Controlled cooling is an important part of steel production industry that affects the properties of the outcome steel. Many of the researches done in controlled cooling are experimental. Due to progress in the numerical techniques and high cost of experimental works in this field the numerical work seems more feasible. Heat transfer analysis is the necessary element of successful controlled cooling and ultimately achievement of novel properties in steel. Heat transfer on the surface of the plate normally contains different regimes such as film boiling, nucleate boiling, transition boiling and radiation heat transfer. This makes the analysis more complicated. In order to perform the heat transfer analysis often empirical correlations are being used. In these correlations the velocity and pressure within the fluid domain is involved. Therefore in order to obtain a better understanding of heat transfer process, study of hydrodynamics of the fluid becomes necessary. Circular jet due to its high efficiency has been used vastly in the industry. Although some experimental studies of round jet arrays have been done, yet the characteristics of a single jet with industrial geometric and flow parameters on the surface of a flat plate is not fully understood. Study of hydrodynamics of the jet impingement is the first step to achieve better understanding of heat transfer process. Finite element method as a popular numerical method has been used vastly to simulate different domains. Traditional approaches of finite element method, Lagrangian and Eulerian, each has its own benefits and drawbacks. Lagrangian approach has been used widely in solid domains and Eulerian approach has been widely used in fluid fields. Jet impingement problem, due to its unknown free surface and the change in the boundary, falls in the category of special problems and none of the traditional approaches is suitable for this application. The Arbitrary Lagrangian Eulerian (ALE) formulation has emerged as a technique that can alleviate many of the shortcomings of the traditional Lagrangian and Eulerian formulations in handling these types of problems. Using the ALE formulation the computational grid need not adhere to the material (Lagrangian) nor be fixed in space (Eulerian) but can be moved arbitrarily. Two distinct techniques are being used to implement the ALE formulation, namely the operator split approach and the fully coupled approach. This thesis presents a fully coupled ALE formulation for the simulation of flow field. ALE form of Navier-Stokes equations are derived from the basic principles of continuum mechanics and conservation laws in the fluid. These formulations are then converted in to ALE finite element equations for the fluid flow. The axi-symmetric form of these equations are then derived in order to be used for jet impingement application. In the ALE Formulation as the mesh or the computational grid can move independent of the material and space, an additional set of unknowns representing mesh movement appears in the equations. Prescribing a mesh motion scheme in order to define these unknowns is problem-dependent and has not been yet generalized for all applications. After investigating different methods, the Winslow method is chosen for jet impingement application. This method is based on adding a specific set of partial differential Equations(Laplace equations) to the existing equations in order to obtain enough equations for the unknowns. Then these set of PDEs are converted to finite element equations and derived in axi-symmetric form to be used in jet impingement application. These equations together with the field equations are then applied to jet impingement problem. Due to the number of equations and nonlinearity of the field equations the solution of the problem faces some challenges in terms of convergence characteristics and modeling strategies. Some suggestions are made to deal with these challenges and convergence problems. Finally the numerical treatment and results of analyzing hydrodynamics of the Jet Impingement is presented. The work in this thesis is confined to the numerical simulation of the jet impingement and the specifications of an industrial test setup only have been used in order to obtain the parameters of the numerical model.

There are three distinct processes that are predominant in models of flowing media with interacting components: advection, reaction, and diffusion. Collectively, these processes are typically modelled with partial differential equations (PDEs) known as advection-reaction-diffusion (ARD) equations.<p> To solve most PDEs in practice, approximation methods known as numerical methods are used. The method of lines is used to approximate PDEs with systems of ordinary differential equations (ODEs) by a process known as semi-discretization. ODEs are more readily analysed and benefit from well-developed numerical methods and software. Each term of an ODE that corresponds to one of the processes of an ARD equation benefits from particular mathematical properties in a numerical method. These properties are often mutually exclusive for many basic numerical methods.<p> A limitation to the widespread use of more complex numerical methods is that the development of the appropriate software to provide comparisons to existing numerical methods is not straightforward. Scientific and numerical software is often inflexible, motivating the development of a class of software known as problem-solving environments (PSEs). Many existing PSEs such as Matlab have solvers for ODEs and PDEs but lack specific features, beyond a scripting language, to readily experiment with novel or existing solution methods. The PSE developed during the course of this thesis solves ODEs known as initial-value problems, where only the initial state is fully known. The PSE is used to assess the performance of new numerical methods for ODEs that integrate each term of a semi-discretized ARD equation. This PSE is part of the PSE pythODE that uses object-oriented and software-engineering techniques to allow implementations of many existing and novel solution methods for ODEs with minimal effort spent on code modification and integration.<p> The new numerical methods use a commutator-free exponential Runge-Kutta (CFERK) method to solve the advection term of an ARD equation. A matrix exponential is used as the exponential function, but CFERK methods can use other numerical methods that model the flowing medium. The reaction term is solved separately using an explicit Runge-Kutta method because solving it along with the diffusion term can result in stepsize restrictions and hence inefficiency. The diffusion term is solved using a Runge-Kutta-Chebyshev method that takes advantage of the spatially symmetric nature of the diffusion process to avoid stepsize restrictions from a property known as stiffness. The resulting methods, known as Integrating-factor-based 2-additive Runge-Kutta methods, are shown to be able to find higher-accuracy solutions in less computational time than competing methods for certain challenging semi-discretized ARD equations. This demonstrates the practical viability both of using CFERK methods for advection and a 3-splitting in general.

