Theses & Dissertations

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https://hdl.handle.net/20.500.14170/2002

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Now showing 1 - 5 of 56
  • Publication
    Trigonometric b-spline based approach for solving initial and boundary value problems of dispersive equations
    ( 2019)
    Hamad Mohammed Salih
    Various type of numerical methods are developed by employing spline function for solving dispersive PDEs such as finite difference method (FDM), finite element method (FEM) and finite volume method (FVM). Each method inherits certain drawback like complexity, high computational cost and required the trial function or limitation to certain cases. Due to those constraints, FDM incorporated with B-spline function is introduced to solve partial differential equation (PDE). The main aim of this thesis is to explore the accurate and reliable solution to dispersive PDEs. The cubic trigonometric B-spline method (CuTBS), cubic hybrid B-spline method (CuHBS) and two new methods namely quintic trigonometric B-spline method (QuTBS) and hybrid quintic B-spline (QuHBS) method are chosen with the finite difference scheme to solve the third order dispersive PDEs called Modified Regularised Long Wave equation (MRLW), Benjamin -Bona- Mahony-Burgers equation (BBM-Burgers) and Modified Equal Width equation (MEW). The proposed methods produce the numerical solutions that are found to be better or in good compliance with those present methods in literature. Comparison of the maximum error ( L ) and the Euclidean error ( 2 L ) from the literatures are also done for each example. The performance of the proposed methods are identified to be more accurate than CuTBS and QuTBS method. In order to analyze the stability of the proposed methods, Von-Neumann stability analysis is applied to the linearized schemes. The schemes have been identified to be unconditionally stable. The highlights of the proposed method can be counted as follows: The diagonal matrix obtained from these methods helps in computing accurate solution and can be employed to easily solve PDEs with certain conditions. These methods have an edge over various methods as it approximates the solution at all point in the domain rather than the grid points. The main contribution of this thesis are the development of the quantic splines methods and the applicability to solving dispersive partial differential equations.
  • Publication
    Stability analysis on convection boundary layer stagnation-point flows over a permeable stretching/shrinking surface
    ( 2019)
    Fatinnabila Kamal
    In this thesis, several problems of convection boundary layer flow and heat transfer towards a stretching/shrinking surface along with stability analysis for viscous, nanofluid and micropolar fluids are investigated. There are five problems considered, namely (i) stagnation-point flow and heat transfer over a permeable stretching/shrinking sheet with heat source effect; (ii) magnetohydrodynamic stagnation-point flow towards a permeable stretching/shrinking sheet with slip and heat source/sink effects; (iii) effect three-dimensional stagnation-point flow and heat transfer over a permeable stretching/shrinking sheet with heat source effects in viscous fluid; (iv) MHD stagnation-point flow towards a permeable stretching/shrinking sheet in a nanofluid with chemical reaction; and (v) stagnation-point flow and heat transfer in a micropolar fluid towards a nonlinearly permeable stretching/shrinking sheet. The study starts with the formulations of the mathematical models for every problems. Next, in solving these problems, the governing nonlinear partial differential boundary layer equations are transformed into ordinary differential equations using similarity transformations before being solved numerically using the boundary value problem solver, bvp4c built in Matlab software. The numerical results are then presented in tables and graphs for the skin friction coefficient, the local Nusselt number and the local Sherwood number as well as the velocity, temperature and concentration profiles. The effects of governing parameters have been analysed such as the heat source parameter, the chemical reaction parameter, the suction/injection parameter, the micropolar parameter and the stretching/shrinking parameter. It is observed that the suction/injection effect increase the skin friction coefficient, the local Nusselt number, and the local Sherwood number. Heat source effect has decrease the heat transfer rate. Furthermore, the effect of chemical reaction effect has decrease the local Sherwood number while Micropolar parameter has decrease the skin friction coefficient and heat transfer rate. Further, dual solutions are found for a certain range of the stretching/shrinking parameter. A stability analysis has been carried out to determine which solution is stable for dual solutions exist in all problems considered. The first solution is found to be stable and physically reliable, whereas the second solution is unstable as time passes, thus impractical in the real world applications for a long run.
  • Publication
    Development of linear programming models of water price compliant to the regulation of Ministry of Home Affairs, Indonesia
    ( 2024)
    Tan Kim Hek
    The water tariff and price in Medan, North Sumatera was last reviewed in 2017. The tariff, which is the structure mechanism for determining the water price, must be reviewed once every five years as stipulated in the Regulation of the Ministry of Home Affairs, Indonesia, No. 23, 2006. Currently, the water tariff and price based on the that regulation without any secondary affirmation. Futhermore, the inaccurate water tariff and price that currently being implemented may lead to suboptimal revenue and profit thus affected the business financially. In Medan, the Perusahaan Daerah Air Minum (PDAM) Tirtanadi, is the water operator responsibles for treatment, supplies and distributes the clean and treated water thus it has obligation to charge the customers the price based on the stipulated water regulation. Therefore, the aim of this research is to develop a comprehensive linear programming (LP) model for optimizing the water pricing in Medan within the regulatory framework of the Ministry of Home Affairs, Indonesia. This study is motivated by the pressing need to address the complex interplay between economic efficiency and social equity in water resource management. With Medan's diverse geographical and socio-economic landscape, achieving a balanced water pricing model that meets regulatory compliance while ensuring equitable access, economic viability, and sustainable resource use represents a significant challenge. The research employs a robust LP approach to model water pricing strategies, incorporating various constraints such as production cost, social cost, subsidy, revenue and profit that complied to the water regulatory guidelines. By analysing different water pricing based on customers group and block, this study aims to identify optimal water pricing byrecognising the current error in tariff structure and ensure the potential of new water price in Medan. Key contributions of this research include the development of a novel LP framework that integrates environmental, economic, and social considerations into water pricing decisions. The study also provides empirical insights into the effectiveness of different water pricing mechanisms, offering valuable policy recommendations for water resource management in Medan and similar contexts. Through a rigorous analysis of water pricing strategies, this research contributes to the broader field of water resource management by advancing understanding of how LP can be effectively applied to resolve complex decision-making problems in the context of regulatory compliance and sustainable development goals. This research not only addresses a critical gap in the literature on water pricing and management but also offers practical tools for policymakers, water utilities, and stakeholders involved in the governance of water resources. By proposing a scalable and adaptable LP model, the study underscores the potential for analytical approaches to inform and improve water pricing policies, ultimately contributing to the sustainable management of vital water resources in Medan.
