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Teleparallel Homothetic Vector Fields of Static Spherically Symmetric Space-Times in f(T) gravity. In general relativity, Einstein Field Equations (EFEs) are fundamental equations which are used to explain how geometry of a space-time is affected with the presence of massive objects. EFEs are the set of non-linear differential equations of second order that govern the behavior of metric tensor. Since the beginning of this theory, a wide range of physically interesting exact solutions to these equations have been discovered. Considering the non-linearity of EFEs, deriving their exact solutions poses a significant challenge. This task may be achieved by placing certain symmetry limitations on the metrics. The static spherically symmetric (SS) solutions to EFEs in f (T) (extended general relativity theory) gravity already exist in the literature. These solutions are further classified which arose 20 cases. In this thesis, we solved each case individually to see the existence of Teleparallel Homothetic Vector Fields (THVFs) of static spherically symmetric space-times in f (T) gravity. We find that no such case exists for which the space-times admit THVFs and for all the cases THVFs become TKVFs. To complete the study, the energy density and pressure of each model is computed. Additionally, the solutions are categorized based on energy conditions. Not to mention, the results of all the cases have been shown by designing certain tables. iii
Teleparallel Killing Vector Fields of Static Spherically Symmetric Space-Times in f(T) gravity. Symmetries principle play a crucial role in solving various problems,as they underpin conservation laws and fundamental interactions. The connection between conservation principle and symmetry in physics is both fundamentally important and highly useful. Curved space-time symmetries are produced by Killing vectors, also known as isometries. These symmetries aid in the classification and solution solving in connection with Einstein field equations (EFEs). As a result, symmetries are important for explaining space-time geometry. A fascinating theory that has gained traction in recent decades is teleparallel gravity (TG) in which torsion takes the place of curvature. It accomplishes by this replacing the Levi-Civita connection, which is built on curvature, with a teleparallel connection, which is based on torsion. This thesis provides a comprehensive analysis of Teleparallel Killing vector fields (TKVFs) of static spherically symmetric space-times within the framework of f (T) gravity, an extended theory of gravity based on torsion rather than curvature. Static spherically symmetric solutions to Einstein field equations in f (T) gravity have already been existed in the literature.The classification of those solutions via TKVFs have been done. In this study, 20 distinct solutions have been explored. Ten coupled partial differential equations were obtained for each solution. To determine the TKVFs these equations were solved using the direct integration technique. Teleparallel Killing vector fields were found in all those 20 cases. Every scenario is thoroughly examined to investigate the ways in which the changed gravity framework affects the presence and characteristics of teleparallel Killing vector fields. The study concludes with a thorough analysis of the findings that emphasizes the main distinctions from general relativity.
Analysis of Peristaltic MHD Ellis Fluid in a Porous Inclined Asymmetric Channel This thesis aims to investigate the effects of heat and mass transfer on the peristaltic flow and investigate the peristaltic transport of Ellis fluid in a porous inclined asymmetric channel. The study also considers slip conditions. The governing equations for Ellis fluid are introduced. Stream functions are taken into account to reduce the number of dependent variables in the governing PDEs. These equations are then solved using the perturbation method to provide temperature and velocity profiles. The impact of various parameters on temperature, pressure, velocity, and streamlines is examined. The graphs were generated using the Mathematica software.
Thermally Radiative and Magnetohydrodynamic Flow of Hybrid Nanofluid in the presence of Joule Heating. Hybrid nanofluids are an advanced group of nanofluids which offer extremely efficient heat transfer and fluid flow properties when two distinct nanoparticles are blended with a basefluid. Consequently, they prove to be of great significance when the industrial, technological and engineering sectors are concerned. These fluids are playing a role in revolutionizing industries by offering superior heat transfer and energy efficiency. Their potential applications continue to expand, making them a critical innovation in thermal management, and energy systems. This analysis focuses on the examination of the Darcy Forchheimer flow of three unique fluids, two nanofluids (𝑍𝑛𝑂/πΎπ‘’π‘Ÿπ‘œπ‘ π‘’π‘›π‘’ π‘œπ‘–π‘™ ) and (𝐴𝑙2𝑂3/πΎπ‘’π‘Ÿπ‘œπ‘ π‘›π‘’ π‘œπ‘–π‘™) and their resulting hybrid nanofluid (π‘π‘›π‘œ βˆ’ 𝐴𝑙2𝑂3/πΎπ‘’π‘Ÿπ‘œπ‘ π‘’π‘›π‘’ π‘œπ‘–π‘™). The fluids are flowing over a shrinking sheet placed in a porous medium. The effects of magnetohydrodynamics, thermal radiation, combined with Joule heating are also of importance in this study. The flow model, based on the partial differential equations, is reduced into a system of ordinary differential equations by employing sufficient similarity transformations. This model is further solved using the bvp4c tool in MATLAB software, which provides the numerical results along with graphical outcomes. Influence of various notable parameters on the velocity and temperature distribution have been investigated. It has been observed that the temperature profile increases for higher values of Eckert number, magnetic parameter, radiation parameter and Biot number respectively. The velocity profile declines when the porosity parameter, Forchheimer number, inclination angle and the nanoparticles concentration is enhanced. The critical parameters of Skin friction coefficient and Nusselt number have also been interpreted for different involved factors. The skin fraction coefficient amplifies for the velocity ratio parameter, magnetic and porosity parameter. On the other hand, Nusselt number reduces for the Eckert number, magnetic parameter as well as the radiation parameter.
