Thesis (M.S.)--Massachusetts Institute of Technology, Dept. of Earth and Planetary Science, 1981. / MICROFICHE COPY AVAILABLE IN ARCHIVES AND LINDGREN. / Bibliography: leaves 99-110. / by David Samuel Goldberg. / M.S.

The thermal conductivities of polystyrene in benzene solutions at concentrations of 0.l to 15 weight percent were measured at 25° C and atmospheric pressure. Osmotic pressure measurements and information supplied by the manufacturer indicated number average molecular weights (M̅_N) of 21,000, 264,000, and 660,000 for the three polystyrene polymers studied. The following equation was obtained by regression analysis of the results and predicts the measured thermal conductivity within ± 2 percent in the range of variables studied. K = 0.1088 - 0.1311 C + 0.57629 C² - 6.40 x 10⁻⁵ (M̅_N x 10⁻⁵)² - 4.2 x 10⁻³ C(M̅_N x 10⁻⁵) where: K = thermal conductivity of solution, Btu/hr-ft-°F C = weight fraction polymer M̅_N = number average molecular weight The conductivities were measured in a steady-state concentric cylinder apparatus developed for measuring the thermal conductivity of viscous liquids. The annular gap was 0.052 inches and guard heaters were employed to minimize end losses and distortion of the steady-state temperature distribution at the ends. The apparatus was calibrated with three liquids of known thermal conductivity, water, cyclohexanol and ethylene glycol. The calibration factor was found to be constant to within experimental error (± 3 percent) over the range of measurements. / Master of Science

<p> This study focuses on developing a new online recursive numerical algorithm for a coupled nonlinear inverse heat conduction-microstructure problem. This algorithm is essential in identifying, designing and controlling many industrial applications such as the quenching process for heat treating of materials, chemical vapor deposition and industrial baking. In order to develop the above algorithm, a systematic four stage research plan has been conducted. </P> <p> The first and second stages were devoted to thoroughly reviewing the existing inverse heat conduction techniques. Unlike most inverse heat conduction solution methods that are batch form techniques, the online input estimation algorithm can be used for controlling the process in real time. Therefore, in the first stage, the effect of different parameters of the online input estimation algorithm on the estimate bias has been investigated. These parameters are the stabilizing parameter, the measurement errors standard deviation, the temporal step size, the spatial step size, the location of the thermocouple as well as the initial assumption of the state error covariance and error covariance of the input estimate. Furthermore, three different discretization schemes; namely: explicit, implicit and Crank-Nicholson have been employed in the input estimation algorithm to evaluate their effect on the algorithm performance. </p> <p> The effect of changing the stabilizing parameter has been investigated using three different forms of boundary conditions covering most practical boundary heat flux conditions. These cases are: square, triangular and mixed function heat fluxes. The most important finding of this investigation is that a robust range of the stabilizing parameter has been found which achieves the desired trade-off between the filter tracking ability and its sensitivity to measurement errors. For the three considered cases, it has been found that there is a common optimal value of the stabilizing parameter at which the estimate bias is minimal. This finding is important for practical applications since this parameter is usually unknown. Therefore, this study provides a needed guidance for assuming this parameter. </p> <p> In stage three of this study, a new, more efficient direct numerical algorithm has been developed to predict the thermal and microstructure fields during quenching of steel rods. The present algorithm solves the full nonlinear heat conduction equation using a central finite-difference scheme coupled with a fourth-order Runge-Kutta nonlinear solver. Numerical results obtained using the present algorithm have been validated using experimental data and numerical results available in the literature. In addition to its accurate predictions, the present algorithm does not require iterations; hence, it is computationally more efficient than previous numerical algorithms. </p> <p> The work performed in stage four of this research focused on developing and applying an inverse algorithm to estimate the surface temperatures and surface heat flux of a steel cylinder during the quenching process. The conventional online input estimation algorithm has been modified and used for the first time to handle this coupled nonlinear problem. The nonlinearity of the problem has been treated explicitly which resulted in a non-iterative algorithm suitable for real-time control of the quenching process. The obtained results have been validated using experimental data and numerical results obtained by solving the direct problem using the direct solver developed in stage three of this work. These results showed that the algorithm is efficiently reconstructing the shape of the convective surface heat flux. </p> / Thesis / Doctor of Philosophy (PhD)

