Maxwell–Cattaneo double-diffusive convection: limiting cases

Double-diffusive convection, in which a fluid is acted upon by two fields (such as temperature and salinity) that affect the density, has been widely studied in areas as diverse as the oceans and stellar atmospheres. Assuming classical Fickian diffusion for both heat and salt, the evolution of temperature and salinity are governed by parabolic advection–diffusion equations. In reality, there are small extra terms in these equations that render the equations hyperbolic (the Maxwell–Cattaneo effect). Although these corrections are nominally small, they represent a singular perturbation and hence can lead to significant effects when the underlying differences of salinity and temperature are large. In this paper, we investigate the linear stability of a double-diffusive fluid layer and show that amending Fick's law for the temperature, or the salinity, alone can lead to new modes of oscillation and to very large changes in the preferred wavelength of oscillatory convection at onset. In particular, the salt finger regime of classical double diffusion is here replaced by Maxwell–Cattaneo oscillations when the salt concentration is very high. The more complicated case when both laws are amended is left to a future paper, now in preparation.

Instability thresholds for thermal convection in a Kelvin–Voigt fluid of variable order

We present numerical techniques for calculating instability thresholds in a model for thermal convection in a complex viscoelastic fluid of Kelvin–Voigt type. The theory presented is valid for various orders of an exponential fading memory term, and the strategy for obtaining the neutral curves and instability thresholds is discussed in the general case. Specific numerical results are presented for a fluid of order zero, also known as a Navier–Stokes–Voigt fluid, and fluids of order 1 and 2. For the latter cases it is shown that oscillatory convection may occur, and the nature of the stationary and oscillatory convection branches is investigated in detail, including where the transition from one to the other takes place.

Magneto-thermal-convection stability in an inclined cylindrical annulus filled with a molten metal

Purpose Metal-cooled reactors generally use molten metals such as sodium, potassium or a combination of sodium and potassium because of their excellent heat transfer properties so that the reactor can operate at much lower pressures and higher temperatures. The purpose of this paper is to investigate the stability of natural convection in an inclined ring filled with molten potassium under the influence of a radial magnetism. Design/methodology/approach A numerical simulation of electrically conductive fluid natural convection stability is performed on an inclined cylindrical annulus under the influence of a radial magnetism. The upper and lower walls are adiabatic, while the internal and external cylinders are kept at even temperatures. The equations governing this fluid system are solved numerically using finite volume method. The SIMPLER algorithm is used for pressure-speed coupling in the momentum equation. Findings Numerical results for various effective parameters that solve the problem in the initial oscillatory state are discussed in terms of isobars, isotherms and flow lines in the annulus for a wide range of Hartmann numbers (0 ≤ Ha ≤ 80), inclination angles (0 ≤ γ ≤ 90°) and radii ratios λ ≤ 6. The dependency stability diagrams between complicated situations with the critical value of the Rayleigh number RaCr and the corresponding frequency FrCr are established on the basis of the numeric data of this investigation. The angle of inclination and the radii ratio of the annulus have a significant effect on the stabilization of the magneto-convective flux and show that the best stabilization of the natural oscillatory convection is obtained by the intensity of the strongest magnetic field, the high radii ratio and inclination of the annulus at γ = 30°. Practical implications This numerical model is selected for its various applications in technology and industry. Originality/value To the best of the authors’ knowledge, the influence of the inclination of the cylindrical annulus (ring), with various radii ratio, on natural oscillatory convection under a radial magnetism has never been investigated.

Heated and Salted Below Porous Convection with Generalized Temperature and Solute Boundary Conditions

We address the problem of initiation of convective motion in the case of a fluid saturated porous layer, containing a salt in solution, which is heated and salted below. We amplify the very interesting recent results of Nield and Kuznetsov and examine in detail a whole range of temperature and salt boundary conditions allowing for a combination of prescribed heat flux and temperature. The behaviour of the transition from stationary to oscillatory convection is examined in detail as the boundary conditions vary from prescribed temperature and salt concentration toward those of prescribed heat flux and salt flux.

On the linear convective stability of a TiO2 particle–based nanofluid layer heated from below

The linear hydrodynamics of Rayleigh convection in a horizontal nanofluid layer heated from below was studied. The hydrodynamic stability of the fluid layer bounded by two horizontal perfect thermal conducting walls was extended to analyze steady and oscillatory convection, and the role played by thermophoresis. Experimental data of TiO2 particle–based nanofluid was used to discuss the stability of the fluid layer. Results on the relationship between thermal and volume faction Rayleigh numbers are used to discuss experiments in nanofluid Rayleigh convection, while the absence of thermophoresis in the model equations was also considered. For this nanofluid, steady convection sets in at critical wavenumber ac = 3.12, but thermal RT and nanoparticle volume fraction RV Rayleigh numbers are given by an implicit relationship. For the onset of oscillatory convection, the wavenumber is also obtained from an implicit equation involving RT and RV. Results are discussed in terms of physical dimensionless parameters of the system like the Lewis and Prandtl numbers. This work complements the earlier efforts of Tzou and more recently by Nield and Kuznetsov.