S.P. Liaw

Framework for a Unified Model for Nucleate and Transition Pool Boiling

An area and time-averaged model for saturated pool boiling heat fluxes has been developed. In the model, which is valid in the upper end of nucleate boiling and in transition boiling, the existence of stationary vapor stems at the wall is assumed. The energy from the wall is conducted into the liquid macro/micro thermal layer surrounding the stems and is utilized in evaporation at the stationary liquid-vapor interface. The heat transfer rate into the thermal layer and the temperature distribution in it are determined by solving a two-dimensional steady-state conduction equation. The evaporation rate is given by the kinetic theory. The heater surface area over which the vapor stems exist is taken to be dry. Employing experimentally observed void fractions, not only the nucleate and transition boiling heat fluxes but also the maximum and minimum heat fluxes are predicted from the model. The maximum heat fluxes obtained from the model are valid only for surfaces that are not well wetted and includes the contact angle as one of the parameters.

Void fraction measurements during saturated pool boiling of water on partially wetted vertical surfaces

Void fraction profiles adjacent to a vertical wall 6.3 cm wide and 10.3 cm high were measured during nucleate boling. The experiments were conducted in saturated water at 1 atm pressure. In the experiments, the wettability of the surface was varied by controlling the degree of oxidation of the surface. Static contact angle was used as an indicator of the surface wettability. The void fraction was measured with a gamma densitometer. The experimental results show that the maximum void fraction occurs about 1--1.5 mm away from the heater surface. The wall void fraction, the maximum void fraction, and the thickness of the void layer increase with wall heat flux. It is found that for a given heat flux, the wall void fraction increases as the surface becomes less wettable, whereas the maximum heat flux decreases with increase in contact angle.

Fins with temperature dependent surface heat flux—I. Single heat transfer mode

Abstract Involved in all possible types of heat transfer, the thermal characteristics of a single fin with and without heat transfer at its tip is studied. The heat transfer coefficient is assumed to vary with a power-law-type formula. Based on the value of the exponent, the problem is categorized into three regimes. The temperature distribution and heat transfer rate are given in implicit forms and solved exactly. No solution is found when the fin parameter exceeds a specific value for a negative exponent. Besides, two solutions are detected when the fin parameter is smaller than this value, which is related to the thermal instability. Results from analysis are compared with experimental data.

Fins with temperature dependent surface heat flux—II. Multi-boiling heat transfer

Abstract An analytical and experimental study is conducted for a fin when various types of boiling occur simultaneously at adjacent locations on its surface. The heat transfer coefficient is taken as a power function of wall superheat in each heat transfer mode. The temperature distribution as well as the variation of length in each section is calculated for different base temperatures. Hysteresis effects and the sudden change in total heat transfer rate are particularly noted. Experiments were carried out with 2.5 cm diameter copper rods with boiling liquids of water and isopropyl alcohol. The results from theory are compared with experimental data.

An exact solution for thermal characteristics of fins with power-law heat transfer coefficient

Abstract The thermal characteristics of a single fin with all possible types of heat transfer is analyzed. The heat transfer coefficient is assumed to vary following a power-law type formula. The temperature distribution, tip temperature, and fin efficiency are given in implicit forms and solved by iterative procedures. The results are plotted against fin parameter for various exponents. No solution is found when the fin parameter exceeds a specific value, and which is believed to be related to thermal instability.

Optimum configuration of a fin for boiling heat transfer

Abstract Based on the principle of minimum volume, an optimum shape of fin is proposed in this study. The outer appearance is essentially like a cylindrical fin and the excavated part is in the inner portion of the fin. First, the surface heat flux is assumed to follow a power-law dependence. With the aid of one-dimensional analysis, the temperature distributions and the profiles of the excavation hole are calculated for various single heat transfer modes. Secondly, the boiling curve of isopropyl alcohol on copper surface is used as an input to the model. The base temperature in the film boiling regine is taken and the optimum geometry is presented. Finally, the efficiency based on the volume and heat duty is discussed.

Transient Three-Dimensional Analysis of Gas Tungsten Arc Welding Plates

In this study, a numerical scheme of Douglas-Gunn is employed to solve the three-dimensional transient heat conduction problem in welded plates. The heat transfer characteristics as well as the physical properties of base materials for this problem are affected by the moving heat source powered by input voltage. Therefore, to simulate the real situations, the intensity of the heat source is assumed to follow a Gaussian distribution in spatial coordinates. Various parameters such as heat input, welding speed, radius of heat source, dimension, and material of the welded plates are considered. In the welding of thin plates, the welding problem can be mostly assumed to be two-dimensional in heat transfer if full penetration of the weld pool is obtained. In addition, good quality of welding is obtained if the workpiece is properly preheated in welding 6061 aluminum plates. Finally, a series of experiments is conducted to verify the theoretical results.

Computation of boiling water on circular finned tubes

This study investigates the maximum heat transfer rate and the critical temperature of circular finned tubes in a boiling liquid. The analysis is conducted numerically by solving a two-dimensional heat conduction equation in a steady state. The dependence between heat flux and the temperature at the inner wall of the tube is quantified. Varying the width, height, and pitch of fins, an optimal finned tube with efficient heat transfer rate can be obtained. In the theoretical approach the successive over relaxation (S.O.R.) accompanied with Multi-grid scheme is used. The local heat transfer rates are assumed to follow power-law-type temperature dependence. The initial guess at very high temperatures or so-called a cooling process is also executed in a same way. The results reveal that increasing either the width or the height of a fin increases the total heat transfer rate.

Sliding effect of gas-lubricated porous rectangular thrust bearings

Abstract A theoretical model has been developed to investigate the dynamic characteristics of porous rectangular thrust bearings lubricated with gas in which pressurized gas is pumped through a porous pad to lubricate the sliding elements. In the model a uniform temperature distribution in the gas lubricating film is assumed and a modified form of the Beaver-Joseph slip velocity boundary condition is applied at the interface between the porous pad and the lubricating film. The pressure in the porous pad is obtained in a closed form when the pad thickness is very small compared with its other two dimensions. A modified Reynolds equation was solved numerically using a finite difference method. The load capacity, mass flow rate of gas and stiffness are obtained in dimensionless forms and calculated numerically for different operating parameters. A higher load capacity is observed for a thinner film with and without relative motion. The effect of sliding is to reduce the load capacity and the stiffness, whereas it increases the mass flow rate of gas. It is also noted that when the pad shape ratio is very small, the effect introduced by sliding becomes less significant.

Boiling heat transfer from an excavated fin

Abstract A single pin fin with excavation at base is proposed to enhance boiling heat transfer. The temperature distribution in the fin is obtained numerically by solving a two-dimensional heat conduction equation. A copper fin boiling in isopropyl alcohol is taken as an example. When the operating temperature exceeds a specific value, the heat duty decreases drastically, and the whole fin is governed by film boiling. This highest operating temperature limit (burnout) is raised by digging a hole at the fin base. Two distinct solutions are found by using different initial guesses into the code. This hysteresis effect becomes noticeable for a bigger hole. A model is also developed to predict the burnout temperatures.