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Varying diameter ratios associated with smooth concentric tube-in-tube heat exchangers are known to have an effect on its convective heat transfer capabilities. Much literature exists for predicting the inner tube’s heat transfer coefficients, however, limited research has been conducted for the annulus and some of the existing correlations are known to have large errors. Linear and nonlinear regression models exist for determining the heat transfer coefficients, however, these are complex and time consuming methods and require much experimental data in order to obtain accurate solutions. A direct solution to obtain the heat transfer coefficients in the annulus is sought after. In this study a large dataset of experimental measurements on heat exchangers with annular diameter ratios of 0.483, 0.579, 0.593 and 0.712 was gathered. The annular diameter ratio is defined as the ratio of the outer diameter of the inner tube to the inner diameter of the outer tube. Using various methods, the data was processed to determine local and average Nusselt numbers in the turbulent flow regime. These methods included the modified Wilson plot technique, a nonlinear regression scheme, as well as the log mean temperature difference method. The inner tube Reynolds number exponent was assumed to be a constant 0.8 for both the modified Wilson plot and nonlinear regression methods. The logarithmic mean temperature difference method was used for both a mean analysis on the full length of the heat exchanger, and a local analysis on finite control volumes. Friction factors were calculated directly from measured pressure drops across the annuli. The heat exchangers were tested for both a heated and cooled annulus, and arranged in a horizontal counter-flow configuration with water as the working medium. Data was gathered for Reynolds numbers (based on the hydraulic diameter) varying from 10 000 to 28 000 for a heated annulus and 10 000 to 45 000 for a cooled annulus. Local inner wall temperatures which are generally difficult to determine, were measured with thermocouples embedded within the wall. Flow obstructions within the annuli were minimized, with only the support structures maintaining concentricity of the inner and outer tubes impeding flow. / Dissertation (MEng)--University of Pretoria, 2013. / gm2014 / Mechanical and Aeronautical Engineering / unrestricted

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Master of Science / Department of Statistics / Weixin Yao / In the fitting of mixtures of linear regression models, the normal assumption has been traditionally used for the error term and then the regression parameters are estimated by the maximum likelihood estimate (MLE) using the EM algorithm. Under the normal assumption, the M step of the EM algorithm uses a weighted least squares estimate (LSE) for the regression parameters. It is well known that the LSE is sensitive to outliers or heavy tailed error distributions. In this report, we propose a robust mixture of linear regression model, which replaces the least square criterion with some robust criteria in the M step of the EM algorithm. In addition, we will use a simulation study to demonstrate how sensitive the traditional mixture regression estimation method is to outliers or heavy tailed error distributions and compare it with our proposed robust mixture regression estimation method. Based on our empirical studies, our proposed robust estimation method works comparably to the traditional estimation method when there are no outliers and the error is normally distributed but is much better if there are outliers or the error has heavy tails (such as t-distribution). A real data set application is also provided to illustrate the effectiveness of our proposed methodology.

Researchers who make predictions from educational data are interested in choosing the best regression model possible. Many criteria have been devised for choosing a full or restricted model, and also for selecting the best subset from an all-possible-subsets regression. The relative practical usefulness of three of the criteria used in selecting a regression model was compared in this study: (a) Mallows' C_p, (b) Amemiya's prediction criterion, and (c) Hagerty and Srinivasan's method involving predictive power. Target correlation matrices with 10,000 cases were simulated so that the matrices had varying degrees of effect sizes. The amount of power for each matrix was calculated after one or two predictors was dropped from the full regression model, for sample sizes ranging from n = 25 to n = 150. Also, the null case, when one predictor was uncorrelated with the other predictors, was considered. In addition, comparisons for regression models selected using C_p and prediction criterion were performed using data from the National Educational Longitudinal Study of 1988.

