The interest in aerodynamic heating problems has been increasing rapidly in the last decade. This interest is no longer concentrated on the heating of simple shapes for which adequate heat transfer theory has been developed« Because of the increasing Mach number ranges of aircraft, the need for information on the aerodynamic heating of various components has become imperative. Only when the magnitude of the problem has been exposed can the design for reducing the severity of local heating be optimized. Definition of these problems is of interest, not only because of the flow phenomena, but because of possible design limitations of re-entry vehicles and supersonic aircraft inlets, wings, rudders, etc.

Due to constraints and changes in operating conditions, heat exchangers are often forced to operate under conditions of transitional flow. However, the heat transfer and flow behaviour in this regime is relatively unknown. By describing the transitional characteristics it would be possible to design heat exchangers to operate under these conditions and improve the efficiency of the system. The purpose of this study was to experimentally measure the heat transfer and pressure drop characteristics of smooth tubes at a constant heat flux in the transitional flow regime. The measurements were used to describe the flow behaviour of this regime and attempt to develop a correlation that can be used in the design of a heat exchanger. An experimental set-up was developed, consisting of an overall set-up, a removable test section as well as a controller, which ensured a uniform heat flux boundary. The test section allowed for the measurement of the temperature along the length of the test section, the pressure drop across the test section, the heat flux input and the flow rate. The measurements were used to determine the heat transfer coefficients and friction factor of the system. Three test sections were developed with outer diameters of 6, 8 and 10 mm in order to investigate the influence of heat exchanger size. Each test section was subject to four different heat flux cases of approximately 1 500, 3 000, 4 500 and 6 000 W/m2. The experiments covered a Reynolds number range of 450 to 10 300, a Prandtl number range of 4 to 7, a Nusselt number range of 2.3 to 67, and a Grashoff number range of 60 to 23 000. Good comparison was found between the measurements of this experiment and currently available literature. The experiments showed a smooth transition from laminar to turbulent flow with the onset of transition dependent on the heat flux of the system and with further data capturing, a correlation can be found to describe the Nusselt number in the transitional flow regime. / Dissertation (MEng)--University of Pretoria, 2011. / Mechanical and Aeronautical Engineering / unrestricted

Permittivity values of a co-solvent system decrease with increasing temperature and decrease as mole fraction of water decreases. Fit to a cubic polynomial, the coefficients can be used to determine relative permittivity of the co-solvent system knowing temperature and mole fraction. A Brookhaven Instruments BI 870 Dielectric Meter was used. Pure water from 15.0 to 55.0 °C was measured to validate the method. Solutions of acetone and tetrahydrofuran were measured from 15.0 to 55.0 °C. A cubic polynomial fit was used to determine the polynomial coefficients for determining permittivity as a function of temperature and mole fraction. These coefficients may also be used to interpolate the dielectric constant between temperatures. Literature values for acetonitrile, 1,4-dioxane, methanol, ethanol, isopropanol and N,N-dimethylformamide in water were used to determine the polynomial coefficients.

