• Transactions of the Korean Society of Mechanical Engineers
• /
• v.16 no.1
• /
• pp.132-141
• /
• 1992

The critical condition for onset of Benard convection with variable viscosity .nu.=.nu.$_{0}$exp(-CT) has been obtained using a linear stability theory. The bottom wall is rigid while the upper surface may be either free or rigid. The two boundaries are subject to convective heat transfer. The critical Rayleigh numbers are presented up to maximum viscosity ratio of 3000. It is greater for smaller upper and/or lower surface Biot numbers. Its dependence on the viscosity ratio is complicated. However, a simple sublayer theory is found to be applicable for extremely large viscosity ratio. In such cases, the critical Rayleigh number and the critical wave number are functions of viscosity ratio and lower surface Biot number.r.

• Journal of computational fluids engineering
• /
• v.3 no.1
• /
• pp.73-81
• /
• 1998

The effect of vertical or horizontal throughflow on natural convection in horizontal porous layer was investigated. The computations were performed by employing Darcy-Brinkman-Forchheimer equation to consider the effect of inertia and viscous effect. The patterns of streamlines and isotherms are observed by changing the strength of throughflow. The vertical throughflow stabilizes the natural convection in porous layer. It also disturbs the developing vertical and horizontal velocity component of natural convection cell and increases the critical modified Rayleigh number. The horizontal throughflow influences the stabilization of natural convection in porous layer much more than the vertical throughflow. And it changes a stable convection into a oscillatory convection.

• Journal of computational fluids engineering
• /
• v.4 no.2
• /
• pp.1-8
• /
• 1999

Natural convection in a horizontal annulus with the inner cylinder heated by the application of a constant heat flux and the isothermally cooled outer cylinder is considered, and the transition of flows and the bifurcation phenomenon are numerically investigated for air with Pr=0.7. The zero initial condition always induces a crescent-sheped eddy flow. A bicellular flow in which the fluid descends along the vertical central plane of the annulus can be obtained at high Rayleigh number by introducing artificial numerical disturbances. Dual solutions are found above a certain critical Rayleigh number. Hysteresis phenomena have not been observed.

• Journal of Ocean Engineering and Technology
• /
• v.13 no.2 s.32
• /
• pp.129-137
• /
• 1999

The time of the onset of double-diffusive convection in time-dependent, nonlinear concentration fields is investigated theoretically. The initially quiescent horizontal fluid layer with a uniform temperature gradient experiences a sudden concentration change from below, but its stable thermal stratification affects concentration effects in such way to invoke convective motion. The related stability analysis, including Soret effect, is conducted on the basis of the propagation theory. Under the linear stability theory the concentration penetration depth is used as a length scaling factor, and the similarity transform for the linearized perturbation equations. The newlly obtained stability equations are solved numerically. The resulting critical time to mark the onset of regular cells are obtained as a function of the thermal Rayleigh number, the solute Rayleigh number, and the Soret effect coefficient. For a certain value of the Soret effect coefficient, the stable thermal gradient promote double-diffusive convective motion.

• Transactions of the Korean Society of Mechanical Engineers B
• /
• v.34 no.8
• /
• pp.739-747
• /
• 2010

Numerical calculations are carried out for evaluating the natural convection induced by the temperature difference between a hot inner circular cylinder and a cold outer square enclosure. A two-dimensional solution for unsteady natural convection is obtained by using the finite volume method to model an inner circular cylinder that was designed by using the immersed boundary method (IBM) for a Rayleigh number of $10^7$. In this study, we investigate the effect of the location ($\delta$) of the inner cylinder, which is located along the vertical central axis of the outer enclosure, on the heat transfer and fluid flow. The natural convection changes from unsteady to steady state depending on the $\delta$. The two critical lower bound and upper bound positions are ${\delta}_{C,L}$ = 0.05 and ${\delta}_{C,U}$ = 0.18, respectively. Within these defined bounds, the thermal and flow fields are in steady state.

• Journal of the Korean Society for Aeronautical & Space Sciences
• /
• v.48 no.9
• /
• pp.711-716
• /
• 2020

Injection visualization of heated mixed simulant droplets based on hydrocarbon fuel was performed under supercritical state environment. Mixed simulant consisted of Decane and Methylcyclohexane with different critical pressure and critical temperature. Flows injected into the supercritical state environment created droplet by Rayleigh breakup mechanism, and the Oh number and Re number were determined to confirm the breakup area. The temperature of the mixed simulant varied from Tr=0.49 to Tr=1.34. The flow rate was maintained at 0.7 to 0.8 g/s. Droplet became shorter in breakup length as heated and into a lumped form. Second droplet was formed and when Tr=1.34, the phase was not visible in the supercritical state with local unsteady flow.

