http://103.99.128.19:8080/xmlui/handle/123456789/124 Thesis published in Dept. of Mathematics 2026-10-05T08:47:52Z http://103.99.128.19:8080/xmlui/handle/123456789/602 Title: SIMULATION OF HEAT TRANSFER ENHANCEMENT IN A PIPE USING RECTANGULAR CUT TWISTED TAPE INSERT: A FEM APPROACH Authors: Anika, Onamika Ibnath; ID :, 21MMATH009F Abstract: A simulation analysis has been conducted to investigate heat transfer enhancement using rectangular-cut twisted tape inserts in a U-shaped pipe. Numerical simulations have also been carried out for a plain tube and a tube with smooth twisted tape (TT) inserts, and the results have been compared across three configurations: rectangular-cut TT inserts, smooth TT inserts, and the plain tube. The analysis has utilized a U-bend pipe with a length of 1935.6 mm and an inner diameter of 26.6 mm. For non-isothermal turbulent flow, water has been selected as the working fluid, and the Reynolds number (Re) range has been considered from 5319.4 to 17288.05. The rectangular-cut twisted tape inserts have demonstrated superior heat transfer performance compared to the other two configurations due to enhanced fluid mixing in the turbulent flow regime. In this study, the dimensionless Nusselt number (Nu) has consistently been higher for the rectangular-cut twisted tape configuration and has shown a gradual increase with rising Reynolds numbers. The results have also indicated improved thermal performance (ɳ), with a thermal performance factor of 1.04 and favorable friction factor values for the pipe fitted with rectangular cut twisted tape inserts. Description: A Master of Philosophy (M.Phil.) Thesis in Mathematics Department at Chittagong University of Engineering and Technology (CUET). 2025-04-08T00:00:00Z http://103.99.128.19:8080/xmlui/handle/123456789/599 Title: NUMERICAL INVESTIGATIONOFNONLINEAR ACOUSTICWAVEPHENOMENA INSTRONGLYAND WEAKLYCOUPLEDPLASMAS Authors: Islam, Md. Nazrul Abstract: This thesis investigates nonlinear acoustic wave phenomena in both strongly and weakly coupled collisionless unmagnetized plasmas using analytical and numerical methods. By developing mathematical models for different plasma environments, the study employs the reductive perturbation technique (RPT) to derive nonlinear evolution equations (NLEEs). These equations are then used to analyze the propagation of shock waves, solitons, and periodic waves in various plasma configurations. In Chapter 2, Burgers equations involving quadratic, cubic, and combined quadratic-cubic nonlinearities are derived for a coupled complex plasma system consisting of Boltzmann-distributed electrons, nonthermal ions, and charged dust particles. The generalized Riccati equation mapping method (GREMM) is employed to obtain both shock and oscillatory wave solutions from these equations, while parametric effects on wave characteristics are systematically examined. Chapter 3 investigates heavy ion-acoustic shock waves (HIASWs) in a plasma comprising inertial heavy ions, Maxwellian light ions, and (α,q)-distributed electrons, by deriving the Burgers, modified Burgers, and mixed modified Burgers equations. The study presents stationary shock wave solutions for these equations and examines how plasma parameters influence shock wave characteristics. Chapter 4 investigates the dust acoustic (DA) shock wave phenomena in an strongly coupled dusty plasma. By deriving Burgers equations with quadratic, cubic, and quartic nonlinearities, we analyze shock wave behavior near critical values (CVs) and super-critical values (SCVs), revealing how polarization force and coupling parameter modifies shock wave excitations. Chapter 5 analyzes heavy ion-acoustic (HIA) solitons and dressed solitons in weakly/strongly coupled plasmas with nonthermal electrons. Chapter 6 advances the Chapter 3 framework by examining HIASWs near CVs and SCVs, deriving a non-integrable NLEE with combined cubic-quartic nonlinearities that necessitates numerical solution via Runge-Kutta-Fehlberg analysis. Thus, the thesis enhances understanding of nonlinear coherent structures observed in various space and astrophysical environments. Description: A Doctor of Philosophy (Ph.D.) Thesis in Mathematics Department at Chittagong University of Engineering and Technology (CUET). 2025-07-17T00:00:00Z http://103.99.128.19:8080/xmlui/handle/123456789/589 Title: DESIGNING CONTROL SCHEMS FOR CHAOTIC SYSTEMS VIA SLIDING MODE CONTROL Authors: AFROJA, AFSANA; ID:, 21MMATH002P Abstract: Among various robust control methods, Sliding Mode Control (SMC) has attracted considerable interest in theoretical research due to its unique features. SMC is well known for its robustness to matched and bounded uncertainties, reduction in the order of the system during the sliding phase, simplified decoupling of system dynamics, and its ability to achieve zero steady-state error. These characteristics make SMC a powerful tool in designing control systems for uncertain and nonlinear environments. This thesis presents a comprehensive study on the control and synchronization of chaotic systems, focusing on the Modified Lorenz System (MLS) and the Liu financial dynamical system. Chaotic behavior, with its sensitivity to initial conditions, presents major challenges in nonlinear control. Sliding Mode Control (SMC) is applied to coupled MLS to ensure robust synchronization through a designed sliding surface and control law, with convergence proven via Lyapunov stability and validated through numerical simulations. In the Liu financial system, both SMC and Passive Control (PC) are implemented and compared. While SMC provides rapid synchronization (within 𝑡 ≥ 1, error reduced from 5.67 to 0.02), PC achieves synchronization more gradually (within 𝑡 ≤ 13, error reduced from 6.21 to 0.03) using a simpler, single-controller strategy. The results highlight key trade-offs between speed, robustness, and implementation complexity, offering valuable insights into managing chaos in nonlinear and financial systems. These limitations have motivated ongoing research aimed at improving SMC design. The core challenge remains how to develop a simple yet effective sliding mode control technique that retains its robustness and zero-error tracking while minimizing chattering and relaxing the need for precise uncertainty bounds. Description: A Master of Philosophy (M.Phil.) Thesis in Mathematics Department at Chittagong University of Engineering and Technology (CUET). 2025-07-07T00:00:00Z http://103.99.128.19:8080/xmlui/handle/123456789/567 Title: ISOTROPIC SOLUTION OF EINSTEIN’S EQUATIONS ONTHE FLUIDSPHERE Authors: HOSSAIN, MD.IMRAN; ID:, 21MMATH005 Abstract: This thesis investigates the theoretical framework of spherically symmetric perfect fluid spheres within the realm of general relativity. Our work seeks exact solutions to the Einstein field equations thereby facilitating a better knowledge of minuscule objects. The thesis begins by examining the fundamental aspects of special relativity, including the Lorentz transformations and the structure of spacetime. We then explore general relativity, with an eye towards the Einstein field equations and the geometric justification of gravity. Examining matter dispersion in astrophysical systems depends on first looking at the behavior of ideal fluids. The thesis delves into the intricacies of the Einstein field equations and their application to spacetimes with spherical symmetry. The key achievement of the research is the formulation of new exact solutions for static spherically symmetric ideal fluid spheres. Implementing two techniques in the context of static spherically symmetric ideal fluid line elements, we develop two new approaches that validate their characteristics and ensure that they satisfy Buchdhal criteria. The physical characteristics and possible astrophysical implications of these solutions are thoroughly investigated. Combining the ideas of general relativity with the simplified model of perfect fluids helps this work provide new understanding on the interactions between compact objects and their gravitational interactions. Description: An M.Phil. Thesis in Mathematics Department at Chittagong University of Engineering and Technology (CUET). 2025-03-20T00:00:00Z