The quality of crystals grown from melt depends on the flow field in the melt. To simulate melt conditions, a finite element analysis is performed on flow in a heated cavity under the driving forces of natural convection, thermocapillary effects, and rotation. In addition, the gravity field is modulated to simulate a microgravitational environment. The purpose for conducting this research is to determine whether the use of baffles can effectively reduce convection and suppress temperature oscillations. The results show that the baffle is able to suppress convection and reduce the amplitude of the temperature oscillations when placed perpendicular to the modulation direction. Under crystal and crucible rotation, the results with and without baffles are similar. In all cases, baffles did not induce temperature oscillations. From this study, it can be concluded that the effects of baffles on the flow behavior depends greatly on the direction of gravity modulation and frequency.

The effect of coal particle coagulation during pulverized coal combustion is studied using a plug-flow model of a practical coal combustor. The model incorporates turbulent coagulation, in addition to the combustion equations, to explore certain combustor and coal parameters that may be used for optimizing a chosen output parameter (e.g., burnout time). This routine has been used to develop relations describing the effects of turbulent coagulation on pulverized coal combustion as an aid in combustor design or retrofitting. The results of this work indicate that, in agreement with general observations, coagulation will have little impact on pulverized coal combustion in typical combustors.

A novel method of analysis for nonlinear stochastic dynamical systems under Gaussian white noise excitation is developed. The system response is Markovian and its probability density function (p.d.f.) is governed by the Fokker-Planck-Kolmogorov (FPK) equation. Of interest is the prediction of statistics of the response. For this purpose, the FPK equation is not solved but is used in a variety of approaches to derive exact analytical representations of the response statistics. One procedure involves the derivation of infinite hierarchies of equations governing the statistics. Another procedure exploits a formal series expansion of the transition p.d.f. All unknowns are expressed in the form of perturbation expansions of a system parameter, or in power series of the variable of interest. These series-type solutions are then recast in various approximations of the Pade-type. Results are obtained for stationary and nonstationary moments, correlation functions, power spectral densities, and Wiener kernels for second-order systems with analytical nonlinearities, and additive/multiplicative excitations. They are validated with exact solutions or Monte Carlo simulations. The pivotal point of this dissertation is that series-type representation after proper transformations can yield quite reliable global solutions by exploiting the local information contained in the first few series coefficients.

A three-dimensional model of the deflected configuration of the portion of a circular rod constrained to be in contact with a circular cylinder is developed in this thesis. This work involves the development of an analytical method to determine the postbuckling behavior of tubular members in inclined holes. The analytical method introduces the concept of the critical hole inclination angle, $\alpha\sb{\rm cr}$, and the buckling, $\alpha\sb{\rm cr*}$, to determine the configurations of the rod. For hole inclination angles less than $\alpha\sb{\rm cr}$, a rod is in a helical form. A formula for the wall contact force in this region is derived to explain the existence of hysteresis during a cycle of axial loading followed by a corresponding load decrease. Torque effects and gravity effects are found to affect the helical configuration of the rod slightly. When the hole inclination lies between these two angles, a rod falls into a sinusoidal configuration. (Abstract shortened with permission of author.)

This work introduces the Method of Exergy Multipliers. Having asserted the utility of the exergy concept, this method aims to streamline the calculation procedures used in exergy analysis and its study. The method defines the exergy multipliers of a given process in terms of ratios of the work, heat transfer, irreversibility, and exergy output of the process with its incoming exergy. Algebraic properties of these multipliers aid in reducing the number of calculations. Many exergy and traditional concepts can be expressed in terms of the multipliers. Examples for a simple, closed Brayton cycle follow: the first optimizes the distribution of heat exchanger resources, the second optimizes the distribution of turbomachinery efficiency, and the third shows how to decide whether to improve the boiler or the turbine. The role of irreversibility in cycle performance is called into question and further study is recommended. Finally, limitations of the method are explained.

A simple model for the filtration of a destabilized colloidal suspension was proposed by Cohen (3). It was shown mathematically that the cake permeability was a function of flocculation rate $\omega$. Thus by controlling the flocculation rate it is possible to alter the structure of the cake formed which in turn affected the efficiency of the filtration process. The mathematical model provided two equations that related the transmembrane velocity to the rate of coagulation; one for the stable case and the other for the destabilized case. In the following thesis an experimental investigation was carried out to determine the validity of the above mathematical model. Several experiments were conducted both for the stable and the destabilized feed, and the data obtained was compared to those predicted by theory. Analysis showed that an excellent correlation exists between the gathered data and those predicted by the model. Thus the validity of the model proposed by Cohen (3) was established.

