Thermal convective instability in an Oldroyd-B nanofluid saturated porous layer

The onset of convective instability in a layer of porous medium saturated by the Oldroyd-B viscoelastic nanofluid heated from below is investigated by incorporating the effects of Brownian diffusion and thermophoresis. The flux of volume fraction of nanoparticles is taken to be zero on the boundaries. The resulting eigenvalue problem is solved numerically using the Galerkin method. The onset of convective instability is oscillatory only if the strain retardation parameter is less than the stress relaxation parameter and also when the strain retardation parameter does not exceed a threshold value which in turn depends on other physical parameters. The oscillatory onset is delayed with increasing strain retardation parameter, while an opposite trend is noticed with increasing stress relaxation parameter. The effect of increasing modified diffusivity ratio, concentration Darcy–Rayleigh number, modified particle density increment and Lewis number is to hasten the onset of stationary and oscillatory convection and also to decrease the ranges of the strain retardation parameter within which oscillatory convection is preferred.postprin

A thermal non-equilibrium model with Cattaneo effect for convection in a Brinkman porous layer

This paper aims to investigate the onset of thermal convection in a layer of fluid-saturated Brinkman porous medium taking into account fluid inertia and local thermal non-equilibrium (LTNE) between the solid and fluid phases with Cattaneo effect in the solid. A two-field model is used for the energy equations each representing the solid and fluid phases separately. The usual Fourier heat-transfer law is retained in the fluid phase while the solid phase is allowed to transfer heat via a Cattaneo heat flux theory. It is observed that the Cattaneo effect has a profound influence on the nature of convective instability. In contrast to the standard Brinkman convection with LTNE model, instability is found to occur through oscillatory convection depending on the value of solid thermal relaxation time parameter which in turn depends on other parametric values. The instability characteristics of the system are analyzed in detail for a wide range of parametric values including those for copper oxide and aluminium oxide solid skeletons.postprin

Stability of fluid flow in a Brinkman porous medium - a numerical study

The stability of fluid flow in a horizontal layer of Brinkman porous medium with fluid viscosity different from effective viscosity is investigated. A modified Orr-Sommerfeld equation is derived and solved numerically using the Chebyshev collocation method. The critical Reynolds number Rec, the critical wave number αc and the critical wave speed cc are computed for various values of porous parameter and ratio of viscosities. Based on these parameters, the stability characteristics of the system are discussed in detail. Streamlines are presented for selected values of parameters at their critical state.postprin

The dynamics and rheology of a dilute suspension of periodically forced neutrally buoyant spherical particles in a quiescent Newtonian fluid at low Reynolds numbers

We study the effects of both convective and unsteady inertia on the dynamics and rheology of a dilute suspension of periodically forced neutrally buoyant spherical particles, at low Reynolds numbers, in a quiescent Newtonian fluid. The inclusion of inertia results in additional terms in the equation governing the dynamics of the particle that represent a fading memory of the entire history of the particle motion. The inclusion of convective inertia in the low Reynolds number limit makes the memory term nonlinear. Several tests were performed to show that the results presented in this paper are physically reasonable and correct. A perturbation analysis of the problem yields strong evidence that the results of our simulations are correct. It is observed that there is a preferred direction in this system which manifests itself in the properties of the solution. This preferred direction is identified as the direction of the initial motion of the particle. We present here results on the behavior of various parameters with respect to Reynolds numbers and the amplitude of the periodic force. These include phase-space plots between particle displacement and particle velocity and the variation of a rheological parameter, namely a ‘normal stress’ with respect to Reynolds number and the amplitude of the periodic force. We believe that our results may be technologically important since the rheological parameter depends strongly on controllable parameters such as the Reynolds number and the amplitude of the periodic force. Further, this system is one of the simplest systems whose rheology shows non-Newtonian behavior, such as the presence of a normal stress. In addition, this system represents a physically realizable system for experimentally testing the frameworks developed to calculate the collective behavior of systems of oscillators with memory

Numerical simulation of the dynamics of a periodically forced spherical particle in a quiescent Newtonian fluid at low Reynolds numbers

In this paper we present the results of a numerical simulation of the dynamics of a periodically forced spherical particle in a quiescent Newtonian fluid at low Reynolds number. We describe the simulation and tests performed to validate our simulation. We have obtained results which are physically reasonable and hence we have confidence in our results. We include the effects of both convective and unsteady inertia on the dynamics at low Reynolds numbers. The inclusion of inertia results in additional linear and nonlinear terms in the equations representing a fading memory of the entire history of the motion. The nonlinearity though small in the parametric regime of interest, gives rise to some interesting features in the solution of the proble

Ferromagnetic convection in a heterogeneous porous medium

The effect of vertical heterogeneity of permeability on the onset convection in a horizontal layer of magnetized ferrofluid-saturated Darcy porous medium is investigated. Four different forms of vertical heterogeneity permeability function (Formula presented.) are considered for discussion. The eigenvalue problem is solved numerically using the Galerkin method for three types of temperature boundary conditions namely, (i) isothermal, (ii) insulated to temperature perturbations, and (iii) lower insulated to temperature perturbations and upper isothermal. The general quadratic variation in the vertical heterogeneity of permeability is to hasten the onset of ferromagnetic convection compared with other forms of (Formula presented.). The measure of nonlinearity of magnetization and the magnetic susceptibility is found to influence the onset if the boundaries are either isothermal or lower insulated and upper isothermal. Increasing the magnetic number is to augment the onset of ferromagnetic convection. The system is more stabilizing when the boundaries are isothermal and least stable for insulated ones. Compared to the homogeneous porous medium case, the critical wave number is higher if the permeability of the porous medium is heterogeneous and the boundaries are isothermal. © 2014, King Fahd University of Petroleum and Minerals