The Onset of Double-Diffusive Nanofluid Convection in a Layer of a Saturated Porous Medium

The onset of convection in a horizontal layer of a porous medium saturated by a nanofluid is studied analytically. The model used for the nanofluid incorporates the effects of Brownian motion and thermophoresis. For the porous medium, the Brinkman model is employed. Three cases of free–free, rigid–rigid, and rigid–free boundaries are considered. The analysis reveals that for a typical nanofluid (with large Lewis number), the prime effect of the nanofluids is via a buoyancy effect coupled with the conservation of nanoparticles, whereas the contribution of nanoparticles to the thermal energy equation is a second-order effect. It is found that the critical thermal Rayleigh number can be reduced or increased by a substantial amount, depending on whether the basic nanoparticle distribution is top-heavy or bottom-heavy, by the presence of the nanoparticles. Oscillatory instability is possible in the case of a bottom-heavy nanoparticle distribution.     

The onset of convection in a horizontal nanofluid layer of finite depth

This paper presents a linear stability analysis for the onset of natural convection in a horizontal nanofluid layer. The employed model incorporates the effects of Brownian motion and thermophoresis. Both monotonic and oscillatory convection for free–free, rigid–rigid, and rigid–free boundaries are investigated. The oscillatory instability is possible when nanoparticles concentrate near the bottom of the layer, so that the density gradient caused by such a bottom-heavy nanoparticle distribution competes with the density variation caused by heating from the bottom. It is established that the instability is almost purely a phenomenon due to buoyancy coupled with the conservation of nanoparticles. It is independent of the contributions of Brownian motion and thermophoresis to the thermal energy equation. Rather, the Brownian motion and thermophoresis enter to produce their effects directly into the equation expressing the conservation of nanoparticles so that the temperature and the particle density are coupled in a particular way, and that results in the thermal and concentration buoyancy effects being coupled in the same way.     

Measurement of the polarization in backward-angle π−p elastic scattering at 2.93 and 3.25 GeV/c

Polarization in π^?p elastic scattering, with emphasis over the backward region, has been measured at 2.93 and 3.25 GeV/c. We observe large changes in polarization compared with existing data above and below these energies. Our data may be useful in determining the properties of resonances and in understanding baryon exchanges.     

A Note on a Brinkman–Brinkman Forced Convection Problem

The problem of fully developed forced convection in a parallel-plates channel filled with a saturated porous medium (involving a Brinkman model for the momentum equation), with the effect of viscous dissipation (involving a Brinkman number), is discussed. Some general matters relating to the possibility of fully developed convection are also discussed.     

Effects of Viscous Dissipation and Flow Work on Forced Convection in a Channel Filled by a Saturated Porous Medium

Fully developed forced convection in a parallel plate channel filled by a saturated porous medium, with walls held either at uniform temperature or at uniform heat flux, with the effects of viscous dissipation and flow work included, is treated analytically. The Brinkman model is employed. The analysis leads to expressions for the Nusselt number, as a function of the Darcy number and Brinkman number.     

Convective heat transfer in porous media with columnar structure

An analysis is made of convective heat transport, produced by uniform heating from below, in a horizontal layer of a porous medium consisting of vertical slabs or columns of different permeabilities. Estimates of the heat flux are made on the assumption that flow in one column does not interact with flow in adjacent columns. The results are compared with those for a homogeneous layer, for which previous work is reviewed. It is found that an inhomogeneous layer transports less heat than a homogeneous layer for which the mean Rayleigh number is the same, if the Rayleigh number is supercritical throughout the layer. If the Rayleigh number is subcritical in part of the layer, the inhomogeneous layer may transport more heat than the equivalent homogeneous layer.     

Modelling the Effect of Surface Tension on Immiscible Displacement in a Saturated Porous Medium

Comments are made about the model employed by Chen and Vafai for forced convection in a porous medium channel, with a surface tension effect at the moving interface between two fluids, when one fluid is displaced by the other. A simple situation is analysed, and the circumstances under which surface tension effects are important in this case are clarified.     

Forced Convection with Laminar Pulsating Flow in a Saturated Porous Channel or Tube

A perturbation approach is used to obtain analytical expressions for the velocity, temperature distribution, and transient Nusselt number for the problem of forced convection, in a parallel-plates channel or a circular tube occupied by a saturated porous medium modeled by the Brinkman equation, produced by an applied pressure gradient that fluctuates with small amplitude harmonically in time about a non-zero mean. It is shown that the fluctuating part of this Nusselt number alters in magnitude and phase as the dimensionless frequency increases. The magnitude increases from zero, goes through a peak, and then decreases to zero. The height of the peak decreases as the modified Prandtl number increases. The phase (relative to that of the steady component) decreases from π/2 to − π/2. The height of the peak at first increases, goes through a maximum, and then decreases as the Darcy number decreases.     

The onset of convection in a shallow box occupied by a heterogeneous porous medium with constant flux boundaries

The effects of hydrodynamic and thermal heterogeneity, for the case of variation in both the horizontal and vertical directions, on the onset of convection in a horizontal layer of a saturated porous medium uniformly heated from below, are studied analytically using linear stability theory for the case of weak heterogeneity. Attention is focused on the case of constant flux upper and lower boundaries, a case for which the critical horizontal wavenumber is zero, and attention is also concentrated on the case of a shallow layer. It is found that the effect of such heterogeneity on the critical value of the Rayleigh number Ra based on mean properties is of second order if the properties vary in a piecewise constant or linear fashion. The effects of horizontal heterogeneity and vertical heterogeneity are then comparable once the aspect ratio is taken into account, and to a first approximation are independent. The combination of permeability heterogeneity and conductivity heterogeneity can be either stabilizing or destabilizing for the present case.     

Forced Convection with Laminar Pulsating Counterflow in a Saturated Porous Circular Tube

An analytical solution is obtained for forced convection in a circular tube occupied by a core–sheath-layered saturated porous medium with counterflow produced by pulsating pressure gradients. The case of the constant heat-flux boundary conditions is considered, and the Brinkman model is employed for the porous medium. A perturbation approach is used to obtain analytical expressions for the velocity, temperature distribution, and transient Nusselt number for convection produced by an applied pressure gradient that fluctuates with small amplitude harmonically in time about a non-zero mean. It is shown that the fluctuating part of the Nusselt number alters in magnitude and phase as the dimensionless frequency increases. The magnitude increases from zero, goes through a peak, and then decreases to zero. The height of the peak depends on the values of various parameters. The phase (relative to that of the steady component) decreases from π/2 to − π/2 as the frequency increases.