Min Chan Kim

Buoyancy-driven convection in plane Poiseuille flow

Abstract Buoyancy effects in plane Poiseuille flow heated isothermally from below were analyzed. By employing the propagation theory we have developed the critical streamwise position to mark the onset of stationary longitudinal vortex rolls was predicted as a function of the Prandtl number. Combining the present stability criteria with the boundary-layer instability model, a new correlation of transport properties on mixed convection was derived. Even though the present modelling is rather simple, theoretical results compare well with experiments of both air and ionic mass transfer in aqueous CuSO 4 solution systems.

Analysis of onset of buoyancy-driven convection in a fluid layer saturated in anisotropic porous media by the relaxed energy method

A theoretical analysis of buoyancy-driven instability under transient basic fields is conducted in an initially quiescent, fluid-saturated, horizontal porous layer. Darcy’s law is used to explain characteristics of fluid motion, and the anisotropy of permeability is considered. Under the Boussinesq approximation, the energy stability equations are derived following the energy formulation. The stability equations are analyzed numerically under the relaxed energy stability concept. For the various anisotropic ratios, the critical times are predicted as a function of the Darcy-Rayleigh number, and the critical Darcy-Rayleigh number is also obtained. The present predictions are compared with existing theoretical ones.

Onset of buoyancy-driven convection in a liquid-saturated cylindrical porous layer supported by a gas layer

A theoretical analysis of convective instability driven by buoyancy forces under the transient concentration fields is conducted in an initially quiescent, liquid-saturated, cylindrical porous layer with gas diffusion from below. Darcy’s law and Boussinesq approximation are used to explain the characteristics of fluid motion, and linear stability theory is employed to predict the onset of buoyancy-driven motion. Under the principle of exchange of stabilities, the stability equations are derived on the basis of the propagation theory and the dominant mode method, which have been developed in a self-similar boundary layer coordinate system. The present predictions suggest the critical Darcy–Rayleigh number RD, which is quite different from the previous ones. The onset time becomes smaller with increasing RD and follows the asymptotic relation derived in the infinite horizontal porous layer.

Onset of buoyancy-driven convection in the horizontal fluid layer heated from below with time-dependent manner

The onset of buoyancy-driven convection in an initially isothermal, quiescent fluid layer heated from below with time-dependent manner is analyzed by using propagation theory. Here the dimensionless critical time Τc to mark the onset of convective instability is presented as a function of the Rayleigh number RaØ and the Prandtl number Pr. The present stability analysis predicts that Τc decreases with increasing Pr for a given RaØ. The present predictions compare reasonably well with existing experimental results. It is found that in deep-pool systems the deviation of temperature profiles from conduction state occurs starting from a certain time Τ≏(2∼4) Τc.

Onset of radial viscous fingering in a Hele-Shaw cell

AbstractThe onset of viscous fingering in a radial Hele-Shaw cell was analyzed by using linear theory. In the selfsimilar domain, the stability equations were derived under the normal mode analysis. The resulting stability equations were solved analytically by expanding the disturbances as a series of orthogonal functions and also numerically by employing the shooting method. It was found that the long wave mode of disturbances has a negative growth rate and the related system is always stable. For the limiting case of the infinite Péclet number, Pe→∞, the analytically obtained critical conditions are Rc=11.10/

Some theoretical aspects on the onset of buoyancy-driven convection in a fluid-saturated porous medium heated impulsively from below

\sqrt {Pe}

The onset of convective instability in the thermal entrance region of plane Poiseuille flow heated uniformly from below

and nc=0.87

Nonlinear numerical simulation on the onset of Soret-driven motion in a silica nanoparticles suspension

\sqrt {Pe}

Relative energy stability analysis on the onset of Taylor-Görtler vortices in impulsively accelerating Couette flow

. For Pe≥100, these stability conditions explain the system quite well.

THE ONSET OF CONVECTIVE MOTION IN A HORIZONTAL FLUID LAYER HEATED FROM BELOW AND COOLED FROM ABOVE WITH CONSTANT HEAT FLUX

Some theoretical aspects of the onset of buoyancy-driven instability in an initially quiescent, isotropic fluidsaturated porous layer are considered. Darcy’s law is employed to examine characteristics of fluid motion under the Boussinesq approximation. Using linear theory, we derive stability equations and transform them in the similarity domain. Based on linear stability equations in the similarity domain, we prove the principle of exchange of stabilities and show that the stability parameter is stationary. The temperature disturbance field is expressed as a series of orthonormal functions and the vertical velocity one is obtained in simple recursive form. The validity of the quasi-steady state approximation (QSSA) is also proved by comparing the stability characteristics under the QSSA with those obtained from the eigenanalysis without the QSSA.