Master of Science / Department of Statistics / Weixing Song / In the classical Tobit regression model, the regression error term is often assumed to have a zero mean normal distribution with unknown variance, and the regression function is assumed to be linear. If the normality assumption is violated, then the commonly used maximum likelihood estimate becomes inconsistent. Moreover, the likelihood function will be very complicated if the regression function is nonlinear even the error density is normal, which makes the maximum likelihood estimation procedure hard to implement. In the full nonparametric setup when both the regression function and the distribution of the error term [epsilon] are unknown, some nonparametric estimators for the regression function has been proposed. Although the assumption of knowing the distribution is strict, it is a widely adopted assumption in Tobit regression literature, and is also confirmed by many empirical studies conducted in the econometric research. In fact, a majority of the relevant research assumes that [epsilon] possesses a normal distribution with mean 0 and unknown standard deviation. In this report, we will try to develop a semi-parametric estimation procedure for the regression function by assuming that the error term follows a distribution from a class of 0-mean symmetric location and scale family. A minimum distance estimation procedure for estimating the parameters in the regression function when it has a specified parametric form is also constructed. Compare with the existing semiparametric and nonparametric methods in the literature, our method would be more efficient in that more information, in particular the knowledge of the distribution of [epsilon], is used. Moreover, the computation is relative inexpensive. Given lots of application does assume that [epsilon] has normal or other known distribution, the current work no doubt provides some more practical tools for statistical inference in Tobit regression model.

Modelos para dados binários são bastante utilizados em várias situações práticas. Transformações em Análise de Regressão podem ser aplicadas para linearizar ou simplificar o modelo e também para corrigir desvios de suposições. Neste trabalho, descrevemos o uso de transformações nos modelos de regressão logística para dados binários e apresentamos modelos envolvendo parâmetros adicionais de modo a obter um ajuste mais adequado. Posteriormente, analisamos o custo da estimação quando são adicionados parâmetros aos modelos e apresentamos os testes de hipóteses relativos aos parâmetros do modelo de regressão logística de Box-Cox. Finalizando, apresentamos alguns métodos de diagnóstico para avaliar a influência das observações nas estimativas dos parâmetros de transformação da covariável, com aplicação a um conjunto de dados reais. / Binary data models have a lot of utilities in many practical situations. In Regrssion Analisys, transformations can be applied to linearize or simplify the model and correct deviations of the suppositions. In this dissertation, we show the use of the transformations in logistic models to binary data models and models involving additional parameters to obtain more appropriate fits. We also present the cost of the estimation when parameters are added to models, hypothesis tests of the parameters in the Box-Cox logistic regression model and finally, diagnostics methods to evaluate the influence of the observations in the estimation of the transformation covariate parameters with their applications to a real data set.

Modelos para dados binários são bastante utilizados em várias situações práticas. Transformações em Análise de Regressão podem ser aplicadas para linearizar ou simplificar o modelo e também para corrigir desvios de suposições. Neste trabalho, descrevemos o uso de transformações nos modelos de regressão logística para dados binários e apresentamos modelos envolvendo parâmetros adicionais de modo a obter um ajuste mais adequado. Posteriormente, analisamos o custo da estimação quando são adicionados parâmetros aos modelos e apresentamos os testes de hipóteses relativos aos parâmetros do modelo de regressão logística de Box-Cox. Finalizando, apresentamos alguns métodos de diagnóstico para avaliar a influência das observações nas estimativas dos parâmetros de transformação da covariável, com aplicação a um conjunto de dados reais. / Binary data models have a lot of utilities in many practical situations. In Regrssion Analisys, transformations can be applied to linearize or simplify the model and correct deviations of the suppositions. In this dissertation, we show the use of the transformations in logistic models to binary data models and models involving additional parameters to obtain more appropriate fits. We also present the cost of the estimation when parameters are added to models, hypothesis tests of the parameters in the Box-Cox logistic regression model and finally, diagnostics methods to evaluate the influence of the observations in the estimation of the transformation covariate parameters with their applications to a real data set.

The mitigation of outliers serves to increase the strength of a relationship between variables. This study defined outliers in three different ways and used five regression procedures to describe the effects of outliers on 50 data sets. This study also examined the relationship among the shape of the distribution, skewness, and outliers.