• Korean Chemical Engineering Research
• /
• v.55 no.6
• /
• pp.868-873
• /
• 2017

Natural convection is driven by the compositional buoyancy in solidification of a binary melt. The stabilities of convection in a growing mushy layer were analyzed here in the time-dependent solidification system of a near-eutectic melt cooled impulsively from below. The linear stability equations were transformed to self-similar forms by using the depth of the mushy layer as a length scale. In the liquid layer the stability equations are based on the propagation theory and the thermal buoyancy is neglected. The critical Rayleigh number for the mushy layer increases with decreasing the Stefan number and the Prandtl number. The critical conditions for solidification of aqueous ammonium chloride solution are discussed and compared with the results of the previous model for the liquid layer.

• Nuclear Engineering and Technology
• /
• v.44 no.3
• /
• pp.283-296
• /
• 2012

The natural convection in a horizontal enclosure heated from the bottom wall, cooled at the top wall, and having a square adiabatic body in the center is studied. Three different Prandtl numbers (0.01, 0.7 and 7) are considered for the investigation of the effect of the Prandtl number on natural convection. Adiabatic boundary conditions are employed for the side walls. A two-dimensional solution for unsteady natural convection is obtained, using an accurate and efficient Chebyshev spectral methodology for different Rayleigh numbers varying over the range of $10_3$ to $10_6$. It had been experimentally reported that the heat transfer mode becomes oscillatory when Pr is out of a specific Pr band beyond the critical Ra. In this study, we reproduced this phenomenon numerically. It was found that when Ra=$10_6$, only the case for intermediate Pr (=0.7) reached a non-changing steady state and the low and high Pr number cases (Pr=0.01 and 7) showed a periodically oscillatory fashion hydrodynamically and thermally. The variation of time- and surface-averaged Nusselt numbers on the hot and cold walls for different Rayleigh numbers and Prandtl numbers are presented to show the overall heat transfer characteristics in the system. Further, the isotherms and streamline distributions are presented in detail to compare the physics related to their thermal behavior.

• Transactions of the Korean Society of Mechanical Engineers
• /
• v.16 no.10
• /
• pp.1963-1970
• /
• 1992

An oscillatory motion of the natural convection in a two dimensional, partially divided square enclosure heated from below, and fitted with a partition is investigated numerically. The enclosure was composed of the lower hot and the upper cold horizontal walls and the adiabatic vertical walls, and a partition was situated perpendicularly at the mid-height of the one vertical insulated wall. The governing equations are solved by using the finite element method with Galerkin method. The computations were performed with the variation of the length and the thermal conductivity of the partition, and Rayleigh number based on the temperature difference between horizontal walls and the enclosure height with water(Pr=4.95). also, the effect of the inclination angles was studied for the transition to the oscillating flow. As the results, it was found that the intensity and frequency of oscillatory motion were affected significantly by the Rayleigh number and the length of partition. The effect of oscillatory motion was weaken with the increase of the thermal conductivity of partition. The inclination angle for the transition was raised with the increase of Rayleigh number and the length of partition.

• Journal of computational fluids engineering
• /
• v.16 no.3
• /
• pp.29-36
• /
• 2011

The natural convection in a horizontal enclosure heated from the bottom wall, cooled at the top wall, and having a square adiabatic body at its centered area was studied. Three different Prandtl numbers (0.01, 0.7 and 7) were considered for an effect of the Prandtl number on natural convection. A two-dimensional solution for unsteady natural convection was obtained, using Chebyshev spectral methodology for different Rayleigh numbers varying over the range of $10^4$ to $10^6$. It had been experimentally and numerically reported [1,2] that the heat transfer mode becomes oscillatory when Pr is out of a specific Pr band beyond the critical Ra. In this study, we reproduced this phenomenon numerically. The variation of time- and surface-averaged Nusselt numbers on the hot and cold walls for different Rayleigh numbers and Prandtl numbers was presented to show the overall heat transfer characteristics in the system. And also, the isotherms and streamline distributions were presented in detail to compare the physics related to their thermal behavior.