Hazardous winds, such as tornadoes and hurricanes, have a great impact on civil engineering structures and cause significant social and economic disturbances. The wind speed and pressure tested in the conventional wind tunnel experiments are much smaller than the actual wind speed and pressure measured in the field. Therefore, the Wind-induced Damage Simulator (WDS) was constructed at the University of Ottawa to overcome the wind speed limitations of wind tunnels and to simulate different types of wind speed profiles. WDS is an isolated cubic box with dimensions 3.65m x3.65 m and 3.0 m height, with multiple inlets on the side faces of the testing chamber and an outlet on the top side. This unique equipment creates a controlled environment for studying wind speed profiles in a confined space, by regulating the air flow with the aid of an attached industrial blower. To measure the simulated wind velocities inside the WDS and to obtain the wind speed profile in the testing chamber, Aeroprobe (12- Hole Probe) sensor was used for different combinations of opened inlets and at four different locations. The data collected from the Aeroprobe was processed by the use of the Aeroflow 2.7.5.7346 software, to get the velocity of wind in three different directions (u, v and w) and the mean velocity at a single point. After determining the mean velocity at different heights and RPM values at all four positions, Matlab software was used to determine the wind profile and the spectra of the turbulence intensities and these were compared for different heights at the four investigated locations and for various rotations per minute (RPM) values (400 to 800 RPM) for controlling the blower. Once the flow characterization was completed, the wind-induced pressure for three models of the Silsoe Cube were measured as a part of the second phase of the test. The current experiment employed 3 different scales of Silsoe cube: 1:40, 1:30 and 1:20, while the pressure coefficients were determined at 16 different points along a vertical line crossing the faces of the cube. A pressure taps system with 16 channels and a Scanivale pressure scanner were used to measure the pressure at 16 different positions on the cube. Matlab software was used to determine the pressure coefficients from the data measured by pressure taps. The pressure coefficienst for the Silsoe Cube were plotted and compared for the three different scales. Also, for determining the best scale to be used in future experiments. The pressure coefficients of the 3 different scaled model of Silsoe Cubes was compared with full-scale data reported in the literature for the same structure. Based on the results obtained from the experiments, recommendations for the best location in the testing chamber for the future experiments employing the WDS were formulated.

The precision of the estimates of the regression coefficients in a regression analysis is affected by multicollinearity. The effect of certain factors on multicollinearity and the estimates was studied. The response variables were the standard error of the regression coefficients and a standarized statistic that measures the deviation of the regression coefficient from the population parameter. The estimates are not influenced by any one factor in particular, but rather some combination of factors. The larger the sample size, the better the precision of the estimates no matter how "bad" the other factors may be. The standard error of the regression coefficients proved to be the best indication of estimation problems.

A new method to extract composition dependent ternary interdiffusion coefficients from a single diffusion couple experiment is presented. The calculations involve direct determination of interdiffusion fluxes from experimental concentration profiles and local integration and differentiation of Onsager's formalism. This new technique was applied to concentration profiles obtained from selected semi-infinite, single-phase diffusion couple experiments in the Cu-Ni-Zn, Fe-Ni-Al, and Ni-Cr-Al systems. These couples exhibit features such as uphill diffusion and zero flux planes. The interdiffusion coefficients from the new technique along with coefficients reported from other methods are graphed as functions of composition. The coefficients calculated from the new technique are consistent with those determined from Boltzmann-Matano analysis and an alternate analysis based on the concept of average ternary interdiffusion coefficients. The concentration profiles generated from the error function solutions using the calculated interdiffusion coefficients are in good agreement with the experimental profiles including those exhibiting uphill diffusion. The new technique is checked for accuracy and consistency by back-calculating known interdiffusion coefficients; in this exercise, the new method accurately predicts constant diffusivity. After rigorous verification, the new technique is applied to previously unexamined couples in the Ni-Pt-Al system. With Ni as the dependent component, the main coefficients are shown to be relatively constant and the cross coefficients are negative. The interdiffusion coefficient representing the contribution of the concentration gradient of Pt to the interdiffusion flux of Al is relatively large for couples whose Al content is low, indicating that Pt has a significant effect on Al when Al concentration is low. Another important aspect of analyzing diffusional interactions is the movement of single and multi-phase boundaries within a diffusion couple. Phase boundaries for an n-component system are newly classified and boundary movement is analyzed in terms of degrees of freedom. Experimental evidence of a category 2:1 boundary is presented with a solid-to-solid semi-infinite diffusion couple in the Fe-Ni-Al system with two single-phase terminal alloys. The diffusion path for this couple surprisingly passes through the vertex of the equilibrium tie triangle on the phase diagram to exhibit three phase equilibria in a ternary system. Here is shown for the first time experimental verification of this phenomenon.

