Engineering Commons^™

Mathematical Models Of Unsteady Operation Of A Packed Column, Jen-Fu Chao

Dissertations

Analytical solutions of differential equations applicable to extraction, ion exchange, or adsorption processes in packed beds are presented. Results are given for three different cases. The first case accounts for adsorption phenomena only. The second one includes surface adsorption on particles and the effects of longitudinal dispersion in the bed. The third one deals with diffusion in particles and longitudinal dispersion in the bed. In the mathematical modelling of these three cases, a linear equilibrium relationship between the solute in the liquid phase and solute in the solid phase is used. The first case is solved using the single boundary …

The Settling Of An Arbitrary Number Of Spherical Particles Arranged On The Corners Of A Regular Polygon In A Viscous Fluid, Eric Robert Bixon

Dissertations

The creeping motion equation has been solved for the case of planar arrays of spheres settling under the influence of gravity in a viscous fluid. The solution is a general solution which applies to an arbitrary number of spheres. All particles will lie at the corners of a regular polygon. Thus, two particles side by side, three particles in an equilateral triangular array, or four spheres in a square array will be special cases of the general solution.

The solution has been obtained by a unique application of the method of reflections. Only a first correction to the drag has …

Mathematical Model Of Temperature Profiles And Coking In A Crude Oil Heater Tube, Joseph C. Polimeni

Theses

A mathematical model to predict temperature profiles and coking of crude oil in furnace tubes is presented. The model assumes that the coking mechanism is due to a reaction in the laminar sublayer, whose rate depends upon the temperature profile. That profile is obtained by a numerical solution of the appropriate transport equations, with velocity profiles that may be laminar or turbulent, and including the temperature dependence of the crude oil properties. In addition, velocity and temperature profiles were adjusted when necessary to ensure closure of the heat and material balances. As a by-product of this study, a correction was …

Kinetics Of Biodegradation Of Phenol And 2,6-Dichlorophenol, Samir Shrikant Desai

Theses

Biological removal of phenol up to 600 ppm and 2,6-dichlorophenol up to 20 ppm was studied in a well aerated fill-and-draw reactor of 41 capacity at 26 C using an activated sludge obtained from the municipal treatment plant in Livingston, N.J. Experimental evaluation of kinetic parameters showed that biodegradation of both phenol and 2,6-DCP followed zero-order kinetics. As expected, the lag time for both compounds was considerably reduced when acclimated sludge was used. However, the metabolism of 2,6-DCP was very slow even for preacclimated sludge, requiring about 36 hours to degrade only 15 ppm.. This was markedly improved by the …

The Lewis-Matheson Method On Computer, William Raymond Castner

Theses

Lewis and Matheson, in the early 1930's, developed a manual calculation technique for the solution of multicomponent distillation problems. The object of this study was to see if there would be any advantage to using the Lewis-Matheson method, once incorporated onto a computer, over current multicomponent distillation solution techniques. The immediate advantage of using the L-M technique is that it requires fewer preliminary calculations than other computer methods. It was found that the L-M technique uses about half the execution time of a typical Newton-Raphson program, while using only one tenth the computer core (memory). This was not intended to …

The Effect Of Ultrasound On The Hydrolysis Of Carbohydrates, Adel A. Khamis

Dissertations

Acid hydrolysis of dextran and cellulose were studied with and without irradiation with ultrasonic waves of different frequencies (17 - 150 KHz), and powers (0.4 - 200 w/cm²). In the case of both materials, the hydrolysis reaction was found to be first order with respect to the activity of hydrogen ions in the reaction medium. Weight average molecular weight was evaluated at different durations of the reaction course. The reaction rate of dextran was found to be proportional to the weight average molecular weight raised to the power 4/3, and raised to the power 4 for cellulose.

The …

Mathematical Modeling Of The Unsteady State Glucose And Insulin Concentrations In Blood For Normal Subjects And Diabetics, Tung Shih

Theses

A mathematical model of the blood-glucose regulatory system has been developed. This model describes an oral glucose tolerance test adequately and simulates the behavior of the real physiological system using computer techniques.

Regression of the rate constants involved have been effected by conforming the theoretical functions to the data from glucose tolerance test in nonobese normal subjects, obese normal subjects, nonobese mild diabetics, obese mild diabetics, nonobese moderate diabetics and obese moderate diabetics measured by continuous sampling after oral ingestion. Most of the data were conformed within the limits of experimental error. The result of optimal parameters lead to a …

Mathematical Modeling Of Mass Transfer In A Hollow Fiber Dialyzer, Tzyy-Kai Yu

Theses

A mathematical model describing the flow characteristics and mass transfer has been developed for the hollow fiber dialyzer in countercurrent dialysis.

The theoretical expressions are developed from a typical Graetz problem for the stream side, and a first order differential equation for the dialyzate side. The solution of the dimensionless concentration profile is obtained as a summation of orthogonal eigenfunctions in closed form, which are given as product of an exponential function and a confluent hypergeometric function.

The analytical solution of the model has been examined by adjusting system parameters, like Sherwood number, Peclet number and the geometry of the …

Flow Tube Reactions Of Selected Chlorocarbons With Molecular Hydrogen Or Water Vapor In A Microwave Induced Plasma Reactor, Robert Benedict Barat

Theses

The reactions of various chlorinated hydrocarbons with molecular hydrogen or water vapor have been studied in a microwave plasma tubular flow reactor. The investigation of such reactions is desirable because the often toxic parent chlorocarbons are transformed to more thermodynamically stable and relatively non-toxic products by removal of' chlorine atoms as hydrogen chloride. Present detoxification technologies generally employ thermal oxidation as a means of disposal of chlorocarbons, which does not offer a thermodynamically stable sink for the chlorine atoms.

The experimental apparatus included feed introduction systems, a microwave plasma reactor, and full product analyses. The feed systems enabled use of …