• Transactions of the Korean Society of Mechanical Engineers B
• /
• v.38 no.11
• /
• pp.943-950
• /
• 2014

This paper presents a numerical study conducted for analyzing the effect of the Prandtl number on natural convection in a square enclosure with an inner circular cylinder in various positons. Several Prandtl numbers (Pr = 0.1, 0.7, and 7) and Rayleigh numbers (Ra = $10^3$, $10^4$ and $10^5$) are considered in the numerical study, along with different positions of the inner circular cylinder. The position of the inner circular cylinder is changed in steps of 0.1 in the range of -0.2 to 0.2. The effect of the Prandtl number on natural convection in the enclosure is analyzed on the basis of the thermal and flow fields and the distribution of the Nusselt number. Regardless of the position of the cylinder, when the Rayleigh number is $10^5$, the surface-averaged Nusselt number of the inner cylinder and the enclosure increases as the Prandtl number increases.

• 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.

• Journal of Energy Engineering
• /
• v.7 no.2
• /
• pp.187-193
• /
• 1998

The turbulent heat transfer to low Prandtl number fluid flow through rod bundles is analyzed using k-$\varepsilon$ two-equation model. For the prediction of the turbulent flow field, an anisotropic eddy viscosity model is used. In the analysis of the temperature field, the effects of various parameters such as geometry, Reynolds and Prandtl numbers are considered. The calculation in made for Prandtl numbers from 0.001 to 0.1 in order to analyze the heat transfer to low Prandtl number fluid such as liquid metals. The numerical results show that for small P/D (Pitch/Diameter) geometries low Prandtl number makes severe changes of the rod surface temperature.

• 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.

• 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 Institute of Intelligent Systems
• /
• v.24 no.2
• /
• pp.193-200
• /
• 2014

Piezoelectric actuators have been widely used in various applications because they have many advantages such as fast response time, repeatable nanometer motion, and high resolution. However Piezoelectric actuators have the strong hysteresis effect. The hysteresis effect can degrade the performance of the system using piezoelectric actuators. In past study, the parameters of the inverse hysteresis model are computed from the identified parameters using the Generalized Prandtl-Ishlinskii(GPI) model to cancel the hysteresis effect, however according to the identified parameters there exist the cases that can't form the inverse hysteresis loop. Thus in this paper the inverse hysteresis modeling mothod is proposed using the Inverse Generalized Prandtl-Ishlinskii(IGPI) model to handle that problem. The modeling results are verified by experimental results using various input signals.

• Transactions of the Korean Society of Mechanical Engineers
• /
• v.11 no.2
• /
• pp.345-353
• /
• 1987

An analysis is performed to study flow and heat transfer characteristics of mixed free and forced convection about a sphere. Nonsimilar boundary layer equations which are valid over the entire regime of mixed convection are derived in terms of the mixed convection parameter, Gr/Re$^{2}$, through a dimensional analysis. The transformed conservation equations are solved by a finite difference method for the whole range of mixed convection regime. Numerical results for fluids having the Prandtl number 0.7 and 7 are presented. As the mixed convection parameter increases, the local friction coefficient and local heat transfer coefficient increases as well. For small Prandtl number, the friction coefficient is larger, while for large Prandtl number, the heat transfer coefficient is larger. Natural convection effect on the forced flow is more sensitive for small Prandtl number fluid. Flow separation migrates rearward as an increase in the mixed convection parameter. For small Prandtl number, the buoyancy effect is relatively small so that the flow separation occurs earlier.

• 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.

• Journal of Mechanical Science and Technology
• /
• v.19 no.3
• /
• pp.913-923
• /
• 2005

The dynamic mixed model (DMM) combined with a box filter of Zang et. al. (1993) has been generalized for passive scalar transport and applied to large eddy simulation of turbulent channel flows with Prandtl number up to 10. Results from a priori test showed that DMM is capable of predicting both subgrid-scale (SGS) scalar flux and dissipation rather accurately for the Prandtl numbers considered. This would suggest that the favorable feature of DMM, originally developed for the velocity field, works equally well for scalar transport problem. The validity of the DMM has also been tested a posteriori. The results of the large eddy simulation showed that DMM is superior to the dynamic Smagorinsky model in the prediction of scalar field and the model performance of DMM depends to a lesser degree on the ratio of test to grid filter widths, unlike in the a priori test.

• International Journal of Aeronautical and Space Sciences
• /
• v.9 no.2
• /
• pp.9-17
• /
• 2008

When the stagnation temperature of the combustion chamber or ambient air increases, the specific heats and their ratio do not remain constant any more, and start to vary with this temperature. The gas remains perfect, except, it will be calorically imperfect and thermally perfect. A new generalized form of the Prandtl Meyer function is developed, by adding the effect of variation of this temperature, lower than the threshold of dissociation. The new relation is presented in the form of integral of a complex analytical function, having an infinite derivative at the critical temperature. A robust numerical integration quadrature is presented in this context. The classical form of the Prandtl Meyer function of a perfect gas becomes a particular case of the developed form. The comparison is made with the perfect gas model for aim to present a limit of its application. The application is for air.