Man Yeong Ha

A numerical study on three-dimensional conjugate heat transfer of natural convection and conduction in a differentially heated cubic enclosure with a heat-generating cubic conducting body

Abstract A comprehensive numerical study has been conducted to investigate three-dimensional, steady, conjugate heat transfer of natural convection and conduction in a vertical cubic enclosure within which a centered, cubic, heat-conducting body generates heat. The physical model considered here assumes that a temperature difference exists across the enclosure (right cold wall and left hot wall) and the body generates a constant amount of heat. Under these conditions, the flow inside the enclosure is driven by two temperature differences: a temperature difference across the enclosure and a temperature difference caused by the heat source. A ratio of these two temperatures is a key parameter in this study. The steady, three-dimensional governing equations are written in a dimensionless form with dimensionless parameters that decide the heat transfer and flow characteristics in this system. The analysis is conducted by observing variations of the velocity vectors, pathlines, and isotherms for different Rayleigh numbers and temperature-difference ratios. The details of the three-dimensional flow and isotherms are described in order to investigate the effects of three-dimensionalities on the fluid flow and thermal characteristics in the enclosure. The variations of Nusselt numbers on the hot and cold walls are also presented to show the overall heat transfer characteristics inside the enclosure.

Two-dimensional and unsteady natural convection in a horizontal enclosure with a square body

A two-dimensional solution for unsteady natural convection in an enclosure with a square body is obtained using an accurate and efficient Chevyshev spectral collocation method. A spectral multidomain methodology is used to handle a square body located at the center of the computational domain. The physical model considered here is that a square body is located at the center between the bottom hot and top cold walls. To see the effects of the presence of a body on natural convection between the hot and cold walls, we considered the cases that the body maintains the adiabatic and isothermal thermal boundary conditions for different Rayleigh numbers varying in the range of 103 to 106. When the Rayleigh number is small, the flow and temperature distribution between the hot and cold walls shows a symmetrical and steady pattern. At the intermediate Rayleigh number, the fluid flow and temperature fields maintain the steady state but change their shape to the nonsymmetrical pattern. When the Rayleigh number is high, the flow and temperature fields become time dependent, and their time-averaged shapes approach the symmetric pattern again. The Rayleigh number for the fluid flow and temperature fields to become nonsymmetrical and time dependent depends on the thermal boundary conditions of a body. The variation of time- and surface-averaged Nusselt numbers on the hot and cold walls and at the body surfaces for different Rayleigh numbers and thermal boundary conditions are also presented to show the overall heat transfer characteristics in the system.

NUMERICAL STUDY OF HEAT TRANSFER AND FLOW OF NATURAL CONVECTION IN AN ENCLOSURE WITH A HEAT-GENERATING CONDUCTING BODY

A numerical study has been conducted to investigate steady state heat transfer and flow characteristics of natural convection in a vertical square enclosure when a temperature difference exists across an enclosure and, at the same time, a conducting body generates heat within the enclosure. Dimensionless governing equations indicate that the heat transfer and flow characteristics of this system are governed by the Rayleigh and Prandtl numbers, the area ratio, the conductivity ratio, and the temperature-difference ratio. Here the temperature-difference ratio is defined as the ratio of a temperature difference across the enclosure to that caused by the heat source. In the present study, the Rayleigh number ranges from 103 to 104, and the temperature-difference ratio from 0 to 50, while the Prandtl number, the area ratio, and the conductivity ratio are kept constant at 0.71, 0.25, 1, respectively. The analysis is performed by observing variations of streamlines, isotherms, heatlines, and the average Nusselt ...

Interaction between discrete heat sources in horizontal natural convection enclosures

Abstract Steady natural convection induced by multiple discrete heat sources (DHSs) in two-dimensional horizontal enclosures is numerically investigated. A general combined temperature scale method is first implemented to identify the DHSs of both external and internal types. An associated concept of thermal strength is then introduced in terms of the unified heat transfer characteristics of DHSs to analyze the interaction among them. Four different calculation cases are detailed analyzed, and main attention has been focused on the effects of the Rayleigh number (Ra), the thermal strength (Π), and the separation distance (W*) on the interaction between DHSs. Computational results demonstrated that the combined temperature scale method and the unified heat transfer characteristics analysis are convenient and efficient to evaluate the complex interaction between DHSs and its effects on the fluid flow and heat transfer structures in horizontal natural convection enclosures.

NUMERICAL STUDY ON TRANSIENT HEAT TRANSFER AND FLUID FLOW OF NATURAL CONVECTION IN AN ENCLOSURE WITH A HEAT-GENERATING CONDUCTING BODY

A comprehensive numerical study has been conducted to investigate transient heat transfer and flow phenomena of natural convection of three different fluids of sodium, air, and water in a vertical square enclosure within which a centered, squared, heat-conducting body generates heat. The physical model considered here is that a temperature difference exists across the enclosure (right cold wall and left hot wall) all the time and the body generates a constant amount of heat at an initial dimensionless time of tau0. At time tau0 the amount of heat generated by the body is suddenly increased to 10 times as large as that at time tau0. Under this situation, the flow inside the enclosure is driven by two temperature differences: a temperature difference across the enclosure and a temperature difference caused by the heat source. A ratio of these two temperatures is a key parameter in this study. We also consider the effects of Prandtl number and thermal conductivity ratio on the heat transfer and flow in the e...

