Warren F. Phillips

A KINETIC MODEL FOR TRAFFIC FLOW WITH CONTINUUM IMPLICATIONS

A statistical model for the flow of traffic on an n lane highway is presented. The model is based on the hypothesis that each driver will maintain a minimum space, between himself and the next car, which is proportional to his speed. Both the first and second order continuum formulations, which are derived from the basic statistical formulations, are also presented.

Drag on a small sphere moving through a gas

An approximate theoretical solution is presented for the drag force on a small sphere moving through a gas. The result is based on a moment solution to the Boltzmann equation which places no restriction on the Knudsen number. The equation which is obtained for the drag force reduces to the exact solution in the case of both large and small Knudsen number and gives excellent agreement with experimental data.

Effects of stratification on the performance of liquid-based solar heating systems

Abstract A theoretical model is presented which predicts the effects of storage tank stratification on the instantaneous performance of a liquid-based solar heating system. The results are presented in terms of a stratification coefficient which is defined to be the ratio of the actual useful energy gain to the energy gain that would be achieved in a fully mixed tank. This stratification coefficient is shown to be a system constant which depends on only two dimensionless system parameters. The closed form model is compared with a detailed numerical simulation and also with experimental data taken with a solar water heater. Both the simulation data and the experimental data agree favorably with the theoretical model.

Harmonic analysis of climatic data

Abstract The utility of using the fast Fourier transform as a means of consolidating climatic data is presented and discussed in this paper. It is shown that a 20-year data set consisting of 175,320 hourly values of a climatic variable can be represented by only 75 Fourier coefficients with no significant loss of information content. Complete consolidated climatic data sets are presented for Albuquerque, New Mexico; Madison, Wisconsin and Miami, Florida. In addition, some other applications of the Fourier transform to the field of Solar Engineering are discussed.

A new continuum traffic model obtained from kinetic theory

A new continuum traffic flow model has been obtained from a kinetic model which was developed earlier by the author. The continuum model is derived from the kinetic model by taking moments of a Boltzmann equation. While previous continuum formulations have attempted to describe traffic dynamics in terms of only mean speed and traffic density, this new model introduces a new macroscopic variable which is called traffic pressure. The traffic pressure is proportional to the variance in the traffic speed distribution and is analogous to the gas pressure used in the modeling of gas dynamics.

Effects of stratification on the performance of solar air heating systems

Abstract A theoretical model is presented which predicts the effects of stratification in the rock bed storage unit of a solar air heating system. The results are presented in terms of a stratification coefficient which is defined to be the ratio of the actual useful energy gain to the energy gain that would be achieved if the rock bed were maintained at a uniform temperature. This stratification coefficient is shown to be a system constant which depends on only three dimensionless system parameters.

Motion of aerosol particles in a temperature gradient

Theoretical and experimental results are presented which show that the thermal force on an aerosol particle in a temperature gradient depends on the velocity of the particle relative to the gas as well as the temperature gradient in the gas. It is shown that any motion of the particle along a line parallel to the temperature gradient tends to induce a local increase in the temperature gradient and thus an increase in the thermal force. Thermal settling velocity calculations which are made neglecting this motion−induced temperature gradient were found to be as much as fifty percent low when compared with experimental data. Calculations which account for this induced gradient, on the other hand, were able to predict the experimental data within three percent.

The effects of axial conduction on collector heat removal factor

Abstract A closed form solution is presented which predicts the performance of a solar collector and includes the effects of axial conduction in the receiver. The results are presented in terms of the well known collector heat removal factor which is shown to be a function of three dimensionless design parameters. The error, which is introduced by neglecting axial conduction, was found to be less than 30 per cent, for all collectors and less than 12 per cent for most collectors.

A simplified nonlinear model for solar collectors

Abstract An explicit nonlinear model is presented which predicts the performance of a solar collector and includes the effects of radiative losses. This model was obtained from the empirical correlation of simulation data from a total of 3969 separate computer simulations which included 50 different collector designs and a wide range of operating conditions. The detailed computer model, which was used to generate the simulation data, included effects such as radiative losses, axial conduction, edge losses and temperature dependent fluid properties. Results are presented which show that the proposed nonlinear model agrees with the detailed computer simulation much better than does the linear Hottel-Whillier-Bliss model.

Integrated performance of liquid-based solar heating systems

Abstract A closed form model for the integrated performance of liquid-based solar heating systems is presented. The model is general enough to be used for most liquid-based systems. It can be used for systems with either flat plate or concentrating collectors and the load is not restricted to space heating applications. Three new system parameter are introduced by this model. These are the system heat storage factor, the solar distribution factor and the load distribution factor. These three factors respectively account for the reduction in system performancev which results from finite storage, non-uniform solar flux and non-uniform load. These factors are discussed in detail and closed form mathematical expressions, from which numerical values can be calculated, as persented.