In our study, an iterative point successive over-relaxation (PSOR) finite difference scheme has been used to solve the coupled unsteady Navier-Stokes and energy equations for incompressible, viscous and laminar flows in their primitive variable form. Three problems have been studied in detail: (1) two-dimensional and three-dimensional natural convection in a cavity with differentially heated vertical walls; (2) two-dimensional and three-dimensional natural convection in cavity whose surface is cooled while two internal blocks are heated; (3) two-dimensional and three-dimensional natural convection in the region defined by two interconnected cavities of different sizes which are differentially heated. All computations have been performed for a Prandtl number of 1.0, and different values of the Rayleigh number ranging between $10\sp3$ and $10\sp7$ depending on the problem. The scheme has been found to be accurate even for large Rayleigh numbers.

The current study examined the transition region of axisymmetric isothermal and buoyant jets of low Reynolds number, directed vertically upwards into a stagnant, unstratified ambient. These flows were examined experimentally and numerically. The region in which measurements were obtained allows examination of two types of transition occurring in the jet: from nozzle exit dominated to fully developed, and from momentum to buoyancy dominated flow. Velocity data were acquired using a two channel Laser-Doppler Anemometer for isothermal Reynolds numbers of 850 to 7405, and buoyant Froude numbers of 12 to 6425 and Reynolds numbers from 525 to 6500. Curve fit approximations of the data were developed by assuming polynomial similarity profiles for the measured quantities. Correlation equations were developed which allow prediction of the downstream velocity flow field and turbulent flow field as a function of the Reynolds number, Froude number and density ratio at the nozzle exit. Profile width and entrainment increased at low Reynolds number. Axial and radial velocity fluctuations were found to increase at low Reynolds number. The buoyant cases studied were found to have lower velocity fluctuations and significantly lower Reynolds stresses than isothermal cases of similar Reynolds number. Once comprehensive correlation equations were developed predicting mean and turbulent flow quantities, the basis was formed for development of a new turbulence model, the analytic turbulence model. This method involved substitution of correlation equation approximations to the mean flow quantities into the boundary layer forms of the governing equations. The turbulent terms were then solved for explicitly. It was shown that this method predicts the fully developed boundary layer turbulent flow field, and can be used as a criterion for a flow attaining boundary layer form. Comparison of turbulent values predicted analytically with those measured empirically revealed that the transition flow examined experimentally had not fully developed to boundary layer form. Testing of the turbulent correlation equations was performed by using them as a turbulence model in a finite difference numerical solution. While the correlation equations were representative of the turbulent flow field, they did not produce correct results when used in a marching, boundary layer simulation. As verified by the analytic turbulence model, this occurred because the transition flow had not yet reached fully developed boundary layer form.

This thesis deals with the numerical solution of the transient heat conduction problem by using the finite element method and the improved Euler method. In the space domain, the finite element method is used. In the time domain of integration, the improved Euler method is employed. Two examples are demonstrated in this thesis. The first example is a test problem designed to verify the correctness of the computer code. One finds that the combination of the 6 point triangular element or 9 point quadrilateral element with the improved Euler method may be used to obtain both accurate and stable results. The second example is a practical engineering problem--to find the steady state and transient temperature distributions in a turbine blade. The computation results show that the transient solution converges to the steady state solution after a proper period of time. In addition, a general finite element code is developed in the thesis to solve the time-dependent problems. (Abstract shortened with permission of author.)

A plasticity based constitutive model with two yield surfaces is developed to model the nonlinear axial and volumetric behavior observed for rocks in triaxial compression. The failure surface is allowed to soften at low pressures to simulate fracturing. A method for treating the corner where the yield surfaces intersect is developed. In comparisons with experimental data, the model accurately predicts the axial response in triaxial tests. The model predicts too much dilation for low confining pressure triaxial tests. The constitutive model was used in conjunction with a finite element code to simulate axisymmetric indentation of rock. Because of the existence of the corner in the yield surface, the simulation was computationally too slow to be practical.