The objective of this research is to devise a procedure to generate random Set Covering Problem (SCP) instances with known optimal solutions and correlated coefficients. The procedure presented in this work can generate a virtually unlimited number of SCP instances with known optimal solutions and realistic characteristics, thereby facilitating testing of the performance of SCP heuristics and algorithms. A four-phase procedure based on the Karush-Kuhn-Tucker (KKT) conditions is proposed to generate SCP instances with known optimal solutions and correlated coefficients. Given randomly generated values for the objective function coefficients and the sum of the binary constraint coefficients for each variable and a randomly selected optimal solution, the procedure: (1) calculates the range for the number of possible constraints, (2) generates constraint coefficients for the variables with value one in the optimal solution, (3) assigns values to the dual variables, and (4) generates constraint coefficients for variables with value 0 in the optimal solution so that the KKT conditions are satisfied. A computational demonstration of the procedure is provided. A total of 525 SCP instances are simulated under seven correlation levels and three levels for the number of constraints. Each of these instances is solved using three simple heuristic procedures. The performance of the heuristics on the SCP instances generated is summarized and analyzed. The performance of the heuristics generally worsens as the expected correlation between the coefficients increases and as the number of constraints increases. The results provide strong evidence of the benefits of the procedure for generating SCP instances with correlated coefficients, and in particular SCP instances with known optimal solutions.

This thesis describes an experimental study of the air flow in ventilating ducts in the stators of electric motors and/or generators of conventional design. The objective was to facilitate prediction of local heat transfer coefficients in ventilating ducts. Various flow phenomena were observed and compared with theoretical predictions. While the theory usually used for similar cases was found o be inapplicable, a related theory was found that checked well with experimental results. A stall phenomenon was observed under certain identified conditions. Useful relationships for predicting the flow details were obtained. The relevance of the work is discussed and future work is proposed. / Thesis / Master of Engineering (MEngr)

<p> The object of this dissertation is to investigate the properties, associated boundary conditions and generalized resolvents of symmetric ordinary differential operators associated with formally self-adjoint nth order ordinary differential expressions with complex coefficients. </p> <p> While symmetric differential operators with equal deficiency indices have been studied in some detail, expecially the particular case when the underlying differential expression has real coefficients, little research has been done on the properties of symmetric differential operators with unequal deficiency indices which are associated with a differential expression with complex coefficients. </p> <p> By extending the symmetric differential operators with unequal deficiency indices to suitable operators with equal deficiency indices in larger Hilbert spaces and introducing a new type of boundary conditions to these extensions, we obtain important information about the original symmetric differential operators with unequal deficiency indices. We are able to generate some well-known theorems of I. M. Glazman (1950) and E. A. Coddington (1954) dealing with the characterization of self-adjoint extensions of symmetric operators in terms of boundary conditions, the relation between the deficiency indices of operators on the whole real line and on the half-line, and the resolvent of self-adjoint extensions, from the theory of symmetric, in particular real, differential operators with equal deficiency indices. We also generalize the result of W. N. Everitt (1959) concerning the number of integrable-square solutions of differential equations with one particular and one singular end-point to the case in which both end-points are singular. Finally, under certain assumptions, we extend some of the fundamental results of K. Kodaira (1950) based upon the methods of algebraic geometry, concerning Green's functions and the minimal symmetric differential operator associated with an even-order formally self-adjoint ordinary differential expansion with real coefficients to the case of Green's functions and the minimal symmetric differential operator associated with an even-order formally self-adjoint ordinary differential expression with complex coefficients. </p> / Thesis / Doctor of Philosophy (PhD)

We give congruences modulo powers of p in {3, 5, 7} for the Fourier coefficients of certain modular functions in level p with poles only at 0, answering a question posed by Andersen and Jenkins and continuing work done by the Jenkins, the author, and Moss. The congruences involve a modulus that depends on the base p expansion of the modular form's order of vanishing at infinity.