Stability analysis of double-diffusive convection of Maxwell fluid in a porous medium heated from below

Linear stability analysis of Maxwell fluid in the Bénard problem for a double-diffusive mixture in a porous medium is studied based on the Darcy-Maxwell model. The critical Rayleigh number and the corresponding wave number for the exchange of stability are obtained. On the other hand, the effect of the relaxation time of Maxwell fluid on the critical Rayleigh number is discussed. In limiting cases, some results published previously are recovered from our results.     

Thermosolutal convection in a Maxwellian viscoelastic fluid in porous medium

The thermosolutal convection in a layer of Maxwellian viscoelastic fluid heated and soluted from below in porous medium is considered. The effects of uniform magnetic field and uniform rotation on the thermosolutal convection are also considered. For stationary convection, the Maxwellian viscoelastic fluid behaves like a Newtonian fluid. The sufficient conditions for the nonexistence of overstability are obtained. The critical Rayleigh number is found to increase with the increase in magnetic field, rotation and stable solute gradient.     

Velocity overshoot of start-up flow for a Maxwellfluid in a porous half-space

Stokes' first problem has been investigated for a Maxwell fluid in a porous half-space for gaining insight into the effect of viscoelasticity on the start-up flow in a porous medium. An exact solution was obtained by using the Fourier sine transform. It was found that at large values of the relaxation time the velocity overshoot occurs obviously and the system exhibits viscoelastic behaviours. On the other hand, for short relaxation time the velocity overshoot disappears and the system exhibits viscous behaviours. A critical value of the relaxation time was obtained for the emergence of the velocity overshoot. Furthermore, it was found that the velocity overshoot is caused by both the viscoelasticity of the Maxwell fluid and the Darcy resistance resulting from the structure of the micropore in the porous medium.     

Rayleigh wave propagation along the boundary of a non-Newtonian fluid-saturated porous medium

The Frenkel-Biot theory is used to study the reflection of elastic waves from the boundary of a non-Newtonian (Maxwell) fluid-saturated porous medium. The velocity and attenuation of a Rayleigh surface wave propagating along the boundary of the medium are determined. Two models of a fluid-saturated porous medium are used for calculation: with pore channels of a fixed diameter and with a lognormal distribution of pore channels in size. The results of calculations show that, when the fluid in the porous medium is characterized by a small Deborah number (i.e., exhibits non-Newtonian properties), the velocity of Rayleigh waves exhibits a considerable frequency dispersion. The results also suggest that, in principle, it is possible to estimate the Deborah number from the measured frequency dispersion of the Rayleigh wave velocity.     

Effects of transpiration on unsteady MHD flow of an upper convected Maxwell （UCM） fluid passing through a stretching surface in the presence of a first order chemical reaction

The aim of this article is to present the effects of transpiration on the unsteady two-dimensional boundary layer flow of non-Newtonian fluid passing through a stretching sheet in the presence of a first order constructive/destructive chemical reaction. The upper-convected Maxwell （UCM） model is used here to characterize the non-Newtonian behavior of the fluid. Using similarity solutions, the governing nonlinear partial differential equations are transformed into ordinary ones and are then solved numerically by the shooting method. The flow fields and mass transfer are significantly influenced by the governing parameters. The fluid velocity initially decreases as the unsteadiness parameter increases and the concentration decreases significantly due to the increase in the unsteadiness. The effect of increasing values of transpiration （suction） and the Maxwell parameter is to suppress the velocity field; however, the concentration is enhanced as transpiration （suction） and the Maxwell parameter increase. Also, it is found that the fluid velocity decreases as the magnetic parameter increases; however, the concentration increases in this case.     