The current thesis studies a model of two dimensional convection of an ideal gas in a rectangular domain having walls of finite thickness. The temperature outside of walls is considered constant. Heat exchange between walls and outside/inside air is computed using Newton's law of cooling. Heat transfer inside walls is modelled with the heat equation. The mathematical model inside enclosure involves Navier-Stokes equations coupled with equation of state for gas. The model is numerically studied using the method of large particles. One of the main goals of the current thesis was to develop a software in C# language for numerical solution of the above-described model. Physically meaningful results, including stream lines and distribution of parameters of gas and temperature inside solid walls were obtained.

Conventional disposal of waste rock results in the construction of benches with interbedded fine and coarse layers dipping at the angle of repose. The waste rock benches are typically 20-meters in height and are constructed in a vertical sequence to form waste rock dumps commonly greater than 100-meters high. The interbedded structure influences the flow pathways for infiltration water within the waste rock profile. Preferential flow pathways develop when one material becomes more conductive than the surrounding material. The flow of meteoric waters through the interbedded waste rock structure is difficult to describe since the dumps are constructed above natural topography and are generally unsaturated. Two previous research studies were undertaken at the University of Saskatchewan to study end dumped waste rock piles and the relationship to preferential flow for unsaturated conditions. The first study was conducted during the excavation of a large waste rock pile at Golden Sunlight Mine in Montana (Herasymuik, 1996). Field observations showed that the waste rock pile consisted of steeply dipping fine and coarse-grained layers. The results of further laboratory analysis indicated the potential for preferential flow through the fine-grained material under conditions with negative pore-water pressures and unsaturated flow. The second study investigated the mechanism for preferential flow in vertically layered, unsaturated soil systems (Newman, 1999). The investigation included a vertical two-layer column study and a subsequent numerical modelling program showing that water prefers to flow in the finer-grained material. The preferential flow path was determined to be a function of the applied surface flux rates and the unsaturated hydraulic conductivity of the fine-grained material layer. A numerical modelling program to evaluate preferential flow was conducted for the present study in an inclined four-layer system consisting of alternating fine and coarse-grained waste rock. The numerical modelling program was undertaken using the commercial seepage software package, Seep/W, that is commonly used by geotechnical engineers. The result obtained using Seep/W showed preferential flow to occur in the fine-grained layer. However, difficulties with respect to convergence under low flow conditions with steep hydraulic conductivity functions were encountered. A comprehensive sensitivity analysis was completed to investigate the factors that influence convergence in the Seep/W model including: convergence criteria, mesh design and material properties. It was found that the hydraulic conductivity function used for the coarse-grained material was the most important factor. The problem of the steep slope for the hydraulic conductivity function specified for the coarse-grained material was solved by progressively decreasing the slope of the hydraulic conductivity function at 10-8 m/s (for applied fluxes of 10-7 m/s or less). The sensitivity analysis showed that the manipulation of the hydraulic conductivity function had insignificant changes in the flux distribution between the waste rock layers and great significance for achieving convergence. Based on the discoveries of the sensitivity analysis, a 20-meter high multi-layer waste rock profile inclined at 50º with an applied flux of 7.7e10-9 m/s equal to the annual precipitation at the Golden Sunlight Mine was successfully simulated. A parametric study was subsequently conducted for an applied flux rate of 10-5 m/s for slope heights of 1-meter to 20 meters with slope angles varying between 45º and 90º. The parametric study demonstrated that flow in a multi-layered waste rock dump is a function of inclination, contact length between the layers, and the coarse and fine-grained hydraulic properties for the waste rock. An alternative numerical modelling technique based on a modified Kisch solution was also used to investigate preferential flow. The Kisch method helped to verify and simplify the numerical problem as well as to illustrate the mechanics of preferential flow in a two-layered system. In general, commercial seepage modeling packages are powerful and useful tools that are designed to adequately accommodate a wide range of geotechnical problems. The results of this research study indicate that Seep/W may not be the best-suited tool to analyze unsaturated seepage through sloped waste rock layers. However, numerical modelling is a process and working through the process helps to enhance engineering judgment. The Seep/W model provided an adequate solution for a simplified simulation of unsaturated seepage through waste rock layers. The modified Kisch solution independently verified the solution and provided additional confidence for the results of Seep/W model.