Static and dynamic contact angles of water droplet on a solid surface using molecular dynamics simulation.

The present study investigates the variation of static contact angle of a water droplet in equilibrium with a solid surface in the absence of a body force and the dynamic contact angles of water droplet moving on a solid surface for different characteristic energies using the molecular dynamics simulation. With increasing characteristic energy, the static contact angle in equilibrium with a solid surface in the absence of a body force decreases because the hydrophobic surface changes its characteristics to the hydrophilic surface. In order to consider the effect of moving water droplet on the dynamic contact angles, we apply the constant acceleration to an individual oxygen and hydrogen atom. In the presence of a body force, the water droplet changes its shape with larger advancing contact angle than the receding angle. The dynamic contact angles are compared with the static contact angle in order to see the effect of the presence of a body force.

Numerical analysis of secondary cooling and bulging in the continuous casting of slabs

Abstract In this paper, numerical analyses of the secondary cooling and the bulging of the strand are performed, as applied to the continuous casting of slabs. Solidification analyses of the strand under air-mist for each cooling zone are carried out by the one-dimensional finite difference method. The bulging deformation of cast slab is calculated with a two-dimensional elasto-plastic and creep finite element model. For efficient bulging analysis, the temperature distribution and shell thickness resulting from the solidification analysis are automatically transferred to input data for the bulging analysis. The solidification is analyzed more precisely with five sub-zones in the cooling zone and the temperature distribution is fully coupled in the bulging analysis. The adequacy of the model has been confirmed with experimental results. From this study the effects of the process variables such as casting speed, cooling condition, and roll pitch are examined. The results from the analyses are applicable to the design of the continuous casting process.

Effect of the position of a circular cylinder in a square enclosure on natural convection at Rayleigh number of 107

Numerical calculations are carried out for the natural convection induced by temperature difference between a cold outer square cylinder and a hot inner circular cylinder for Rayleigh number of Ra=107. This study investigates the effect of the inner cylinder location on the heat transfer and fluid flow. The location of inner circular cylinder (δ) is changed vertically along the centerline of square enclosure. The natural convection bifurcates from unsteady to steady state according to δ. Two critical positions of δC,L and δC,U as a lower bound and an upper bound are δC,L=0.05 and δC,U=0.18, respectively. Within the defined bounds, the thermal and flow fields are steady state. In the unsteady region, the natural convection shows a single frequency and multiple frequency periodic patterns alternately according to δ. When the inner cylinder locates at δ≥δC,U, the space between the upper surface of inner cylinder and the top surface of the enclosure forms a relatively shallow layer where the natural convectio...

Natural convection in a horizontal layer of fluid with a periodic array of square cylinders in the interior

This study of thermal convection uses the following geometry: a horizontal layer of fluid heated from below and cooled from above, with a periodic array of evenly spaced square cylinders occupying the center of the layer (whose aspect ratio is 6). Periodic boundary conditions are employed in the horizontal direction to allow for lateral freedom for the convection cells. A two-dimensional solution for unsteady natural convection is obtained, using an accurate and efficient Chebyshev spectral multi-domain methodology, for different Rayleigh numbers varying over the range of 103 to 106. In order to assess the impact of different geometric approximations on the flow structure, dynamics and overall heat transfer, the results for the above case, denoted WC (wide aspect ratio cell with periodic side boundaries and six internal bodies), are compared with those for the cases of UCNS (unit cell with no-slip adiabatic side boundaries with a single internal body), UCPC (unit cell with periodic side boundaries with a ...

Unsteady fluid flow and temperature fields in a horizontal enclosure with an adiabatic body

A two-dimensional solution for unsteady natural convection in an enclosure with an adiabatic square body is obtained using an accurate and efficient Chevyshev spectral collocation method. A spectral multi-domain methodology is used to handle an adiabatic body located at the center of computational domain. The physical model considered here is that an adiabatic body is located at the center between the bottom hot and top cold walls. In order to see the effects of the presence of an adiabatic body on time-dependent natural convection between the hot and cold walls, we investigated the detail structure of fluid flow and heat transfer as a function of time for different Rayleigh numbers varying in the range of 103 to 106. When Ra=103, streamlines and isotherms reach the steady state without any oscillatory transients, and the flow and temperature distribution around the body in the enclosure shows a four-fold symmetrical pattern. At Ra=4×103, 104, and 105, streamlines and isotherms reach the steady state afte...