower layer, as compared to the upper layer. The numerical scheme employed for the solution is found to be in good agreement with the previous work.

The analysis is made for two layer liquid system with undeformable interface and free surface. The detailed study of the effect of magnetic field on oscillatory Marangoni convection in two layer system with deformable interface is left for future work.

The approach is useful in optimizing the flow properties of the fluids in a two layer system, particularly the lower layer, to yield the results of potential practical interest.

The results of the study may be of some interest to researchers in the field of semiconductor technology, as the melt control is intensively investigated for the development in the manufacture of defect‐free semiconductors and crystals.

The purpose of this study is to produce a numerical model capable of predicting the mixed convection flows in a rectangular cavity filled with a porous medium and to analyze the effects of several parameters on convective flow in porous media in a differentially heated enclosure.

The authors used the finite volume method.

The authors predicted and analyzed the effects of Richardson number, Darcy number, porosity values and Prandtl number in heat transfer and fluid flow. On other hand, the porosity and Richardson number values lead to reducing the heat transfer rate of mixed convection flow in a porous medium.

A comparison between Darcy–Brinkman–Forchheimer model and Darcy–Brinkman model is discussed and analyzed. The authors finally conclude that the Darcy–Brinkman model overestimates the heat transfer rate.

The purpose of this paper is to consider double‐diffusive convection in a heated porous medium saturated with a fluid. Of particular interest is the case where the fluid has a stabilizing concentration gradient and small diffusivity.

A fully‐coupled stabilized finite element scheme and adaptive mesh refinement (AMR) methodology are introduced to solve the resulting coupled multiphysics application and resolve fine scale solution features. The code is written on top of the open source finite element library LibMesh, and is suitable for parallel, high‐performance simulations of large‐scale problems.

The stabilized adaptive finite element scheme is used to compute steady and unsteady onset of convection in a generalized Horton‐Rogers‐Lapwood problem in both two and three‐dimensional domains. A detailed study confirming the applicability of AMR in obtaining the predicted dependence of solutal Nusselt number on Lewis number is given. A semi‐permeable barrier version of the generalized HRL problem is also studied and is believed to present an interesting benchmark for AMR codes owing to the different boundary and internal layers present in the problem. Finally, some representative adaptive results in a complex 3D heated‐pipe geometry are presented.

This work demonstrates the feasibility of stabilized, adaptive finite element schemes for computing simple double‐diffusive flow models, and it represents an easily‐generalizable starting point for more complex calculations since it is based on a highly‐general finite element library. The complementary nature of h‐adaptivity and stabilized finite element techniques for this class of problem is demonstrated using particularly simple error indicators and stabilization parameters. Finally, an interesting double‐diffusive convection benchmark problem having a semi‐permeable barrier is suggested.

This paper aims to consider numerical analysis of laminar double-diffusive natural convection inside a non-homogeneous closed medium composed of a saturated porous matrix and a clear binary fluid under spatial sinusoidal heating/cooling on one side wall and uniform salting.

The domain of interest is a partially square porous enclosure with sinusoidal wall heating and cooling. The fluid flow, heat and mass transfer dimensionless governing equations associated with the corresponding boundary conditions are discretized using the finite volume method. The resulting algebraic equations are solved by an in-house FORTRAN code and the SIMPLE algorithm to handle the non-linear character of conservation equations. The validity of the in-house FORTRAN code is checked by comparing the current results with previously published experimental and numerical works. The effect of the porous layer thickness, the spatial frequency of heating and cooling, the Darcy number, the Rayleigh number and the porous to fluid thermal conductivity ratio is analyzed.

The results demonstrate that for high values of the spatial frequency of heating and cooling (f = 7), temperature contours show periodic variations with positive and negative values providing higher temperature gradient near the thermally active wall. In this case, the temperature variation is mainly in the porous layer, while the temperature of the clear fluid region is practically the same as that imposed on the left vertical wall. This aspect can have a beneficial impact on thermal insulation. Besides, the porous to fluid thermal conductivity ratio, Rk, has practically no effect on Shhot wall, contrary to Nuinterface where a strong increase is observed as Rk is increased from 0.1 to 100, and much heat transfer from the hot wall to the clear fluid via the porous media is obtained.

The findings are useful for devices working on double-diffusive natural convection inside non-homogenous cavities.

The authors believe that the presented results are original and have not been published elsewhere.

The purpose of this paper is to extend the penalty concept to treat partial slip, free surface, contact and related boundary conditions in viscous flow simulation.

The penalty partial‐slip formulation is analysed and related to the classical Navier slip condition. The same penalty scheme also allows partial penetration through a boundary, hence the implementation of porous wall boundaries. The finite element method is used for investigating and interpreting penalty approaches to boundary conditions.

The generalised penalty approach is verified by means of a novel variant of the circular‐Couette flow problem, having partial slip on one of the cylindrical boundaries, for which an analytic solution is derived. Further verificationis provided by consideration of viscous flow over a sphere with partial slip on the surface, and comparison of numerical and classical solutions. Numerical studies illustrate the versatility of the approach.

The penalty approach is applied to some different boundaries: partial slip and partial penetration with no/full slip/penetration as limiting cases; free surface; space‐ and time‐varying boundary conditions which allow progressive contact over time. Application is made to curved and inclined boundaries. Sensitivity of flow to penalty parameters is an avenue for continued research, as is application of the penalty approach for non‐Newtonian flows.

This is the first work to show the relation between penalty formulation of boundary conditions and physical boundary conditions. It provides a method that overcomes past difficulties in implementing partial slip on boundaries of general shape, and which handles progressive contact. It also provides useful benchmark problems for future studies.