A three dimensional numerical investigation of steady laminar flow and heat transfer is undertaken to determine the developing as well as fully developed temperature fields. Physical interpretation is given for the enhancement of heat transfer coefficient at the thermal entrance region and the overall increase in heat transfer in helical ducts compared to straight ducts. The variation of periphery averaged Nusselt number is studied for the constant wall temperature boundary condition. Detailed analysis is given for the peripheral variation of Nusselt number and the temperature field at different cross-sectional planes. The effect of Prandtl number on the temperature field is also studied. The problem is solved using a segregated solution approach which reduces the total computer memory requirements.

An overview of two categories of numerical approaches to phase change problems, front tracking and fixed domain methods, is given. A further comparison of several fixed domain methods is made with some benchmark test problems. The approximation of the latent heat for isothermal phase change is a key point for these numerical approaches. Generally the space-average approach is better than the others. The Euler backward, Crank-Nicolson, and Dupont schemes are the best for thermal analysis involving phase changes. The new effective and apparent capacity methods can eliminate the need of an artificially assumed temperature range for isothermal transformation and obtain accurate results. They are also computationally efficient compared with other methods. The new apparent capacity technique is invoked to model the isothermal part of phase change for several solidification models. The same approach is applied to the thermal analyses of the casting processes and the results are in good agreement with experiment data. A convective type interface element formulation is derived for the heat transfer at the interface of the cast and the mold, which can simplify the element matrix calculation. A thermal elasto-plastic stress model is derived and the public domain software NIKE2D is used for the stress analyses of the casting processes. The initial stage of ingot cooling in the mold and the continuous casting process are simulated. The latent heat released during solidification can affect the temperature field and the phase transformation in the solid state has an essential effect on the stress generation. The cast size, material hardening effect, and cast speed are all important factors for the temperature and stress distributions.

An overview of the methods for finite element adaptive refinement and error estimation for linear elliptic problems is performed. An error estimator, based on nodal averaging of a gradient measure, suitable for linear, steady state, 2D and 3D stress and thermal analysis, is created and interfaced with the FE program FINITE/GP. An adaptive h-refinement method incorporating the above error estimator is implemented for two sample problems and results are presented which indicate that the method works. Conclusions are drawn concerning the usefulness of the method. A separate chapter gives an overview as well as experience gained with solvers for sparse matrices.

A two-dimensional theoretical model for the flow and combustion of pulverized coal by diffusion flames is presented. The model predicts gas flows, species concentrations and temperatures. The conservation equations are solved utilizing the $\kappa$-$\epsilon$ turbulence model. Coal devolatilization is modelled by two-competing-reactions scheme which generates two sets of volatiles and char, each by a specific rate constant which can be described in Arrhenius form, and char combustion from devolatilization occurs by reaction with oxygen, carbon dioxide, and water, and particle dispersion and radiative heat transfer between furnace wall and particles are studied. The model is used to investigate the interaction between flow and combustion in flames produced by arranging the location of primary inlet and secondary inlet. The predictions, which could be valuable for designing furnaces, indicate that an off-center primary inlet, a large recirculation zone, and an asymmetric secondary air inlet are favorable for combustion.

An interactive isoparametric contour plotting and filling program, ISOCON, is developed for use with finite element meshes using common two-dimensional triangular and quadrilateral elements. The program uses the local interpolation functions to compute the contour locations. The predictor-corrector algorithm used to compute the contour locations is derived and discussed. The color filling algorithm is also discussed. The program features are given along with a brief discussion of selected algorithms used in the program. The main feature of ISOCON lies in its portability since most plot drivers are written in FORTRAN 77. Selected contour plots are compared with output from another finite element contour plotting program. The ISOCON-generated plots produce much more realistic looking contours. Partial FORTRAN code along with a flowchart is included.

Heat transfer from a sphere in a traveling sound wave is studied using an axi-symmetric formulation. The effect of a reversing flow on the flow behavior is examined and formation of separation regions and vortex shedding at flow reversal is found even for Reynolds numbers on the order of one. Time dependent thermal displacement and induced transient flows were found to increase the minimum value for transient heat transfer significantly above the conduction limit as predicted by a quasi-steady analysis. The heat transfer is found to decrease with Strouhal number for Reynolds numbers greater than two. Transient effects for the range of low Strouhal numbers are found to be significant for the determination of time-averaged unsteady heat transfer.

An approach for the fully automatic generation of two-dimensional finite element meshes is presented. The method follows from the basic concept of the quadtree encoding technique with the specific modifications made to produce valid, user controllable finite element meshes. The use of quadtree method for mesh generation was pioneered by Shephard and Yerry, (6). Our work is similar but more general than theirs. In this thesis after giving an overview of finite element method and mesh requirements, the quadtree and modified quadtree techniques are introduced. Then paper emphasizes on those algorithmic aspects of the mesh generator especially on transferring quadtree code to finite mesh. Finally, examples are included to demonstrate this technique and conclusions are given.

A method is proposed for determining the thermal diffusivity of high temperature liquid metals that involves levitating a small sample under microgravity conditions, melting it, and predicting its thermal response to a laser pulse from either side at time t = 0. The solution is obtained by determining the initial temperature distribution in the thermal penetration depth created by the laser pulses and then solving the two dimensional conduction equation in spherical coordinates for the cooling history of the droplet. The correct diffusivity is obtained by minimizing the difference between predicted temperatures and experimentally obtained temperatures. The method is demonstrated for nickel, iron, and copper, and is shown to have good accuracy. An error analysis reveals that the result is highly sensitive to bias error in the experimental temperature data, and an example is given in which order of magnitude estimates for diffusivity can be obtained from the curves provided.

Drill-string failure is recognized by the drilling community as one of its most costly and frequently encountered problems. In order to diminish the frequency of such failures, the drilling community has been focusing on the modeling of the static and dynamic behaviors of drill-strings, towards increasing efficiency. Drill-string dynamics involves complex phenomena with excitations in axial, lateral and torsional directions, and coupling of these three and other factors such as mass imbalance, whirling, or stick-slip motion of the bit. The present study focuses on one aspect which has not been studied in detail by the drilling community, namely the consideration of random loads on the BHA studied by a frequency domain approach. A comprehensive literature survey is attempted and elucidating numerical results are provided.

Robot-assisted physical therapy has been shown to aid in the rehabilitation process following neurological injuries. As a therapeutic or training tool, the robot provides a means to implement and evaluate assistance cues to the operator's arm in addition to displaying the forces arising from the dynamics of the virtual environment. Furthermore, training in virtual environments also provides increased repeatability, scalability, safety and a greater control on the experimental setup over training in natural environments. This thesis presents the analysis of various design constraints that apply to the design of such devices. In this context, the author also presents the design of a five degree-of-freedom haptic arm exoskeleton designed for training and rehabilitation in virtual environments. The device has high structural stiffness, minimal backlash, low friction and absence of mechanical singularities in the workspace, which are some of the properties that characterize high quality haptic interfaces. A scheme for the force control of the robot, using a novel joint-based methodology is also presented.