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

Doctor of Philosophy / Department of Statistics / James W. Neill / Checking the adequacy of a proposed parametric nonlinear regression model is important in order to obtain useful predictions and reliable parameter inferences. Lack of fit is said to exist when the regression function does not adequately describe the mean of the response vector. This dissertation considers asymptotics, implementation and a comparative performance for the likelihood ratio tests suggested by Neill and Miller (2003). These tests use constructed alternative models determined by decomposing the lack of fit space according to clusterings of the observations. Clusterings are selected by a maximum power strategy and a sequence of statistical experiments is developed in the sense of Le Cam. L2 differentiability of the parametric array of probability measures associated with the sequence of experiments is established in this dissertation, leading to local asymptotic normality. Utilizing contiguity, the limit noncentral chi-square distribution under local parameter alternatives is then derived. For implementation purposes, standard linear model projection algorithms are used to approximate the likelihood ratio tests, after using the convexity of a class of fuzzy clusterings to form a smooth alternative model which is necessarily used to approximate the corresponding maximum optimal statistical experiment. It is demonstrated empirically that good power can result by allowing cluster selection to vary according to different points along the expectation surface of the proposed nonlinear regression model. However, in some cases, a single maximum clustering suffices, leading to the development of a Bonferroni adjusted multiple testing procedure. In addition, the maximin clustering based likelihood ratio tests were observed to possess markedly better simulated power than the generalized likelihood ratio test with semiparametric alternative model presented by Ciprian and Ruppert (2004).