Peridynamics is an emerging nonlocal continuum theory which allows governing field equations to be applicable at discontinuities. This applicability at discontinuities is achieved by replacing the spatial derivatives, which lose meaning at discontinuities, with integrals that are valid regardless of the existence of a discontinuity. Within the realm of solid mechanics, the peridynamic theory is one of the techniques that has been employed to model material fracture. In this work, the peridynamic theory is used to investigate different fracture problems in order to establish its fidelity for predicting crack growth. Various fracture experiments are modeled and analyzed. The peridynamic predictions are made and compared against experimental findings along with predictions from other commonly used numerical fracture techniques. Additionally, this work applies the peridynamic framework to model heat transfer. Generalized peridynamic heat transfer equation is formulated using the Lagrangian formalism. Peridynamic heat conduction quantites are related to quanties from the classical theory. A numerical procedure based on an explicit time stepping scheme is adopted to solve the peridynamic heat transfer equation and various benchmark problems are considered for verification of the model. This paves the way for the coupling of thermal and structural fields within the framework of peridynamics. The fully coupled peridynamic thermomechanical equations are derived based on thermodynamic considerations, and a nondimensional form of the coupled thermomechanical peridynamic equations is also presented. An explicit staggered algorithm is implemented in order to numerically approximate the solution to these coupled equations. The coupled thermal and structural responses of a thermoelastic semi-infinite bar and a thermoelastic vibrating bar are subsequently investigated.

The boundary element method (BEM) has become a powerful method for the numerical solution of boundary-value problems (BVPs), due to its ability (at least for problems with constant coefficients) of reducing a BVP for a linear partial differential equation (PDE) defined in a domain to an integral equation defined on the boundary, leading to a simplified discretisation process with boundary elements only. On the other hand, the coefficients in the mathematical model of a physical problem typically correspond to the material parameters of the problem. In many physical problems, the governing equation is likely to involve variable coefficients. The application of the BEM to these equations is hampered by the difficulty of finding a fundamental solution. The first part of this thesis will focus on the derivation of the boundary integral equation (BIE) for the Laplace equation, and numerical results are presented for some examples using constant elements. Then, the formulations of the boundary-domain integral or integro-differential equation (BDIE or BDIDE) for heat conduction problems with variable coefficients are presented using a parametrix (Levi function), which is usually available. The second part of this thesis deals with the extension of the BDIE and BDIDE formulations to the treatment of the two-dimensional Helmholtz equation with variable coefficients. Four possible cases are investigated, first of all when both material parameters and wave number are constant, in which case the zero-order Bessel function of the second kind is used as fundamental solution. Moreover, when the material parameters are variable (with constant or variable wave number), a parametrix is adopted to reduce the Helmholtz equation to a BDIE or a BDIDE. Finally, when material parameters are constant (with variable wave number), the standard fundamental solution for the Laplace equation is used in the formulation. In the third part, the radial integration method (RIM) is introduced and discussed in detail. Modifications are introduced to the RIM, particularly the fact that the radial integral is calculated by using a pure boundary-only integral which relaxes the “star-shaped” requirement of the RIM. Then, the RIM is used to convert the domain integrals appearing in both BDIE and BDIDE for heat conduction and Helmholtz equations to equivalent boundary integrals. For domain integrals consisting of known functions the transformation is straightforward, while for domain integrals that include unknown variables the transformation is accomplished with the use of augmented radial basis functions (RBFs). The most attractive feature of the method is that the transformations are very simple and have similar forms for both 2D and 3D problems. Finally, the application of the RIM is discussed for the diffusion equation, in which the parabolic PDE is initially reformulated as a BDIE or a BDIDE and the RIM is used to convert the resulting domain integrals to equivalent boundary integrals. Three cases have been investigated, for homogenous, non-homogeneous and variable coefficient diffusion problems.