Investigation of MHD Hybrid Nanofluid Flow over an Inclined Surface in a Porous Medium. This study analyzes the hybrid nanofluid flow, which is a mixture of copper (Cu) and aluminum oxide (Alβ‚‚O₃) nanoparticles suspended in water (Hβ‚‚O). The hybrid nanofluids are crucial for optimizing thermal management systems, such as heat exchangers, cooling devices, car engines, and electronics, where efficient heat transfer is a dominant feature. The considered fluid flows over an inclined surface within a porous medium. The impact of several physical phenomena on the heat transfer and flow characteristics of this nanofluid is examined. The fluid model involves mixed convection, where both forced and natural convection contribute to the heat transfer process. It also investigates the effects of magnetohydrodynamics, thermal radiation, Joule heating and non-uniform heat source/sink on the considered flow. To model this complex system, a set of partial differential equations (PDEs) is formulated. These PDEs are typically challenging to solve directly due to their complexity, so the similarity transformations are employed. These similarity transformations simplify the PDEs by reducing them to a set of ordinary differential equations (ODEs), making the problem more manageable and solvable. To solve the reduced system of ODEs, a MATLAB’s bvp4c function, is utilized to handle the boundary value problem. This function helps in obtaining numerical solutions for the velocity and temperature profiles of the fluid under the specified conditions. The results from this numerical analysis provide insights into the velocity distribution, temperature profile, skin friction coefficient, which quantifies the drag force exerted by the fluid on the surface, and the Nusselt number, which is a dimensionless measure of the convective heat transfer rate, The velocity profile experiences an upsurge for the rise in stretching parameter and inclination angle. The temperature of the hybrid nanofluid is improved by the Biot number, heat source/sink parameters and Eckert number.
Topological Classes of Stationary Axisymmetric Black Holes In recent years, the study of black holes has gained significant attention, particularly in the context of their topological properties. In this thesis, we investigate the topological numbers of Kiselev black holes, rotating Kiselev black holes, Kerr-Newman black holes, and Kerr-AdS black holes in the presence of a quintessential field. Our primary focus is to analyze whether the quintessential field influences the topological number of these black holes. We classify the black holes into three topological classes based on the topological: βˆ’1, 0, and 1. Through our analysis, we find that the presence of the quintessential field does not affect the topological number of these black holes. Additionally, in the case of Kerr-Ads black holes, we observe the presence of an annihilation point. To further investigate the impact of the quintessential field, we explore the effect of the state parameter Ο‰ within the interval βˆ’1 < Ο‰ < βˆ’1/3 by selecting different values. Our results indicate that while the curves exhibit slight deviations, the winding number and topological number remain unchanged. Similarly, we analyze the impact of varying the quintessential parameter c and find that it does not alter the topological number of black holes. These findings suggest that the quintessential field does not play a role in modifying the topological nature of black holes. Since topological numbers are crucial in understanding black hole thermodynamics, our study provides valuable insights into the stability and classification of black holes in the presence of exotic fields.
General Solutions for Magnetohydrodynamics Flow of a Viscoelastic Fluid through Porous Medium In this thesis, a theoretical investigation is undertaken for simple Couette flow and acceleration flow for non-Newtonian fluid. Exactly, we establish exact solution for the fully developed unsteady laminar flows of an incompressible hydromagnetic Maxwell fluid β„Ž lies between two parallel plates. One of the plate is stationary while the other plate moves with the velocity π‘ˆπ‘“(𝑑), where 𝑓(𝑑)=𝐻(𝑑) or 𝑓(𝑑)=𝐻(𝑑)π‘‘π‘Ž(π‘Ž>0). Also, the effect of porous medium is taken into account and the constant pressure is applied in the direction of the flow. The analytical solution for the velocity field, shear stress and the volume flux are obtained in simple form by means of finite Fourier sine transform. These solution, depending on the initial and boundary condations are presented as a sun of steady and transient solutions. Furthermore, the solutions for Newtonian fluid performing the same motion are also obtained for simple Couette flow and the accelerating flows are also obtained as limiting cases for our general solution. Finally, the effect of the material parameters on the velocity profile and shear stress are spotlighted by means of the graphical illustration.