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A stochastic method is developed, implemented and investigated here for solving Laplace, Poisson's, and standard parabolic wave equations. This method is based on the properties of random walk, diffusion process, Ito formula, Dynkin formula and Monte Carlo simulations. The developed method is a local method i:e: it gives the value of the solution directly at an arbitrary point rather than extracting its value from complete field solution and thus is inherently parallel. Field computation by this method is demonstrated for electrostatic and electrodynamic propagation problems by considering simple examples and numerical results are presented to validate this method. Numerical investigations are carried out to understand efficacy and limitations of this method and to provide qualitative understanding of various parameters involved in this method.

A predominant amount of energy needed in the industrial sector is in the form of heat. A significant number of industries in the world still relies on fossil fuels for meeting their heat requirements. A transition to renewable energy for heating needs is at a snail's pace due to fossil fuel lock-in, cost superiority of conventional fuels, and less government support for renewable technology for thermal requirements. The dairy industry is one of the sectors that need heat energy for its production process. This study deals with a techno-economic analysis on the integration of parabolic trough collectors in the dairy industry. The thesis finds the barriers for solar-thermal collectors to evolve in the dairy sector and the viewpoint of the dairy industry towards the acceptance of solar thermal for meeting their thermal needs. From a literature review, it is observed that the need for dairy product will increase in the coming year. To meet the demand, the production process has to be increased. For sustainable production, companies have to rely on environment-friendly energy sources to meet the thermal demand. In the thesis work, it was also found that for several solar fractions, the LevelizedCost of Heat (LCoH) of solar-assisted heating system is less than the LCoH of the fossil-fueled conventional boiler. Therefore, it is economically viable to integrate solar thermal collectors in the dairy industry. The project also compares the LCoHof solar-assisted heating system when solar integration is done at a) feed water heating, b) direct steam generation, and c) process integration. The effect of integration point on the solar fraction, LCoH, and carbon mitigation potential is presented for a real case dairy unit in Dubai. The simulations are performed using a dynamic simulation tool. Results show that minimum LCoH and solar fraction are achieved for process integration. The process integration results in up to 90 % of the solar fraction. Through process integration, the LCoH of the conventional boiler can be reduced by 60%.

Quantification and prediction of capillary fluid flow in planar nanochannels is essential to the development of many emerging nanofluidic technologies. Planar nanochannels are typically produced using the standard nanofabrication processes of thermal bonding or sacrificial etching. Both approaches may yield nanochannels that are bowed and/or exhibit non-uniform (i.e. non-planar) wall spacing. These variations in wall spacing affect the transient dynamics of a liquid plug filling the nanochannel, causing deviations from the classical behavior in a parallel-plate channel as described by the Washburn model. Non uniform wall spacing impacts the overall frictional resistance and influences the meniscus curvature. In this thesis, a new analytical model that predicts the meniscus location over time in micro- and nanochannels as a function of channel height was compared to experimental filling data of well-characterized channels with different heights. The wall-to-wall spacing of the utilized nanochannels exhibited height variations between 60 and 300 nm. The model was also validated with microscale channels that were fabricated with a linear variation in the wall-to-wall spacing from 100 µm to 400 µm. The filling speed and meniscus shape during the filling process were determined by dynamic imaging of the meniscus front for several different liquids. A modified Washburn equation that utilizes an effective channel height to predict the filling speed corresponding to the location of the tallest height within a channel was derived. A model was also developed to predict the meniscus distortion encountered in a non-constant height channel, provided the cross-sectional channel heights and the distance from the channel entrance are known. The models developed herein account for induced transverse pressure gradients created by non-constant channel heights. The models are compared to experimental data derived from both nanoscale and microscale channels with good qualitative agreement. These results demonstrate that the capillary flow in nanochannels with non-parallel-plate, linear tapered, or parabolic cross sections can be predicted.

