2021
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Item Impact of Dufour effect on MHD convective flow of fractionalized second grade fluid with Newtonian heating(UMT Lahore, 2021) Sehrish AyazThe main purpose of this dissertation is to study the unsteady double convection flow of a magnetohydrodynamics (MHD) differential type fluid in the presence of heat source, newtonian heating and dufour effect over an infinite vertical plate with fractional mass diffusion and thermal transports. The constitutive equations for the mass flux and thermal flux are modeled for non-integer order derivative caputo-fabrizio (CF) with non-singular kernel, respectively. The laplace transform, laplace inversion numerical algorithms and convolution theorem are used to derive the analytical and semi analytical solutions for the dimensionless concentration, temperature, and velocity fields as well as the skin friction and the rates of heat and mass transfer from plate to the fluid. Solutions for ordinary case and some known results from literature are recovered as limiting cases. Further, the influence of flow parameters and fractional parameters α and β on the concentration, temperature and velocity fields are tabularly and graphically underlined and discussed using mathematical software MATHCADE. Finally, a comparison between second grade and viscous fluids for non-integer and integer order is also depicted. It is observed that ordinary fluids have greater velocities than fractional fluids.Item Groundwater flow analytical and numerical solutions(UMT Lahore, 2021) Asima RehmanGroundwater flow models which can be used to determine the aquifer hydraulics of an artificially recharged aquifer of Windhoek in Namibia are investigated. The geology of this aquifer is very complex and heterogeneous, due to the presence of various and randomly distributed fractures and faults as well as the variations in the mineral composition of the water-bearing pure quartzite and micaceous quartzite. Water storage occurs within these rocks and fractures, causing the aquifer to be categorized as a double porosity type aquifer. The flow of the injected water within the Windhoek aquifer has been analyzed using the Forchheimer and Darcy’s law equations. In this study the flow was evaluated in one dimension. Therefore, to replicate the flow of water within a double porosity aquifer, various types of differential operators were applied to these flow equations. Consequently, two distinct models were developed. The first one is based on the classical differentiation as it does not consider the heterogeneity of the geological formations; hence the Laplace transform operator has been utilized to derive the exact solution to this effect. The second model is based on the nonlocal differential operator which has the ability to incorporate the effect of long-range dependency that is expressing memory effect into the mathematical formulation. Therefore, the approximate solution in this case has been derived using numerical methods such as the Adams-Bashforth and the Newton polynomial (Atangana-Seda) schemes. The classical numerical simulations depicted a normal flow when the fractional order was equal to 1; and this defines a flow within a homogeneous medium. Whereas, the model developed using fractional derivative depicted two flow scenarios namely the fast flow and the slow flow; observed when the fractional order was smaller and closer to 1 respectively. Thus, the fast flow has been attributed to the flow within the pure quartzite where the permeability and porosity are considered very high. Moreover, the slow flow has been attributed to the flow occurring in the micaceous quartzite; which has less permeability and low porosity due to less degree of fracturing and increasing mica content in the rock.Item Polynomial based topological indices of pent-heptagonal nanosheets(UMT Lahore, 2021) Hafiza Bushra MumtazThe combination of chemistry, mathematics and information science leads to a new subject called cheminformatics. It studies the quantitative structure–activity and quantitative structure–property relationships that are used to predict the biological activities and properties of chemical compounds. In this thesis we introduce different types of topological indices to study the chemical structures, including first Zagreb index, second Zagreb index, modified second Zagreb connection index, general Randic index, symmetric division index, harmonic index, inverse sum index and augmented index. We use these M-polynomial-based topological indices to study the pent-heptagonal nanosheets of VC₅C₇ and HC₅C₇, and examples are also presented to strengthen the main results of the thesis work.Item Fixed points of some generalized contractions of metric space(UMT Lahore, 2021) Sana RamzanThe purpose of this study is to obtain some fixed point theorems for more generalized multivalued contractions mappings on metric spaces. The metric preserving function is a real valued function. The function whose composition with metric gives another metric is known as metric preserving function in the literature. We study the conditions of metric preserving functions and related fixed point theorems for the sake of convenience. We extend the notion of local radial contraction to local radial h contraction mapping for metric preserving function, where h is a non expansive mapping.Item On the combinatorial properties of the graph associated to numerical semigroup <3,3n + 2>(UMT Lahore, 2021) Ammara MehmoodItem Solution Of Generalized Casson Fluid By HBIM And DIM(UMT Lahore, 2021) Muhammad Taqi JawadThe fractional Casson fluid model has been considered in this thesis in the context of the Goodman boundary conditions. A new approach for getting the solutions of the Casson fluid models has been proposed. There is the Double Integral Method and the Heat Balance Integral Method. These two methods constitute the integral balance method. In these methods, the exponent of the approximate solutions is an open main problem, but this issue is intuitively solved by using the matching method. The graphical representations of the solutions of the fractional Casson fluid model support the main results that have been presented. In our investigations, the Caputo derivative has been used.Item Transport phenomena of a casson fluid flow in microchannel(UMT Lahore, 2021) Sana AfzalIn this research work, we use a partial time derivative with an unequal core to investigate the typical bonding flow of Casson fluid flowing through a vertical microchannel at a constant wall temperature. The recently introduced fractional derivative, the Caputo-Fabrizio fractional derivative, is