Onset of triply diffusive convection in a Maxwell fluid saturated porous layer

The linear stability of triply diffusive convection in a binary Maxwell fluid saturated porous layer is investigated. Applying the normal mode method theory, the criterion for the onset of stationary and oscillatory convection is obtained. The modified Darcy–Maxwell model is used as the analysis model, this allows us to make a thorough investigation of the processes of viscoelasticity and diffusions that causes the convection to set in through oscillatory rather than stationary. The effects of Vadasz number, normalized porosity parameter, relaxation parameter, Lewis number and solute Rayleigh number on the system are presented numerically and graphically.     

Lattice BGK simulations of double diffusive natural convection in a rectangular enclosure in the presences of magnetic field and heat source

In this paper, we develop a temperature-concentration lattice Bhatnagar-Gross-Krook (TCLBGK) model, with a robust boundary scheme for simulating the two-dimensional, hydromagnetic, double-diffusive convective flow of a binary gas mixture in a rectangular enclosure, in which the upper and lower walls are insulated, while the left and right walls are at a constant temperature and concentration and a uniform magnetic field is applied in the $x$-direction. In the model, the velocity, temperature and concentration fields are solved by three independent LBGK equations which are combined into a coupled equation for the whole system. In our simulations, we take the Prandtl number $Pr=1$, the Lewis number $Le=2$, the thermal Rayleigh number $R{a}_T={10}^5,{10}^6$, the Hartmann number $Ha=0,10,25,50$, the dimensionless heat generation or absorption $?=0.0,?1.0$, the buoyancy ratio $N=0.8,1.3$, and the aspect ratio $A=2$ for the enclosure. The numerical results are found to be in good agreement with those of previous studies [A.J. Chamkha, H. Al-Naser, Hydromagnetic double-diffusive convection in a rectangular enclosure with opposing temperature and concentration gradients, Int. J. Heat Mass Transfer 45 (2002) 2465C2483].     

On the characterization of non-oscillatory motions in ferromagnetic convection with magnetic field dependent viscosity in a rotating porous medium

In the present paper, a sufficient condition is derived for the validity of the “principle of the exchange of stabilities” in ferromagnetic convection with magnetic field dependent viscosity, for the case of free boundaries, in porous medium in the presence of a uniform vertical magnetic field and uniform rotation about the vertical axis.     

Thermomagnetic convection in magnetic fluids influenced by a time-modulated magnetic field

Material– and flow properties of magnetic fluids can be influenced by applying an external magnetic field. In this work we will particularly consider the onset of convection in magnetic fluids which is influenced by a magnetic force. In a horizontal magnetic fluid layer the force arises if a temperature gradient and an external magnetic field is applied. The behaviour of the onset of convection is investigated for a static and a time–modulated magnetic field. For the case of a static magnetic field the onset of convection depends on the strength of the field and for a time–modulated magnetic field an additional dependence on the frequency of magnetic field variation is found. The experimental results presented here confirm in principle the theoretical predictions about the influence of static and time–modulated magnetic forces on the onset of convection. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Free convection flow about a cone under mixed thermal boundary conditions and a magnetic field

A similarity analysis was performed to investigate the laminar free-convection boundary-layer flow in the presence of a transverse magnetic field over a vertical down-pointing cone with mixed thermal boundary conditions. Boundary layer velocity and temperature profiles were determined numerically for various values of the magnetic parameter and the Prandtl number. The results show that the magnetic field suppresses the velocity profiles and increases the skin friction. The temperature profiles were expanded with increasing values of the magnetic parameter resulting in higher surface temperatures. A transformation relating the similarity solutions of the boundary-layer velocity and temperature profiles associated with different values of the mixed thermal boundary condition parameter was obtained.     

Effect of rotation on the onset of double diffusive convection in a Darcy porous medium saturated with a couple stress fluid

The effect of rotation on the onset of double diffusive convection in a horizontal couple stress fluid-saturated porous layer, which is heated and salted from below, is studied analytically using both linear and weak nonlinear stability analyses. The extended Darcy model, which includes the time derivative and Coriolis terms, has been employed in the momentum equation. The onset criterion for stationary, oscillatory and finite amplitude convection is derived analytically. The effect of Taylor number, couple stress parameter, solute Rayleigh number, Lewis number, Darcy–Prandtl number, and normalized porosity on the stationary, oscillatory, and finite amplitude convection is shown graphically. It is found that the rotation, couple stress parameter and solute Rayleigh number have stabilizing effect on the stationary, oscillatory, and finite amplitude convection. The Lewis number has a stabilizing effect in the case of stationary and finite amplitude modes, with a destabilizing effect in the case of oscillatory convection. The Darcy–Prandtl number and normalized porosity advances the onset of oscillatory convection. A weak nonlinear theory based on the truncated representation of Fourier series method is used to find the finite amplitude Rayleigh number and heat and mass transfer. The transient behavior of the Nusselt number and Sherwood number is investigated by solving the finite amplitude equations using Runge–Kutta method.     

Modeling microgeometric structures of porous media with a predominant axis for predicting diffusive flow in capillaries

This paper presents a method for modeling microgeometric structures of porous media with a predominant using successive cross-sections. The proposed model takes into account the properties of diffusive flow in capillaries. In order to characterize uncertainty and imprecision occurring in geometric features of cross-sections, we introduce the concept of connection degrees as well as tracking degrees based on fuzzy theory. The proposed model can be used for classifying different types of media and finding the relationship between the geometric structure of a porous medium and its physical properties. This model has been successfully applied to polyester yarn structure.     