Using nanofluid saturated porous media to enhance free convective heat transfer around a spherical electronic device

The thermophysical properties of the nanofluid saturated porous media are used in this work to optimize the thermal design of a spherical electronic device. Quantification of free convective heat transfer has been numerically determined by means of the finite volume method using the SIMPLE algorithm. The Rayleigh number based on the component diameter and water characteristics varies between 6.5x10⁶ and 1.32x10⁹, given the power generated during operation of this active component. The latter is disposed in the center of another sphere maintained isothermal. Its cooling is achieved by means of a porous medium saturated with a water based - Copper nanofluid whose volume fraction varies between 0 (pure water) and 10%. The thermal conductivity of the porous material's matrix ranges from 0 to 40 times that of the base fluid (water). Results of this work show that convective heat transfer systematically increases with this ratio according to a function depending on the Rayleigh number in the whole range of the considered volume fraction. The average Nusselt number also increases with the Rayleigh number according to a conventional power type law while influence of the fraction volume is moderate in the 2-10% range. The results are in agreement with those of previous works for particular thermal conditions. In order to optimize the thermal design of this electronic device, a correlation is proposed, allowing determination of the Nusselt number for any combination of the three influencing parameters for applications in various engineering fields, includind electronics.     

On micropolar fluids heated from below in hydromagnetics in porous medium

The thermal instability of electrically conducting micropolar fluids heated from below in the presence of uniform vertical magnetic field in porous medium has been considered. It is found that the presence of coupling between thermal and micropolar effects, magnetic field and permeability may introduce oscillatory motions in the system. The increase in Rayleigh number for stationary convection and decrease in Rayleigh number for overstability with the increase in magnetic field is depicted graphically. Also the Rayleigh number is found to decrease with the increase in permeability.     

The extended conformal Einstein field equations with matter: The Einstein–Maxwell field

A discussion is given of the conformal Einstein field equations coupled with matter whose energy–momentum tensor is trace-free. These resulting equations are expressed in terms of a generic Weyl connection. The article shows how in the presence of matter it is possible to construct a conformal gauge which allows to know a priori the location of the conformal boundary. In vacuum this gauge reduces to the so-called conformal Gaussian gauge. These ideas are applied to obtain (i) a new proof of the stability of Einstein–Maxwell de Sitter-like spacetimes; (ii) a proof of the semi-global stability of purely radiative Einstein–Maxwell spacetimes.     

基于Biot-喷射流统一模型Maxwell流体饱和孔隙介质中的弹性波

推广Biot-Tsiklauri声学模型的同时借鉴Dvorkin和Nur的工作,建立了具有任意孔径分布并顾及喷射流动机制的非牛顿流体饱和孔隙介质声学模型,研究了非牛顿流体(Maxwell流体)饱和孔隙介质中的弹性波的衰减和频散特性.着重讨论充孔隙Maxwell流体的非牛顿流效应对弹性波的频散和衰减的影响.研究表明,饱和流体的非牛顿流效应和喷射流动机制均是引起弹性波波频散和衰减的重要因素.依据非牛顿流体(Maxwell流体)饱和各向同性孔隙介质的Biot-喷射流声学模型,喷射流动只影响纵波的频散和衰减,而饱和流体的非牛顿流效应不仅影响纵波,而且还影响横波的频散和衰减.     

含孔隙分层半空间中瑞利波的传播特性研究

为了研究含孔隙介质分层半空间中瑞利波的传播规律,分析孔隙介质参数对瑞利波频散曲线的影响,本文进行了数值模拟研究。采用传递矩阵算法,计算了含孔隙分层半空间中一定频率范围内瑞利波所有模式的频散及激发强度曲线,并与均匀弹性固体分层半空间情况作了类比分析,在含孔隙覆盖层的两层模型和含低速孔隙夹层的三层模型下,详细研究了孔隙度、渗透率、层厚度等参数对瑞利波各模式的影响,发现孔隙度及层厚度的变化对频散曲线影响较大,而渗透率的变化对频散曲线影响较小。      

Thermal convection in Rivlin-Ericksen elastico-viscous fluid in porous medium in hydromagnetics

The thermal instability of a layer of Rivlin-Ericksen elastico-viscous fluid in porous medium acted on by a uniform magnetic field is considered. For stationary convection, Rivlin-Ericksen elastico-viscous fluid behaves like a Newtonian fluid. The magnetic field is found to have stabilizing effect whereas medium permeability has destabilizing effect. The magnetic field introduces oscillatory modes in the system, A sufficient condition for the non-existence of overstability is also obtained.     