  • Publication
    New approximation methods based on fuzzy transform for solving ordinary differential equations
    ( 2018)
    Hussein Ahmad Alkasasbeh
    Real world probelms in science and engineering are modelled by using differential equations. In many cases, the differential equations cannot be solved analytically so that numerical methods are required. As time goes on, researchers realized that fuzzy approaches are particularly that has been proposed in the literature is the fuzzy transform (FzT). There has been a growing interest in investigating the properties of fuzzy partitions. In this research, new representations of basic functions are proposed. This is achieved by introducing new generalized uniform fuzzy partitions called power of the triangular and raised cosine generalied uniform fuzzy partitions. The main properties of the new generalized uniform fuzzy partitions are proposed. Further, the simpler from of FzT is given alongside with some of its fundamental results. New theorems and lemmas are proposed and proved mathematically. Then, the new generalized uniform fuzzy partitions are used in three approximation methods based on FzT to solve Cauchy problems. The first approximation method used Trapezoidal rule with FzT and new iteration method (NIM). The results proved that the first approximation method convereged to the exact solution. The second approximation method used Adams Moulton method with FzT and NIM while the thrid approximation method used Adams Moulton method with FzT and NIM. From the numerical results, all the proposed fuzzy approximation methods outperform the classical Trapezoidal rule and classical Adams Moulton method. Further, it is also observed that the proposed fuzzy approximation methods are more accurate in comparison with the existing fuzzy approximation methods. This result is an important improvement to the previous results for Cauchy problems. Furthermore, two approximation methods are used in the fuzzy partitions to solve system of differential equations based on FzT and a one step method. The first approximation method used Euler method with FzT and the second approximation method used Trapezoidal rule with FzT. From the numerical results, it is observed that both fuzzy approximation methods yield more accurate results in comparison with the classical Euler method and classical Trapezoidal rule. This result is an important improvement to the previous results for solving system of differential equations. The discussion continued in last part with more advanced techniques, In the last part, the new generalized uniform fuzzy partitions are used in three approximation methods based on FzT to solve system of differential equations. In accordance with the three approximation methods for Cauchy problem, Trapezoidal rule and Adams Moulton method are improved using FzT and NIM. From the numerical results, it is observed that the new fuzzy approximation methods yield more accurate results in comparison with the classical Trapezoidal rule and classical Adams Moulton method. Hence, the new fuzzy approximation methods provide alternative techniques for solving differential equations with better results.
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  • Publication
    New process capability indices based on six sigma statistical approach for measuring the process performance in industries: a case study in Aden's oil refinery Yemen
    ( 2018)
    Faisal Ali Mohammed Ali
    The purpose of this study is to measure and evaluate the process performance of the industrial processes through the use of Process Capability Indices (PCIs) and Six Sigma (SS) concept. In light of this, this study proposed four different cases to estimate and measure the univariate process yield index SSS *pk* based on C *p*, C *pk*, S *pk*, SSC *pk*, SSQL *pk* indices. Moreover, this study extends the proposed univariate process yield index SSS *pk* to a multivariate generalized yield index called SMS *pk* and SSMS *pk PC* based on Tolerance Limits (TL) and Principal Component Analysis (PCA) respectively to measure the overall process yield of industrial processes. Overall, this study provided a statistical approach based on PCIs and SS concept to measure and improve process performance of the univariate and multivariate processes in industries. To demonstrate the applicability of the proposed approach, this study presents an industrial case study to assess the process performance of oil refinery in Aden, Yemen. Toward this end, the data for three essential quality characteristics of petroleum products namely density, octane number and vapor pressure were collected randomly from Aden refinery. The findings of this study indicated that the proposed indices SSMS *pk* and SSMS *pk.PC*outperformed the existing indices TS *pk,PC* , T *pk ..PC* and TS *pk, PC ,B*. The obtained results for SSMS *pk* by TL model for A, B, C and D cases are 0.7114, 1.19, 0.525 and 0.525 respectively. The obtained results for SSMS *pk.. PC* by PCA model is 0.367213. Meanwhile, the yield process results for TS *pk, PC*, S *T pk...PC* and TS *pk...PC ,B* indicators are 0.154, 0.25 and 0.28 respectively. This study has important implications for industrial practitioners, researchers and quality control experts interested in the evaluation of process performance. Finally, the proposed PCIs based on SS concept is a promising approach and thus can be extended and or utilized by other industries and practitioners to assess process performance in the aspect of precision and quality control.
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