• 한국전산유체공학회:학술대회논문집
• /
• 2008.08a
• /
• pp.84.2-84.2
• /
• 2008

• Transactions of the Korean Society of Mechanical Engineers B
• /
• v.38 no.11
• /
• pp.935-942
• /
• 2014

A numerical analysis of the effect of the Prandtl number on the natural convection in a cold outer tilted square enclosure with an inner hot circular cylinder is presented. Several Prandtl numbers (Pr=0.1, 0.7, 7) are considered, with different angles($0^{\circ}$, $15^{\circ}$, $30^{\circ}$, $45^{\circ}$) for the enclosure and Rayleigh numbers ($Ra=10^3$, $10^4$, $10^5$). The effect of the Prandtl number on the natural convection is analyzed using isotherms and streamline and surface-averaged Nusselt numbers. The flow and heat transfer characteristics are found to be dependent on the time for $Ra=10^5$ and Pr=0.1 at angles of $0^{\circ}$ and $45^{\circ}$. However, in the other cases, the flow and heat transfer characteristics are independent of the time.The surfaceaveraged Nusselt number increases with an increase in the Prandtl number. As the Prandtl number increases, the Nusselt number becomes larger regardless of the angle for $Ra=10^5$. In particular, the Nusselt number steeply increases when the angle is $45^{\circ}$ for $Ra=10^5$ and Pr=0.1.

• 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.

• Transactions of the Korean Society of Mechanical Engineers B
• /
• v.26 no.8
• /
• pp.1172-1182
• /
• 2002

In the present study a general criterion for local thermal equilibrium is presented in terms of parameters of engineering importance which include the Darcy number, the effective Prandtl number of fluid, and the Reynolds number. For this, an order of magnitude analysis is performed for the case when the effect of convection heat transfer is dominant in a porous structure. The criterion proposed in this study is more general than the previous criterion suggested by Carbonell and Whitaker, because the latter is applicable only when conduction is the dominant heat transfer mode in a porous medium while the former can be applied even when convection heat transfer prevails. In order to check the validity of the proposed criterion for local thermal equilibrium, the forced convection phenomena in a porous medium with a microchanneled structure subject to an impinging jet are studied using a similarity transformation. The proposed criterion is also validated with the existing experimental and numerical results for convection heat transfer in various porous materials that include some of the parameters used in the criterion such as a microchannel heat sink with a parallel flow, a packed bed, a cellular ceramic, and a sintered metal. It is shown that the criterion presented in this work well-predicts the validity of the assumption of local thermal equilibrium in a porous medium.

• Transactions of the Korean Society of Mechanical Engineers B
• /
• v.38 no.12
• /
• pp.975-982
• /
• 2014

This study evaluates the effect of a heated circular cylinder's size on three-dimensional natural convection in a cubical enclosure. The Rayleigh number was varied between $10^3$ and $10^5$, and the Prandtl number was maintained at 0.7. In this study, the radius of the circular cylinder was changed by 0.1 L within a range of 0.1-0.4 L. The thermal and fluid flow characteristics were regarded to be independent of time in the range of the Rayleigh number and cylinder radius considered in this study. The surface-averaged Nusselt numbers of the cylinder and the enclosure were found to increase with the increase in the radius of the cylinder. The effect of the cylinder's size on natural convection in the enclosure was analyzed across the thermal and flow fields, and the distributions of the Nusselt numbers.

• Transactions of the Korean Society of Mechanical Engineers
• /
• v.12 no.3
• /
• pp.541-550
• /
• 1988

Natural convection in a square enclosure was investigated numerically for low prandtl number fluids using Finite Element Method. In case of Ra=10$^{4}$, 10$^{5}$ and 10$^{6}$ the temperature gradient decreases gradually at the lower end of the hot wall(or at the upper end of the cold wall) as prandtl number decreases in the range of 0.01 .leq. Pr .leq. 10. Maximum heat transfer occurs at a somewhat higher point from the lower end of hot wall(or at somewhat lower point from the upper end of the cold wall) and it draws near to the lower end of the hot wall(or draws near to the upper end of the cold wall) with increasing prandtl number. The flow in the enclosure appears as an Unicell Pattern for Ra .leq. 10$^{4}$ and secondarily flows(or tertiary flows) appears in the core region for Ra .geq. 10$^{5}$ . The line joining the center of secondary cells skewes in a clockwise direction as the Prandtl number decreases.

• Journal of the Korean Magnetics Society
• /
• v.17 no.6
• /
• pp.253-258
• /
• 2007

In this study, an analysis of natural convection of magnetic fluids in a closed-semicircular pipe was performed by the numerical methods. For the numerical method GSMAC method of Siliomis is used. From the results of numerical methods it is verified that the natural convection of the magnetic fluid, I investigated the nature convection phenomenon of the magnetic fluid with numerical analysis and was going to study the thermodynamic characteristic of the magnetic fluid. Because the effect of magnetic field control natural convection, we needed to find effective method to eliminate heat in the cure of heat transfer.

• Journal of the Korean Society for Industrial and Applied Mathematics
• /
• v.12 no.4
• /
• pp.201-202
• /
• 2008

Because of the importance of suction or injection in the fields of aerodynamics, space science and many other industrial applications, our present study is motivated. The effect of natural convection on MHD flow past a vertical plate with suction or injection is studied. We have tried to solve the dimensionless governing equations by using finite difference scheme. To ensure the validity of our numerical solutions, we have compared our numerical solutions for temperature and velocity for the case of suction and injection for unit Prandtl number with the available exact solutions in the literature. The corresponding codes were written in Mathematica 5.0 for calculating numerical solutions for temperature and velocity and the comparison between the exact and numerical solutions. For the purpose of discussing the results some numerical calculations are carried out for non-dimensional temperature T, velocity u, skin friction ${\tau}$ and the Nusselt number $N_u$, by making use of it, the rate of heat transfer is studied.

• Korean Journal of Air-Conditioning and Refrigeration Engineering
• /
• v.1 no.4
• /
• pp.305-312
• /
• 1989

Laminal natural convection heat transfer in the annulus between isothermal horizontal non-circular cylinders is studied by solving the Navier-Stokes and energy equation using an elliptic numerical procedure. Results are obtained to determine the effects of the diameter ratio($D_o/D_i$) and Rayleigh number on heat transfer. The diameter ratio is varied from 1.5 to 13.0 at Pr=0.7, H/L=1.5 and $10^3{\leqslant}Ra_L{\leqslant}4{\times}10^4$. It is found that the diameter ratio causes a more significant on the local heat transfer coefficient of lower semi-circular cylinder and plate than upper semi-circular cylinder. The mean Nusselt number increases as the diameter ratio and Rayleigh number increase, and is higher than that of the circular annulus with a same wetted perimeter.

• Transactions of the Korean Society of Mechanical Engineers B
• /
• v.24 no.2
• /
• pp.169-176
• /
• 2000

Natural convection in a wide-gap horizontal annulus is considered, and the transition of flows and the bifurcation phenomenon are investigated for the fluids with Pr=0.2 and 0.3. At Pr=0.2, a bicellular flow pattern is observed at high Rayleigh number, and the solution is unique. At Pr=0.3, both the steady unicellular and bicellular flows exist above a certain critical Rayleigh number. For the fluids of Pr=0.2, the bicellular flow can be obtained by the impulsive heating of the inner cylinder, but it is not obtained from the zero initial condition for Pr=0.3. Hysteresis phenomena have not been observed. A transition from a bicellular flow to a unicellular flow occurs for Pr=0.3.