EHD convection in dielectric micropolar fluid layer

The onset of instability in a layer of dielectric micropolar fluid under the simultaneous action of an AC electric field and temperature gradient has been investigated. The dispersion relation has been derived and various critical values of non-dimensional Rayleigh number in the fluid layer have been determined. The influence of micropolar viscosity and electric Rayleigh number on the onset of convection has been analyzed. Thermal Rayleigh number has been computed for various values of electric Rayleigh number for the onset of instability. The stabilizing and destabilizing effects of electric Rayleigh number, micropolar viscosity and Prandtl number have been discussed.     

Cross-diffusive effects on the onset of double-diffusive convection in a horizontal saturated porous fluid layer heated and salted from above

Double-diffusive stationary and oscillatory instabilities at the marginal state in a saturated porous horizontal fluid layer heated and salted from above are investigated theoretically under the Darcy's framework for a porous medium. The contributions of Soret and Dufour coefficients are taken into account in the analysis. Linear stability analysis shows that the critical value of the Darcy-Rayleigh number depends on cross-diffusive parameters at marginally stationary convection, while the marginal state characterized by oscillatory convection does not depend on the cross-diffusion terms even if the condition and frequency of oscillatory convection depends on the cross-diffusive parameters. The critical value of the Darcy-Rayleigh number increases with increasing value of the solutal Darcy-Rayleigh number in the absence of cross-diffusive parameters. The critical Darcy-Rayleigh number decreases with increasing Soret number, resulting in destabilization of the system, while its value increases with increasing Dufour number, resulting in stabilization of the system at the marginal state characterized by stationary convection. The analysis reveals that the Dufour and Soret parameters as well as the porosity parameter play an important role in deciding the type of instability at the onset. This analysis also indicates that the stationary convection is followed by the oscillatory convection for certain fluid mixtures. It is interesting to note that the roles of cross-diffusive parameters on the double-diffusive system heated and salted from above are reciprocal to the double-diffusive system heated and salted from below.     

生物过滤器中非均匀性流动的数值研究

生物过滤技术因其具有有效性、低成本和环境友好等优点引起了人们的广泛关注.该技术主要通过生物过滤器去除含有H2S等废气的有毒有害气体.运用格子Boltzmann方法对三种生物过滤器模型中多孔介质的非均匀性流动进行了数值模拟.数值模拟结果表明,多孔介质的性质和进口流动条件对临界Rayleigh数有显著影响,临界Rayleigh数随着多孔介质的孔隙度和Darcy数的增大而逐渐变小,并随着进口Reynolds数的增大而逐渐变大.所得结果可望为生物过滤器的优化设计提供一个合理的理论依据.     

Pressure and Maxwell Tensor in a Coulomb Fluid

The pressure in a classical Coulomb fluid at equilibrium is obtained from the Maxwell tensor at some point inside the fluid, by a suitable statistical average. For fluids in a Euclidean space, this is a fresh look at known results. But for fluids in a curved space, a case which is of some interest, these unambiguous results from the Maxwell tensor approach have not been obtained by other methods.     

Thermosolutal convection of micropolar fluids in hydromagnetics

The thermosolutal convection in a layer of electrically conducting micropolar fluids heated and soluted from below in the presence of a uniform vertical magnetic field is considered. The presence of coupling between thermosolutal and micropolar effects may bring overstability in the system. The magnetic field also introduces oscillatory modes in the system and the Rayleigh number is found to increase with the increase in magnetic field. The possibility of oscillatory motions and the increase in Rayleigh number with increase in magnetic field is depicted graphically.     