Lau Kin Wing. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2000. / Includes bibliographical references (leaves 80-83). / Abstracts in English and Chinese. / Chapter 1 --- Introduction --- p.3 / Chapter 1.1 --- Heat conduction problem --- p.3 / Chapter 1.2 --- Direct problem --- p.4 / Chapter 1.3 --- Inverse problem --- p.4 / Chapter 1.4 --- Difficulty of the inverse problems --- p.5 / Chapter 1.5 --- A simple but important example for instability --- p.5 / Chapter 1.6 --- The purpose of this thesis --- p.7 / Chapter 2 --- Stability of the inverse problem --- p.9 / Chapter 2.1 --- Conditional stability results --- p.9 / Chapter 2.2 --- Stability of the inverse problems --- p.11 / Chapter 3 --- The continuous formulation --- p.30 / Chapter 3.1 --- Constrained minimization problem --- p.30 / Chapter 3.2 --- Existence of minimizers to the minimization problem --- p.31 / Chapter 4 --- Discretization and its convergence --- p.36 / Chapter 4.1 --- Finite element space --- p.36 / Chapter 4.2 --- Two important discrete projection operators --- p.37 / Chapter 4.3 --- Finite element problem --- p.39 / Chapter 4.4 --- Existence of minimizers to the finite element problem --- p.39 / Chapter 4.5 --- Discrete minimizers and global minimizers --- p.42 / Chapter 5 --- Numerical algorithms --- p.51 / Chapter 5.1 --- Gateaux derivative --- p.51 / Chapter 5.2 --- Nonlinear single-grid gradient method --- p.53 / Chapter 5.3 --- Nonlinear multigrid gradient method --- p.55 / Chapter 6 --- Numerical experiments --- p.60 / Chapter 6.1 --- One dimensional examples --- p.60 / Chapter 6.2 --- Two dimensional examples --- p.66

Chan Kai Yam. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2001. / Includes bibliographical references (leaves 80-82). / Abstracts in English and Chinese. / Chapter 1 --- Introduction --- p.1 / Chapter 1.1 --- Parameter Identification in Heat Conduction Systems --- p.1 / Chapter 1.2 --- Inverse Problems --- p.3 / Chapter 1.3 --- Challenges in Inverse Problems --- p.6 / Chapter 2 --- Tools in Parameter Identification --- p.9 / Chapter 2.1 --- Output Least Squares Method --- p.10 / Chapter 2.2 --- Tikhonov Regularization --- p.11 / Chapter 2.3 --- Our Approach --- p.14 / Chapter 3 --- Numerical Implementations --- p.20 / Chapter 3.1 --- Finite Element Discretization and Its Convergence --- p.20 / Chapter 3.2 --- Steepest Descent Method --- p.22 / Chapter 3.3 --- Multigrid Techniques --- p.26 / Chapter 4 --- Numerical Experiments --- p.29 / Chapter 4.1 --- One Dimensional Examples --- p.30 / Chapter 4.1.1 --- Selection of mk --- p.31 / Chapter 4.1.2 --- Selection of nk --- p.34 / Chapter 4.1.3 --- Selection of Number of Levels in the Coarse Grid Correction Step --- p.37 / Chapter 4.1.4 --- Convergence with Different Regularization Pa- rameters γ --- p.39 / Chapter 4.1.5 --- Convergence with Different Initial Guesses --- p.42 / Chapter 4.1.6 --- Comparisons between MG and SG Methods --- p.44 / Chapter 4.1.7 --- Comparisons between MG and RMG Methods --- p.46 / Chapter 4.1.8 --- More Examples --- p.49 / Chapter 4.1.9 --- Coarse Grid Correction in Another Approach --- p.60 / Chapter 4.2 --- Two Dimensional Examples --- p.71 / Chapter 4.3 --- Conclusions --- p.78 / Bibliography --- p.80

Digitized by Kansas Correctional Industries

Thesis (M.S.)--Massachusetts Institute of Technology, Dept. of Mechanical Engineering, 1979. / MICROFICHE COPY AVAILABLE IN ARCHIVES AND ENGINEERING. / Includes bibliographical references. / by James R. Rinderle. / M.S.

Xie Jian Li. / "August 2003." / Thesis (Ph.D.)--Chinese University of Hong Kong, 2003. / Includes bibliographical references (p. 106-109). / Electronic reproduction. Hong Kong : Chinese University of Hong Kong, [2012] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Mode of access: World Wide Web. / Abstracts in English and Chinese.