Tae Joon Chung

The onset of vortex instability in laminar forced convection flow through a horizontal porous channel

Abstract The onset of convective instability in a fluid-saturated porous layer between the two horizontal plates heated isothermally from below has been analyzed theoretically by using propagation theory. In the analysis the thermal dispersion coefficient is assumed to be proportional to the streamwise velocity. The results show that both inertia and thermal dispersion stabilize the system.

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.

The Temporal Evolution of Thermal Instability in Fluid Layers Isothermally Heated from Below

The temporal development of thermal disturbances in the fluid layer heated isothermally from below is investigated, based on propagation theory. This theory is examined by using scaling. To examine the behavior of thermal instability the mean-field approximation is employed and resulting equations are solved by Galerkin method. The stability criteria to mark the onset of convective instability are newly suggested as the intersection point of the growth rate of averaged temperature with that of its fluctuation. The resulting critical time is close to that derived from propagation theory. By considering the nonlinear effects, the characteristic times to represent the detection time of manifest convection and also to exhibit the minimum Nusselt number are discussed.

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

Abstract The onset condition of regular longitudinal vortex rolls in the thermal entrance region of plane Poiseuille flow heated from below is analyzed. Under propagation theory the stability equations are produced self-similarly, based on scale analysis. The onset position of secondary flow, which represents the starting point of mixed convection, is predicted as a function of the Prandtl number, Reynolds number and Rayleigh number. As expected, the critical position moves upstream as the Rayleigh number increases and an increase in Reynolds number makes the system more stable. The present predictions compare favorably with existing experimental data of water and air.