Mathematics http://103.99.128.19:8080/xmlui/handle/123456789/5 2026-04-19T09:22:49Z 2026-04-19T09:22:49Z Acherjee, Simul http://103.99.128.19:8080/xmlui/handle/123456789/514 2025-09-23T05:26:08Z 2024-08-21T00:00:00Z

Title: The Effect of the Angle of Perforation on Inserts in a Pipe Flow for Heat Transfer Analysis Authors: Acherjee, Simul Abstract: A numerical simulation study of heat transfer analysis is considered with perforated inserts using a different angle of perforation in a circular pipe. In our simulation, we have used 0°, 5°, 10°, 15°, 16°, 17°, 20°, 30°, 40°, 50°, 60°, 65°, 68° and 70° angles of perforation respectively in a perforated axial insert considering the non-isothermal laminar flow. The inserts are used perpendicular to the fluid flow inside a pipe. A uniform heat-flux around the circular tube is assumed for our simulations. The temperature and pressure distribution are measured for a different angle of perforation. The relation between heat transfer rate and wall temperature is observed and found that the heat transfer rate increases inversely with the wall temperature. The effect of Nusselt number and friction factor are the diagnosis for all including angles and Reynolds numbers. The Thermal Performance Evaluation Criterion (PEC) is also analyzed in this study. Description: An M.Phil. Thesis from the Department of Mathematics.

2024-08-21T00:00:00Z Chowdhury, Md. Thowhidul Hoque http://103.99.128.19:8080/xmlui/handle/123456789/495 2025-09-14T10:47:22Z 2023-12-19T00:00:00Z

Title: Numerical Investigation of Single and Double Differential Cross-Section for the Ionization of Metastable 2S State Hydrogen Atom by Electron Impact Authors: Chowdhury, Md. Thowhidul Hoque Abstract: This thesis focuses on the ionization of hydrogen atoms by electrons in an asymmetric coplanar geometry, which plays a crucial role in atomic ionization problems. The Double Differential Cross Sections (DDCS) from the ionization of hydrogen atoms with different kinematic conditions offer valuable insights into various fields, including Applied Mathematics, Applied Physics, Atomic Physics, Astrophysics, Plasma Physics, and Fusion Technology. The present study uses a multiple scattering theory to examine the ionization of metastable 2S-state hydrogen atoms by non-relativistic intermediate and high-energy electrons. This theory has already proven to be successful in previous studies of DDCS results in the ground state and Triple Differential Cross Sections (TDCS) results for metastable 2S, 2P, 3P, 3S and 3D states of hydrogen atoms by electrons. We start our work by discussing the multiple scattering theory and other relevant theories related to the ionization of hydrogen atoms by electrons. The first Born DDCS for H(2S) ionization at incident energies of 150eV and 250eV are also investigated and the results show significant curve structures. The DDCS for the ionization of metastable 2S state hydrogen atoms by electrons, taking into account the direct T-matrix element and its exchange effects in coplanar asymmetric geometry, produces intriguing curve structures. The results of the simulation show good qualitative accord with theoretical and experimental data for the hydrogenic ground state. The physical origins of the curve shapes in the cross section results are explained clearly in the study. Further calculations using other familiar methods would also be of interest. Description: An M.Phil. Thesis from the Department of Mathematics

2023-12-19T00:00:00Z Rahman, Md. Obaidur http://103.99.128.19:8080/xmlui/handle/123456789/490 2025-09-14T10:45:08Z 2024-09-01T00:00:00Z