A large proportion of water and wastewater systems have traditionally been analyzed and designed without the consideration of the nature, risk, and potential consequence of hydraulic transients. Recent advancements in numerical hydraulic modeling have spawned a specialty hydraulic field based on numerical transient analysis. The current practice within this field often lacks physical understanding and can be misguided by both the current knowledge, technology based limitations, and by the sole reliance on numerical models. This thesis aims to provide insights into some of the shortcomings of current practice and to develop the importance and application of field data based confirmations. The thesis examines the advances in the current field oriented technology for recording transient pressures, and provides examples and insights on how this data can be used both in conjunction with numerical modeling and on its own as a first step to a proposed frequency based transient risk assessment methodology. The thesis establishes definitions and a preliminary methodology for a Transient Risk Index.

A large proportion of water and wastewater systems have traditionally been analyzed and designed without the consideration of the nature, risk, and potential consequence of hydraulic transients. Recent advancements in numerical hydraulic modeling have spawned a specialty hydraulic field based on numerical transient analysis. The current practice within this field often lacks physical understanding and can be misguided by both the current knowledge, technology based limitations, and by the sole reliance on numerical models. This thesis aims to provide insights into some of the shortcomings of current practice and to develop the importance and application of field data based confirmations. The thesis examines the advances in the current field oriented technology for recording transient pressures, and provides examples and insights on how this data can be used both in conjunction with numerical modeling and on its own as a first step to a proposed frequency based transient risk assessment methodology. The thesis establishes definitions and a preliminary methodology for a Transient Risk Index.

Propagation of radiation in a waveguides is theoretically described by Maxwell&amp / #8217 / s equations. The gradient of refractive index and an influence on the waveguide by a superstrate requires a numerical solution of the differential equation. Iterative methods such as the Runge-Kutta approaches are used to calculate the effective refractive index in the waveguide depending on the superstrate&amp / #8217 / s and the waveguide&amp / #8217 / s local refractive indices. In this study,the refractive indices, and the model fields of the TE00 modes are calculated. The calculated fields of the 00 TE modes give information about the propagation of the light in the waveguide. Also, the precision of the Runge-Kutta aproaches has been tested. The advantages and disadvantages of the Runge-Kutta aproaches are discussed.

