• Transactions of the Korean Society of Mechanical Engineers B
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• v.38 no.11
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• pp.943-950
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• 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
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• v.38 no.11
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• pp.935-942
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• 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.

• Korean Journal of Air-Conditioning and Refrigeration Engineering
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• v.21 no.6
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• pp.340-346
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• 2009

This paper numerically investigates thermo-flow characteristics of offset strip fins to obtain a correlation between heat transfer and pressure drop. The flow was divided into three regimes, i.e. laminar, transition and turbulent. The predicted j and f values from the SST k-$\omega$ turbulence model agreed with previous correlations with the error less than 20% in transition and turbulent regimes. Heat transfer and pressure drop were predicted by varying Prandtl number from 0.5 to 40. The Prandtl number showed little effects on pressure drop but had great effect on the heat transfer characteristics. An overall correlation to predict j was suggested by incorporating the effect of Pr and a new j correlation was suggested for each Pr.

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

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

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

• Proceedings of the SAREK Conference
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• 2008.11a
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• pp.233-238
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• 2008

This paper numerically investigates thermo-flow characteristics of offset strip fins to obtain a correlation between heat transfer and pressure drop. The flow was divided into three regimes, i.e. laminar, transition and turbulent. The predicted j and f values from the SST k-$\omega$ turbulence model agreed with previous correlations with the error less than 20% in transition and turbulent regimes. Heat transfer and pressure drop were predicted by varying Prandtl number from 0.5 to 40. The Prandtl number showed little effects on pressure drop but had great effect on the heat transfer characteristics. An overall correlation to predict j was suggested by incorporating the effect of Pr and a new j correlation was suggested for each Pr.

• Proceedings of the KSME Conference
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• 2008.11b
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• pp.2248-2253
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• 2008

A numerical study on oscillatory thermocapillary flow in half-zone has performed to understand the effect of axial rotation. 2d unsteady code is developed to observe the onset of oscillation. 2cs Silicone oil with Prandtl number of 26.5 is used as a working fluid. The critical temperature difference at onset of oscillation is investigated under the different aspect ratios and rotation modes. It is shown that the onset of oscillation is delayed when aspect ratio reduces and rotating speed increases. The oscillatory flow is strongly reduced under top rotation and co-rotation modes, while it is augmented under bottom rotation and counter-rotation modes. It is thought that interaction between return flow and bottom wall is important to explain the oscillatory flow.

• Korean Journal of Air-Conditioning and Refrigeration Engineering
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• v.6 no.4
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• pp.325-336
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• 1994

A numerical simulation of velocity and temperature fields and Nusselt number distributions is performed by using the algebraic stress model (ASM) for the velocity profiles and low Reynolds number ${\kappa}-{\varepsilon}$ model and the algebraic heat flux model(AHFM) for turbulent heat transfer in a $180^{\circ}$ bend with a constant wall heat flux. In the low Reynolds number ${\kappa}-{\varepsilon}$ model, turbulent Prandtl number is modified by considering the streamline curvature effect and the non-equilibrium effect between turbulent kinetic energy production and dissipation rate. Every heat flux term presented in the transport equation of turbulent heat flux is reduced to algebraic expressions in a way similar to algebraic stress model. Also. in the wall region, low Reynods number algebraic heat flux model(AHFM) is applied.

• Journal of Energy Engineering
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• v.7 no.1
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• pp.113-121
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• 1998

In natural convection flows, the fluid velocities are highly dependent on the thermal field and property variations can have a strong effect on both the flow and thermal fields. To examine the effect of property variations, at first, numerical analyses covering wide range of the Prandtl number under the same Rayleigh numbers have been carried out. Next, we have modeled the viscosity and thermal conductivity as parabolic functions of temperature and a comprehensive set of numerical solutions have been obtained to understand the effect. The Prandtl number dependence of Nusselt number is fairly strong even though the effect is still weak compared to the Rayleigh number dependence. When thermophysical properties are dependent on temperature, the flow field showed a fairly weak variation except near boundaries, whereas the temperature field is strongly affected, especially by the temperature dependent thermal conductivity.