The growth of a vapor bubble in a superheated liquid is controlled by three factors: the inertia of the liquid, the surface tension, and the vapor pressure. As the bubble grows, evaporation takes place at the bubble boundary, and the temperature and vapor pressure in the bubble are thereby decreased. The heat inflow requirement of evaporation, however, depends on the rate of bubble growth, so that the dynamic problem is linked with a heat diffusion problem. Since the heat diffusion problem has been solved, a quantitative formulation of the dynamic problem can be given. A solution for the radius of the vapor bubble as a function of time is obtained which is valid for sufficiently large radius. This asymptotic solution covers the range of physical interest since the radius at which it becomes valid is near the lower limit of experimental observation. It shows the strong effect of heat diffusion on the rate of bubble growth. Comparison of the predicted radius‐time behavior is made with experimental observations in superheated water, and very good agreement is found.

The growth of vapor bubbles in superheated liquids. report no. 26-6

Finite element methods for incompressible viscous flow

Publisher Summary The first part of the chapter focuses on determining equations for the local and mean rate of laminar heat transfer, which are approximately valid for different geometries By use of these equations, several new correlations are obtained for various laminar heat transfer problems, and the results compared with experiments The problems considered involve heat transfer (1) from a cylinder, (2) from a sphere, (3) between concentric cylinders, (4) between concentric and eccentric spheres, (5) between vertical plates, and (6) from a nonisothermal vertical plate Attention is then turned to turbulent free convection heat transfer where the heat transfer from inclined plates and between differentially heated plates is considered A method of solving problems involving both laminar and turbulent convection is then outlined The criterion developed for the regions of applicability of the laminar and turbulent equations is shown to accurately predict the experimentally determined onset of instability of the laminar flow for free convection from an isolated plate A recommendation is then made for correlating heat transfer results in a clearer and more convenient way

A General Method of Obtaining Approximate Solutions to Laminar and Turbulent Free Convection Problems

Maximum bubble diameter, maximum bubble-growth time and bubble-growth rate during the subcooled nucleate flow boiling of water up to 17.7 MN/m2

Publisher Summary Thermal control of electronic components has one principal objective, to maintain relatively constant component temperature equal to or below the manufacturer's maximum specified service temperature, typically between 85 and 100°C. It is noted that even a single component operating 10°C beyond this temperature can reduce the reliability of certain systems by as much as 50%. Therefore, it is important for the new thermal control schemes to be capable of eliminating hot spots within the electronic devices, removing heat from these devices and dissipating this heat to the surrounding environment. Several strategies have developed over the years for controlling and removing the heat generated in multichip modules, which include advanced air-cooling schemes, direct cooling, and miniature thermosyphons or free-falling liquid films. The chapter summarizes analytical, numerical, and experimental work in literature, in order to facilitate the improvement of existing schemes and provide a basis for the development of new ones. The chapter focuses on investigations performed over the past decade and includes information on the thermal control of semiconductor devices, modules, and total systems.

Thermal Control of Electronic Equipment and Devices

Developing laminar free convection between vertical flat plates with asymmetric heating

The initial vapor bubble growth on a heated wall during nucleate boiling

Natural convection in an open cavity

The transport phenomena underlying the extrusion of non-Newtonian fluids in single-screw extruders is investigated numerically and experimentally. The viscosity of the investigated fluids is a strong function of the temperature and, for the non-Newtonian case, of the shear rate. Therefore, the governing equations of motion are coupled to the energy equation through the viscosity. The velocity in the down channel direction of the screw extruder is a result of both shear and pressure driven transport. The pressure acts in a direction opposite to that of the drag flow, and comparatively high pressures arise at the die in typical extruders. When a narrow die is used in the screw extruder, the pressure gradient in the down-channel direction becomes so large that the down-channel velocity near the screw root becomes negative in terms of the coordinate system fixed to the screw. The conventional marching schemes fail to simulate the fluid flow when the down-channel velocity becomes negative, since the downstream conditions are not known. Two different numerical schemes used to simulate the fluid flow in a single-screw extruder for this circumstance, which often arises when dies with high flow resistance are used and which is termed as pressure back flow in the literature, have been discussed. One scheme is based on including the down-channel thermal diffusion, making the problem elliptic, and the other scheme uses a different coordinate system. Both formulations are found to yield results that are fairly close. Experiments were also carried out to measure the pressures at three different locations in a single-screw extruder. The computed results were found to be in good agreement with the experimental results. The pressures at the die obtained numerically by treating the flow as isothermal are found to be lower than those obtained when the flow is treated as nonisothermal, indicating the strong influence of thermal transport in this problem.

Valentinas Sernas

Papers

Developing laminar free convection between vertical flat plates with asymmetric heating

The initial vapor bubble growth on a heated wall during nucleate boiling

Natural convection in an open cavity

Extrusion of non-Newtonian fluids in a single-screw extruder with pressure back flow

Natural convection in an open cavity