Conventional disposal of waste rock results in the construction of benches with interbedded fine and coarse layers dipping at the angle of repose. The waste rock benches are typically 20-meters in height and are constructed in a vertical sequence to form waste rock dumps commonly greater than 100-meters high. The interbedded structure influences the flow pathways for infiltration water within the waste rock profile. Preferential flow pathways develop when one material becomes more conductive than the surrounding material. The flow of meteoric waters through the interbedded waste rock structure is difficult to describe since the dumps are constructed above natural topography and are generally unsaturated. Two previous research studies were undertaken at the University of Saskatchewan to study end dumped waste rock piles and the relationship to preferential flow for unsaturated conditions. The first study was conducted during the excavation of a large waste rock pile at Golden Sunlight Mine in Montana (Herasymuik, 1996). Field observations showed that the waste rock pile consisted of steeply dipping fine and coarse-grained layers. The results of further laboratory analysis indicated the potential for preferential flow through the fine-grained material under conditions with negative pore-water pressures and unsaturated flow. The second study investigated the mechanism for preferential flow in vertically layered, unsaturated soil systems (Newman, 1999). The investigation included a vertical two-layer column study and a subsequent numerical modelling program showing that water prefers to flow in the finer-grained material. The preferential flow path was determined to be a function of the applied surface flux rates and the unsaturated hydraulic conductivity of the fine-grained material layer. A numerical modelling program to evaluate preferential flow was conducted for the present study in an inclined four-layer system consisting of alternating fine and coarse-grained waste rock. The numerical modelling program was undertaken using the commercial seepage software package, Seep/W, that is commonly used by geotechnical engineers. The result obtained using Seep/W showed preferential flow to occur in the fine-grained layer. However, difficulties with respect to convergence under low flow conditions with steep hydraulic conductivity functions were encountered. A comprehensive sensitivity analysis was completed to investigate the factors that influence convergence in the Seep/W model including: convergence criteria, mesh design and material properties. It was found that the hydraulic conductivity function used for the coarse-grained material was the most important factor. The problem of the steep slope for the hydraulic conductivity function specified for the coarse-grained material was solved by progressively decreasing the slope of the hydraulic conductivity function at 10-8 m/s (for applied fluxes of 10-7 m/s or less). The sensitivity analysis showed that the manipulation of the hydraulic conductivity function had insignificant changes in the flux distribution between the waste rock layers and great significance for achieving convergence. Based on the discoveries of the sensitivity analysis, a 20-meter high multi-layer waste rock profile inclined at 50º with an applied flux of 7.7e10-9 m/s equal to the annual precipitation at the Golden Sunlight Mine was successfully simulated. A parametric study was subsequently conducted for an applied flux rate of 10-5 m/s for slope heights of 1-meter to 20 meters with slope angles varying between 45º and 90º. The parametric study demonstrated that flow in a multi-layered waste rock dump is a function of inclination, contact length between the layers, and the coarse and fine-grained hydraulic properties for the waste rock. An alternative numerical modelling technique based on a modified Kisch solution was also used to investigate preferential flow. The Kisch method helped to verify and simplify the numerical problem as well as to illustrate the mechanics of preferential flow in a two-layered system. In general, commercial seepage modeling packages are powerful and useful tools that are designed to adequately accommodate a wide range of geotechnical problems. The results of this research study indicate that Seep/W may not be the best-suited tool to analyze unsaturated seepage through sloped waste rock layers. However, numerical modelling is a process and working through the process helps to enhance engineering judgment. The Seep/W model provided an adequate solution for a simplified simulation of unsaturated seepage through waste rock layers. The modified Kisch solution independently verified the solution and provided additional confidence for the results of Seep/W model.

The energy requirements of forage harvesters can be quite high and can sometimes determine the size of tractor needed on a farm. Therefore, improving the energy efficiency of the forage harvester could allow a farm to reduce costs by using a smaller tractor that is less expensive and more efficient. The objective of this research was to increase the throwing distance of a forage harvester by modeling the flow of forage in the spout and the air flow in the blower and spout. These models can then be used to compare the efficiencies of prototype designs. The air flow in the blower and spout was modeled using the commercial computational fluid dynamics software FLUENT. The simulation results of air velocities and flow patterns were compared to experimental values and it was found that both were of the same order of magnitude with the model predicting slightly higher air velocities than those measured. The flow of forage in the spout was modeled analytically by taking into account the friction between the forage and the spout surface and the aerodynamic resistance after the forage leaves the spout. From this model, two improved prototype spouts that should theoretically result in longer throwing distances were designed. However, field testing of the two prototypes did not reveal any significant improvements over the current design. It was also found that the model under-predicted the throwing distance of one prototype by 2 % and over estimated the other by 12 %.

Internal waves in lakes and oceans are ubiquitous whenever a density stratification is present. These waves are relatively slow moving, can be large in extent and have long time scales. As these waves are so common, it is suspected that they play a role in recirculating nutrients throughout the water column. The various factors contributing to this recirculation are commonly referred to as the nutrient circulation system. This thesis analyses three potential mechanisms of internal wave forcing of the nutrient circulation system over a range of length scales. Namely, we discuss internal wave shear induced sediment resuspension, non-Newtonian fluid mud vortex dynamics and internal wave forced lake bottom seepage. We believe that these demonstrate the significant effect that internal waves can have on distributing nutrients throughout the water column. In conjunction, these mechanisms have the potential to be the dominant source of nutrient circulation in certain regions of lakes and oceans.