Analytical Analysis of Heat Transfer and Entropy Generation in a Tube Filled with Double-Layer Porous Media

The heat transfer and entropy generation in a tube filled with double-layer porous media are analytically investigated. The wall of the tube is subjected to a constant heat flux. The Darcy-Brinkman model is utilized to describe the fluid flow, and the local thermal non-equilibrium model is employed to establish the energy equations. The solutions of the temperature and velocity distributions are analytically derived and validated in limiting case. The analytical solutions of the local and total entropy generation, as well as the Nusselt number, are further derived to analyze the performance of heat transfer and irreversibility of the tube. The influences of the Darcy number, the Biot number, the dimensionless interfacial radius, and the thermal conductivity ratio, on flow and heat transfer are discussed. The results indicate, for the first time, that the Nusselt number for the tube filled with double-layer porous media can be larger than that for the tube filled with single layer porous medium, while the total entropy generation rate for the tube filled with double-layer porous media can be less than that for the tube filled with single layer porous medium. And the dimensionless interfacial radius corresponding to the maximum value of the Nusselt number is different from that corresponding to the minimum value of the total entropy generation rate.     

The effects of interaction range,porosity and molecular association on the phase equilibrium of a fluid confined in a disordered porous media

Grand-canonical transition-matrix Monte Carlo (GC-TMMC) is employed to analyse the effects of range of interaction, packing fraction and molecular association on phase coexistence properties of square-well (SW) based fluids in disordered pores. The nature of the phase equilibria were studied inside a repulsive disordered porous media with packing fractions, η _m = 0.05 and 0.10. Three values of the SW attractive well range parameter were studied: λ = 1.5, 1.75, and 2.0. Coexistence number probability distribution reflects the signature of the disordered structure of the porous matrix. Yet, no multiple fluid–fluid transition was observed. The effect of strength of molecular association on coexistence densities, density profile, saturation pressure, and monomer fraction for the SW based dimerizing fluids inside a repulsive disordered media is reported. Association is found to increase as the packing fraction of the matrix increase. Critical properties of these confined fluids are calculated via a rectilinear diameter approach. Fractional shift in the critical temperature linearly decreases with the increase in the attractive well width for non-associating fluids. The rate of decrease in the critical temperature shift increases with the increase in packing fraction. Associating sites are found to suppress the shift in the critical temperature.     

Natural convection in a square cavity containing a nanofluid and an adiabatic square block at the center

The problem of free convection fluid flow and heat transfer of Cu–water nanofluid inside a square cavity having adiabatic square bodies at its center has been investigated numerically. The governing equations have been discretized using the finite volume method. The SIMPLER algorithm was employed to couple velocity and pressure fields. Using the developed code, a parametric study was conducted and the effects of pertinent parameters such as Rayleigh number, size of the adiabatic square body, and volume fraction of the Cu nanoparticles on the fluid flow and thermal fields and heat transfer inside the cavity were investigated. The obtained results show that for all Rayleigh numbers with the exception of Ra = 10⁴ the average Nusselt number increases with increase in the volume fraction of the nanoparticles. At Ra = 10⁴ the average Nusselt number is a decreasing function of the nanoparticles volume fraction. Moreover at low Rayleigh numbers (10³ and 10⁴) the rate of heat transfer decreases when the size of the adiabatic square body increases while at high Rayleigh numbers (10⁵ and 10⁶) it increases.     

Influence of Non-linear Radiation Heat Flux on Rotating Maxwell Fluid over a Deformable Surface: A Numerical Study

Mathematical model for Maxwell fluid flow in rotating frame induced by an isothermal stretching wall is explored numerically. Scale analysis based boundary layer approximations are applied to simplify the conservation relations which are later converted to similar forms via appropriate substitutions. A numerical approach is utilized to derive similarity solutions for broad range of Deborah number. The results predict that velocity distributions are inversely proportional to the stress relaxation time. This outcome is different from that observed for the elastic parameter of second grade fluid. Unlike non-rotating frame, the solution curves are oscillatory decaying functions of similarity variable. As angular velocity enlarges, temperature rises and significant drop in the heat transfer coefficient occurs. We note that the wall slope of temperature has an asymptotically decaying profile against the wall to ambient ratio parameter. From the qualitative view point, temperature ratio parameter and radiation parameter have similar effect on the thermal boundary layer. Furthermore, radiation parameter has a definite role in improving the cooling process of the stretching boundary.A comparative study of current numerical computations and those from the existing studies is also presented in a limiting case. To our knowledge, the phenomenon of non-linear radiation in rotating viscoelastic flow due to linearly stretched plate is just modeled here.