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On a New Subclasses of Starlike Functions Associated with Symmetric Points This research aims to introduce and examine new subclasses of analytic functions within the open unit disc. I will use q-calculus to develop the q-extension of starlike functions related to symmetric points. Additionally, i will explore significant properties such as coefficient bounds for analytic functions,the Fekete-Szego inequality and the Zalcman functional. I will also investigate upper bounds on Hankel Determinants for functions within these new class. The findings will be demonstrated to advance beyond previous results obtained by many researchers in Geometric Function Theory. Special cases of these new results will be presented as corollaries.
On Certain New Subclass of Bi-Univalent Functions using Quasi Subordination and q-Derivative This research work aims to establish and determine the new subclasses of bi-univalent functions. The ideas of quantum calculus will be applied to examine the q-extensions of previously defined classes of bi-univalent functions. We investigate the bounds of initial coefficients of subclasses of q-bi univalent functions by employing quasi-subordination. Also, we analyze the upper bounds of the initial coefficients, Fekete-Szego inequality, and upper bound of second order Hankel determinant of a subclass of bi-starlike functions by employing the q-Salagean operator. It will be indicated that the newly defined results of this research are refined and advanced compared to previous results proved by various researchers in this field. Corollaries of new estimated results will also be shown in this thesis which shows the relation between previously derived and newly estimated results.
Hankel Determinant of Logarithmic coefficient for a new class of q-Starlike functions associated with Lune This thesis aims to introduce and characterize novel subclasses of univalent functions within the open unit disk. The utilization of q-calculus will be employed to establish the q-extension of starlike and convex functions of logrithmic coefficient for Starlike functions associated with lune. Additionally, we will investigate notable properties, including bounds on the coefficients of analytic functions, and the Fekete–Szeg˝o inequality. Furthermore, we will explore Second Hankel Determinants for functions belonging to these newly defined classes. It will be shown that newly obtained results are advanced as compare to the already derived results by numerous researchers in the field of Geometric Function Theory. The special cases of newly derived results will be presented in the form of corollaries.
STUDY OF DARCY FORCHHEIMER FLOW OF HYBRID NANOFLUID DUE TO A STRETCHING SHEET The hybrid nanofluids have shown to be more valuable for heat transfer in engineering applications, according to recent breakthroughs in the field due to their improved thermophysical properties. Hybrid nanofluids provide improved efficiency in applications like solar collectors, automotive engines, electronic devices, solar heating, cooling in buildings, drug reduction and refrigeration because of their better heat transfer properties. Hybrid nanofluids may reduce environmental impact and save energy by increasing the efficiency of thermal systems. The current study examines the flow of electrically conducting hybrid nanofluid in a Darcy Forchheimer porous medium. The hybrid nanofluid is flowing towards an exponentially stretching sheet and the flow is significantly influenced by the presence of thermal radiation, MHD, mixed convection and Joule heating. The consideration of the various effects and the governing equations lead to a set of partial differential equations. The partial differential equations are reduced into a set of ordinary differential equations with the help of the appropriate similarity transformations. These equations are solved using the bvp4c technique in MATLAB software. The study provides the influence of the various parameters such as nanoparticle volume fractions, suction/injection parameter, magnetic parameter, Forchheimer number, Eckert number, porosity parameter, mixed convection parameter and radiation parameter. The outcomes of the associated parameters for velocity, temperature profile, skin friction coefficient and Nusselt number are presented in graphical form. The mixed convection parameter enhances the velocity profile. The heat generation/absorption parameter, magnetic parameter, porosity parameter, Forchheimer number, radiation parameter and Eckert number increases the temperature profile. The results yields from the current study are useful for the use of hybrid nanofluids in engineering, technology and many other fields.
NUMERICAL STUDY OF ENTROPY GENERATION EFFECT IN Al2O3 / METHANOL NANOFLUID FLOW OVER A SWIRLING DISK This thesis presents a comprehensive numerical study for the effects of entropy generation on the flow of an Al2O3/Methanol nanofluid over a Swirling disk. The primary focus is to analyse the steady-state, incompressible flow characteristics and heat transfer dynamics of the nanofluid. The governing equations, which were originally expressed as partial differential equations (PDEs), are transformed into a set of nonlinear ordinary differential equations (ODEs) through similarity transformations. These transformed equations are then solved by using MATLAB’s bvp-4c solver. The results are presented through graphs and tables, providing insights into the influence of these parameters on entropy generation and thermal conductivity. This study contributes to the understanding of nanofluid behaviors in rotating systems, offering potential applications in engineering and industrial processes.
TOPOLOGY OF EQUATORIAL TIMELIKE CIRCULAR ORBITS AROUND KERR-LIKE BLACK HOLES A topological approach has been successfully used to study the properties of the light ring and null circular orbit in generic black hole spacetime. In this work, a detailed review of the general framework is extended to investigate the topology of equatorial timelike circular orbits (TCOs) around a generic asymmetric, stationary, asymptotically flat black hole spacetime. The topological analysis of the Kerr black hole and Kerr-like black holes in a perfect fluid dark matter (PFDM) background is conducted. It is found that the dynamics of test particles affected by the gravitational field of the black hole are examined using a unique topological framework developed for generic axisymmetric stationary, asymptotically flat black holes. Furthermore, when the angular momentum is held constant, there are two possibilities: 1) the absence of timelike circular orbits, or 2) the presence of TCOs occurring in pairs, with one stable and one unstable. Additionally, the stable and unstable timelike circular orbits have positive and negative winding numbers, respectively, and the radii of these circular orbits correspond to the zero points of the constructed n vector field. Similar results are observed for black holes in a PFDM background. However, for any fixed value of the particle parameter, the presence of PFDM increases the radius of TCOs.