The principal objective of this study is to develop, investigate and optimise the Heteroconical Tubular Cavity receiver for a parabolic trough reflector. This study presents a three-stage development process which allowed for the development, investigation and optimisation of the Heteroconical receiver. The first stage of development focused on the investigation into the optical performance of the Heteroconical receiver for different geometric configurations. The effect of cavity geometry on the heat flux distribution on the receiver absorbers as well as on the optical performance of the Heteroconical cavity was investigated. The cavity geometry was varied by varying the cone angle and cavity aperture width of the receiver. This investigation led to identification of optical characteristics of the Heteroconical receiver as well as an optically optimised geometric configuration for the cavity shape of the receiver. The second stage of development focused on the thermal and thermodynamic performance of the Heteroconical receiver for different geometric configurations. This stage of development allowed for the investigation into the effect of cavity shape and concentration ratio on the thermal performance of the Heteroconical receiver. The identification of certain thermal characteristics of the receiver further optimised the shape of the receiver cavity for thermal performance during the second stage of development. The third stage of development and optimisation focused on the absorber tubes of the Heteroconical receiver. This enabled further investigation into the effect of tube diameter on the total performance of the Heteroconical receiver and led to an optimal inner tube diameter for the receiver under given operating conditions. In this work, the thermodynamic performance, conjugate heat transfer and fluid flow of the Heteroconical receiver were analysed by solving the computational governing Equations set out in this work known as the Reynolds-Averaged Navier-Stokes (RANS) Equations as well as the energy Equation by utilising the commercially available CFD code, ANSYS FLUENT®. The optical model of the receiver which modelled the optical performance and produced the nonuniform actual heat flux distribution on the absorbers of the receiver was numerically modelled by solving the rendering Equation using the Monte-Carlo ray tracing method. SolTrace - a raytracing software package developed by the National Renewable Energy Laboratory (NREL), commonly used to analyse CSP systems, was utilised for modelling the optical response and performance of the Heteroconical receiver. These actual non-uniform heat flux distributions were applied in the CFD code by making use of user-defined functions for the thermal model and analysis of the Heteroconical receiver. The numerical model was applied to a simple parabolic trough receiver and reflector and validated against experimental data available in the literature, and good agreement was achieved. It was found that the Heteroconical receiver was able to significantly reduce the amount of reradiation losses as well as improve the uniformity of the heat flux distribution on the absorbers. The receiver was found to produce thermal efficiencies of up to 71% and optical efficiencies of up to 80% for practically sized receivers. The optimal receiver was compared to a widely used parabolic trough receiver, a vacuum tube receiver. It was found that the optimal Heteroconical receiver performed, on average, 4% more efficiently than the vacuum tube receiver across the temperature range of 50-210℃. In summary, it was found that the larger a Heteroconical receiver is the higher its optical efficiency, but the lower its thermal efficiency. Hence, careful consideration needs to be taken when determining cone angle and concentration ratio of the receiver. It was found that absorber tube diameter does not have a significant effect on the performance of the receiver, but its position within the cavity does have a vital role in the performance of the receiver. The Heteroconical receiver was found to successfully reduce energy losses and was found to be a successfully high performance solar thermal tubular cavity receiver.

Parabolic solar trough receivers are used to collect heat via the mean of a heat transfer fluid. This component is one among a myriad of the Concentrated Solar Power (CSP) devices. Parabolic troughs reach high temperatures around 400 ºC. improving the Parabolic Solar Trough's receiver with an IR selective coating will increase the heat transfer absorbed by the heat transfer fluid and reduce the radiative heat loss. Thus, optimizing the receiver will ameliorate the efficiency of the electrical production for a CSP. The parabolic solar receiver existing in industry currently are made of stainless steel with no specific coating for IR solar rays spectrum selection. Therefore, the heat transferred through the absorber is limited to certain light spectrum. Furthermore, numerous receivers proposed are made from materials that contaminates their optical properties when oxidized such as aluminum [1]. The heat transfer and optical analysis of the PTC are essential to optimize and understand its performance under high temperatures and reduce the heat loss. In this paper, our focus is on presenting a super-lattice IR selective coating to minimize the radiative heat loss. Making use of the power of metamaterials to confection optical properties that are inexistent in nature, the coating will serve to maximize the tube's reflectance above 70% in the IR. Not only does the selective coating enhance the optical properties of the receiver, but also it ensures performance stability for high temperatures.

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This work is a numerical study of the 2-D heat equation with Dirichlet boundary conditions over a polygonal domain. The motivation for this study is a chemical vapor deposition (CVD) reactor in which a substrate is heated while being exposed to a gas containing precursor molecules. The interaction between the gas and the substrate results in the deposition of a compound thin film on the substrate. Two different numerical approximations are implemented to produce numerical solutions describing the conduction of thermal energy in the reactor. The first method used is a Crank-Nicholson finite difference technique which tranforms the 2-D heat equation into an algebraic system of equations. For the second method, a semi-discrete method is used which transforms the partial differential equation into a system of ordinary differential equations. The goal of this work is to investigate the influence of boundary conditions, domain geometry, and initial condition on thermal conduction throughout the reactor. Once insight is gained with respect to the aforementioned conditions, optimal design and control can be investigated. This work represents a first step in our long term goal of developing optimal design and control of such CVD systems. This work has been funded through Partnerships in Research Excellence and Transition (PRET) grant number F49620-96-1-0329. / Master of Science