Parameter-dependent systems on the half-line and free convection boundary-layers in porous media

In this paper we use a recently elaborated abstract method, for parameter-dependent ODE systems over the interval (0, ∞), to obtain existence results for the problem of self-similar solutions in boundary-layer free convection in porous media. Using a generalization of the method to exponentially decaying solutions, we are able to recover some known results, and to obtain a new branch of solutions in the case of the so-called backward boundary-layer. The arguments involve the derivation of suitable a priori estimates for the solutions of the problem.     

Steady convection in the presence of an external magnetic field

The problem of the equilibrium of a liquid enclosed in a vessel heated from below has been considered by Sorokin [1], Iudovich and Ukhovskii [2] and Velt [3]. It has been established that if the Rayleigh number λ exceeds a certain critical value λ₀, then secondary steady flows arise in the liquid.

The stability of a conductive liquid heated from below has been studied by many authors. The most complete and general studies are those of Sorokin and Sushkin [4], whose paper contains the appropriate bibliography, and that of Shliomis [5]. The results of [4 and 5] make clear the physical picture of the phenomena associated with the heating of a conductive fluid and indicate the possible existence of secondary steady and periodic flows.

The existence of steady convective flows in a conductive liquid are proved below. Our study is based on the procedure set forth in [2].     

Influence of variable heat flux on natural convection along a corrugated wall in porous media

In this work the coupled non-linear partial differential equations, governing the free convection from a wavy vertical wall under a power law heat flux condition, are solved numerically. For both Darcy and Forchheimer extended non-Darcy models, a wavy to flat surface transformation is applied and the governing equations are reduced to boundary layer equations. A finite difference scheme based on the Keller Box approach has been used in conjunction with a block tri-diagonal solver for obtaining the solution. Detailed simulations are carried out to investigate the effect of varying parameters such as power law heat flux exponent m, wavelength–amplitude ratio a and the transformed Grashof number Gr′. Both surface undulations and inertial forces increase the temperature of the vertical surface while increasing m reduces it. The wavy pattern observed in surface temperature plots, become more prominent with increasing m or a but reduces as Gr′ increases.     

Thermomagnetic convection under alternating magnetic fields

Thermomagnetic convection within a square cavity filled with a magnetic fluid was studied under alternating magnetic field. The aim was to explore the response of the magnetic fluid towards alternating magnetic fields. A set of frequencies for the sinusoidal variation of the magnetic field intensity was used to study the heat transfer characteristics across the problem geometry. The effect on heat transfer was quantified by an averaged Nusselt number. (© 2017 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Natural convection in porous media ‐ a meshless solution of the Brinkman extended Darcy model

A numerical study is performed on steady natural convection inside a differentially heated square cavity. The cavity is filled with porous media which exhibits the Brinkman extended Darcy behavior. The solution procedure for coupled mass, momentum, and energy equations is based on primitive variables and RBF collocation method with r⁷ function. Numerical examples include calculations at filtration with Rayleigh number 100, and Darcy numbers 10^–3 and 10^–5. The solution is compared with reference results of the fine‐grid finite volume method.     

An analytical study of linear and nonlinear double diffusive convection in a fluid saturated anisotropic porous layer with Soret effect

The double diffusive convection in a horizontal anisotropic porous layer saturated with a Boussinesq fluid, which is heated and salted from below in the presence of Soret coefficient is studied analytically using both linear and nonlinear stability analyses. The normal mode technique is used in the linear stability analysis while a weak nonlinear analysis based on a minimal representation of double Fourier series method is used in the nonlinear analysis. The generalized Darcy model including the time derivative term is employed for the momentum equation. The critical Rayleigh number, wavenumber for stationary and oscillatory modes and frequency of oscillations are obtained analytically using linear theory. The effect of anisotropy parameters, solute Rayleigh number, Soret parameter and Lewis number on the stationary, oscillatory, finite amplitude convection and heat and mass transfer are shown graphically.     

Onset of convection in a porous mantle

The problem of thermal instability in a fluid saturated porous spherical shell heated internally, due to uniform internal heat sources and in equilibrium under its own radial gravitational field is studied theoretically. A general disturbance is analysed into modes in terms of spherical harmonics of various orders,l, for different values of the thickness of the mantle and the criteria for the onset of convection for the first fifteen modes is obtained in four different cases when the outer and inner bounding surfaces are either impermeable or permeable. It is shown that as the thickness of the shell decreases, the pattern of convection which sets in at marginal stability shifts progressively to harmonics of higher order for all the three cases except when both the bounding surfaces are permeable, in which case the onset of convection occurs at a harmonic of order 1. A comparison of some representative results of these cases is made with that of continuous fluid shell with rigid or free boundary surfaces. The neutral stability plots for various thickness of the mantle, for five different models of the mantle, are plotted for the different types of boundary surfaces.     

Explicit analytical solutions of the anisotropic Brinkman model for the natural convection in porous media

Some algebraically explicit analytical solutions are derived for the anisotropic Brinkman model-an improved Darcy model-describing the natural convection in porous media. Besides their important theoretical meaning (for example, to analyze the non-Darcy and anisotropic effects on the convection), such analytical solutions can be the benchmark solutions to promoting the development of computational heat and mass transfer. For instance, we can use them to check the accuracy, convergence and effectiveness of various numerical computational methods and to improve numerical calculation skills such as differential schemes and grid generation ways.     

Spatial decay in a double diffusive convection problem in Darcy flow

This paper deals with a model of time-dependent double diffusive convection in Darcy flow. In particular it is concerned with the spatial decay of solutions when the flow is confined to a semi-infinite cylinder. Decay bounds for an energy expression are derived.