RjNet: Convolutional Neural Network for Detecting Dust on Solar Panel Electricity production from fossil fuels causes increasing greenhouse gas emissions in the environment. This climate impact can be considerably reduced by utilizing power with renewable resources, particularly solar energy. Due to this, electricity production from photovoltaic (PV) systems has increased during the recent few decades. However, several factors, most notably the accumulation of dust on the panels, have resulted in a significant reduction in PV energy output. To detect dust and minimize power loss, many techniques are being researched, including thermal imaging, image processing, Internet of Things sensors, machine learning, and deep learning, highlighting various downsides, including high maintenance costs and inconsistent accuracy. In this study, we used a dataset from Kaggle and built another dataset of solar panels from Pakistan. We carefully incorporated a variety of lighting conditions to make the dataset more comprehensive, allowing the model to perform well in a variety of realworld scenarios. These two merged datasets were then tested using the current state-of-theart classification methods (SOTA). Afterward, a new convolutional neural network (CNN) architecture, RjNet, is presented exclusively for detecting dust on solar panels. The suggested RjNet model outperforms other SOTA algorithms, achieving 99.218% accuracy with only 2.14 million trainable parameters. Hence, future research should concentrate on diversifying the dataset for multi-class classification by including images from various global regions and climates, using automated data collection methods such as drones, and incorporating environmental factors while addressing class imbalances to improve model robustness.
Investigation of Unsteady Flow of Micropolar Fluid over an Exponentially Stretching Sheet This thesis presents the investigation of unsteady flow of micropolar fluid over an exponentially stretching sheet. A system of connected nonlinear partial differential equations is turned into nonlinear ordinary differential equations by employing similarity transformations. By using HAM technique, the series solution is obtained. A brief discussion, tabulation, and drawing of the physical parameters influencing the flow and heat transfer phenomena are provided. Temperature drops significantly because of unsteadiness, and fluid velocity reduces as the unsteadiness parameter increases. The velocity field is decreased when the micropolar parameter increases. On the other hand, as the micropolar parameter increases, the temperature rises.
INFLUENCE OF MIXED CONVECTION ON TERNARY HYBRID NANOFLUID FLOW IN THE PRESENCE OF MAGNETOHYDRODYNAMICS This study explores the behavior of fluid flow and heat transfer for a ternary hybrid nanofluid composed of three types of nanoparticles: aluminum oxide (𝐴𝑙2𝑂3), copper (𝐶𝑢), and titanium dioxide (𝑇𝑖𝑂2), suspended in a base fluid. The research focuses on understanding the flow dynamics near the stagnation point when the ternary hybrid nanofluid flows over a symmetrically stretching disk. Several critical factors are considered, such as the variable viscosity of the fluid, the effects of thermal stratification and viscous dissipation, and the influence of magnetohydrodynamics (MHD). These factors significantly affect the flow and heat transfer processes in complex ways. Additionally, the study incorporates the effect of uniform heat source, which, along with mixed convection, plays an essential role in altering the flow characteristics. Mixed convection, a combination of forced and natural convection, is crucial when analyzing fluid behavior in such scenarios as it provides a deeper understanding of how buoyancy and external forces interact with the fluid flow. To mathematically represent the fluid flow and heat transfer, the system is modeled through a set of partial differential equations (PDEs). These governing equations are then simplified using similarity transformations, which convert the complex partial differential equations into a system of nonlinear ordinary differential equations. By doing so, the mathematical complexity is reduced, making the problem more manageable for numerical analysis. The bvp4c approach, a powerful solver in MATLAB, is employed to solve the ODEs and gain insight into the flow and temperature distributions. This research thoroughly investigates how different factors, such as nanoparticle volume fraction, magnetic field, disk stretching intensity, variable viscosity, and the mixed convection intensity, affect the velocity and temperature profiles. The findings provide valuable insights into how these factors interact, contributing to a more comprehensive understanding of fluid flow in complex systems.
Crack Detection in Solar Panel Using B-Net Deep Learning Model Renewable energy is seen as an alternative to fossil fuel consumption to reduce environmental pollution. Solar energy is considered the most potential renewable energy source since it is economical and energy-efficient. Photovoltaic panels are susceptible to physical damage which can significantly decrease efficiency and lead to expensive repairs. Conventional methods are laborious and inclined to human error, emphasizing the need for automated systems. In this work, the B-Net model is developed to detect cracks in solar panels. It is based on a convolutional neural network architecture to enhance accuracy and effectiveness in identifying cracks under various lighting and weather conditions. An inclusive dataset containing cracked and non-cracked images of solar panels is employed to enable the B-Net model to learn differentiating features effectively. Findings indicate that the model attains high accuracy and precision in defect detection, better than traditional techniques. Moreover, the B-Net model’s performance metrics, such as accuracy, precision, recall, loss, and F1-score, are analyzed to determine its effectiveness. This work contributes to the maintenance of solar systems and prepares the path for further enhancement in automated assessment technologies through deep learning models. The implications of this work extend beyond photovoltaic panel maintenance, offering comprehensive applicability to other fields requiring image-based crack detection.