Title: PROPAGATION OF ION ACOUSTIC SOLITON AROUND THE CRITICAL VALUES OF ANY SPECIFIC PARAMETER IN UNMAGNETIZED COLLISIONLESS RELATIVISTIC PLASMAS Authors: Rahman, Md. Obaidur Abstract: The main purpose of the present work is to investigate how electrostatic plasma parameters modify the nonlinear ion acoustic soliton (IAS) propagation in unmagnetized collisionless plasma including higher order Lorentz relativistic expansion terms. The study of IASs in an unmagnetized collisionless relativistic plasma made of relativistic ion fluids, Cairns-distributed electrons and Cairns-distributed positrons. In one dimensional analysis, the reductive perturbation technique is employed to reduce the dynamics of the whole system to the Korteweg-de Vries equation (KdVE) involving various nonlinearity, whose nonlinear and dispersion coefficients are dependent on the related plasma parameters. This indicates that KdVEs have been derived incorporating quadratic, cubic, and quartic nonlinearities. However, as the coefficient of KdVE associated with quadratic nonlinearity approaches zero, the method encounters limitations. To overcome this challenge, adjustments are made to the stretching coordinates, resulting in a cubic nonlinearity KdVE that effectively describes soliton propagation near critical values in these plasma conditions. Additionally, a KdVE with quartic nonlinearity is derived to model super-critical values of specific plasma parameters in relativistic plasmas. Previous studies have primarily focused on relativistic effects on soliton propagation using Lorentz relativistic factor expansions up to three terms. In contrast, this thesis expands this consideration to more higher order Lorentz relativistic expansion terms to minimize truncation errors in modeling nonlinear soliton propagation within these plasmas. The investigation reveals that the relativistic streaming factor significantly alters the wave potential functions with the presence of more higher order Lorentz relativistic expansion terms. Notably, the derived KdVE shows that quadratic nonlinearity supports both compressive and rarefactive soliton propagation, whereas cubic and quartic nonlinearities exclusively support compressive solitons. Furthermore, this study explores how plasma parameters, incorporating more higher order Lorentz relativistic expansion terms, influence the amplitude and width of IASs in the unmagnetized relativistic plasma. It finds that higher order terms of the Lorentz relativistic factor noticeably modify the propagation characteristics of IASs vi within this specific plasma environment. The effect of plasma parameters on the amplitude and width of IASs has also been discussed with the physical interpretations. Description: An M.Phil. Thesis from the Department of Mathematics

2024-09-01T00:00:00Z Barua, Sagar http://103.99.128.19:8080/xmlui/handle/123456789/489 2025-09-14T10:44:39Z 2024-09-01T00:00:00Z

Title: NONLINEAR ACOUSTIC WAVE PHENOMENA IN MAGNETIZED COLLISIONLESS RELATIVISTIC PLASMAS Authors: Barua, Sagar Abstract: The thesis investigates the nonlinear propagation of ion-acoustic solitons (IASs) within a magnetized rotating relativistic plasma environment. This environment comprises relativistic ion fluids and electrons following (α,q)-distributions, alongside positrons. Employing the reductive perturbation technique, the study derives the Korteweg-de Vries equation (KdVE) with quadratic nonlinearity. However, when the coefficient associated with this nonlinearity approaches zero, the method encounters limitations. To address this challenge, adjustments are made to the stretching coordinates, leading to a KdVE with cubic nonlinearity, suitable for describing soliton propagation near critical values in these plasma conditions. Furthermore, a KdVE with quartic nonlinearity is derived, relevant for supercritical values of specific plasma parameters in relativistic plasmas. Prior research has predominantly explored relativistic effects on soliton propagation through expansions of Lorentz relativistic factors up to three terms. In contrast, this thesis extends the consideration to more than ten terms to minimize truncation errors in modeling nonlinear soliton propagation within these plasmas. The investigation reveals that the relativistic streaming factor significantly alters the wave potential functions. Notably, the derived KdVE equations indicate that quadratic nonlinearity supports both compressive and rarefactive soliton propagations, while cubic and quartic nonlinearities exclusively support compressive solitons in these plasma settings. The study further examines how plasma parameters, with the inclusion of the relativistic Lorentz factor up to eleven terms, influence the amplitude and width of IASs for the first time. It finds that higher-order terms of the relativistic Lorentz factor and obliqueness notably modify the propagation characteristics of IASs within this specific plasma environment. Description: An M.Phil. Thesis from the Department of Mathematics

2024-09-01T00:00:00Z