used to generalize the classical partial differential control flow equation. In this work, we use a Laplace transform to solve the problem and the Zakian method is used to obtain the inverse Laplace transform for the velocity and temperature distribution when the temperature of the channel walls is maintained at different constant temperatures. The effects on the flow fields of the radiation parameter and the number of Grashof are discussed through graphs. The effect of radiation is found to decrease the fluid velocity, whereas the effect of the number of Grashof is to increase the vertical channel fluid velocity. Parametric studies are carried out through graphs in which Grashof number, radiation, Prandtl number, and Casson fluid parameter on the velocity and temperature. The fractional Laplace transform technique is used to solve the set of partial differential equations that govern the flow.Item Anisotropic charged compact star core-envelope model(UMT Lahore, 2021) Ayesha KhalidThe main purpose of this research is to study core-envelope model for anisotropic charged sphere by using the Einstein’s Maxwell field equations for compact stars. The equation of state is polytropic for core and linear for envelope. The core, envelope and the Reissner Nordström exterior regions of stars match smoothly. This discussion shows non-singularity, continuity at the collaboration and physical parameters inside stars. The presence of charge electric field in star influence the mass, radius, compactification factor and there effects on gravity. The metric potentials and matter distribution are well behaved.Item M-polynomials and topological indices of cycloalkanes graphs(UMT Lahore, 2021) Ayesha RafiqIn this thesis, we study the M-polynomials of the cycloalkanes and use these polynomials tool to compute the certain degree-based topological indices such as first Zagreb, second Zagreb, second modified Zagreb, general Randic, reciprocal general Randic, symmetric division deg, harmonic, inverse sum and the augmented Zagreb.Item Research on digital image encryption algorithm based on a discrete-time generalized four-dimensional hyper-chaotic Hénon map(UMT Lahore, 2021) Hina NazVisual cryptography and digital image encryption are the backbone in secure internet communication, medical informatics, security locks, multimedia system, and secure sharing of information (military forces), etc. Each category has infolded wide uses for various purposes in our daily life. Security and privacy are the inescapable need of this digital era of technology. Security of personal and institutional secret data is achieved using cryptography. As we are living in the age of technology, internet surfing is the necessity of every basic activity of our life. Information security, data integrity, authenticity, and non-reputability are all taught to IoT users for their feasibility and secrecy. To live without technology is living without the basics of life in this digital era of technology. Modern terms of technology are prevailing everywhere as artificial intelligence covers all information data, but what is the surety to keep it safe and personal from any opponent, it specifies the importance of cryptography in our daily life. Using the characteristics of a chaotic or hyper-chaotic system such as processing ability, sensitivity, randomness, regularity, and unique secret key produces the bulwark and a confidential method of encryption. In this research, digital image encryption processes a method of modifying a digital image into cipher by using a discrete-time generalized hyper-chaotic Hénon map. This process shows excellent and effective encryption and increases the sensitivity in case of any cipher attack on cipher information.Item M-polynomials and degree based topological indices of pseudo-regular graphs(UMT Lahore, 2021) Kashif JavedIn my this work I have computed the topological indices like first Zagreb, second Zagreb, second modified Zagreb, general randic, and symmetry division degree (SDD), harmonic index (H), inverse sum index (IS), and augmented Zagreb index (AZI) of particular three types of Pseudo regular graph with the help of M-polynomialsItem A study on m-polar hesitant fuzzy soft set, classifications and application.(UMT Lahore, 2021) Sania AfzalIn this thesis, a soft hybrid structure of m-polar hesitant fuzzy soft set is introduced, which is a combination of m-polar hesitant fuzzy set and soft set. It allows us to deal with multi-polar data involving uncertainty. Based on the number of selection criteria chosen for application and the properties of the alternatives under consideration, two classifications of m-polar hesitant fuzzy soft set are introduced. A real-life multi-criteria decision-making (MCDM) problem restaurant selection is modelled by using the concept of m-polar hesitant fuzzy soft set in a hesitant fuzzy environment and solved by a well-known MCDM technique fuzzy TOPSIS. The ranking produced by the method is depicted graphically to clear understand the results. The proposed concept can be applied in multiple areas of science and technology.Item Secure communication using minimum and maximum Hamiltonian cycles.(UMT Lahore, 2021) Muhammad Zargam HamidIn this thesis, we will discuss the algorithms to compute minimum Hamiltonian cycle and maximum Hamiltonian cycle of a complete weighted undirected graph. Next, we will show how we can use both minimum and maximum Hamiltonian cycles for secure communication. We provide an unique cryptographic technique that may be implemented in any computer language, such as Microsoft.Net, Java and C++. This method encrypts data for transmission by employing an encoding table and graph theory properties such as complete graph and minimum (maximum) Hamiltonian cycles. This symmetric encryption approach employs the concept of shared keys, which must be predefined and shared by two parties. When the plain text message is large, the cipher text size increases in our suggested approach, showing that the proposed technique is more efficient when the plain text message is tiny. We will also provide the examples of encryption and decryption.Item Reverse topological properties of convex polytopes and their line graphs(UMT Lahore, 2021) Bushra IshaqIn this thesis, we will compute total reverse vertex degree index, first reverse Zagreb alpha index, first and second reverse Zagreb and hyper-Zagreb indices, reverse atom bond connectivity index, reverse geometric arithmetic index, sum connectivity reverse index, product connectivity reverse index, first and second reverse Zagreb polynomials and reverse hyper-Zagreb polynomials for convex polytopes Rn, Sn, Qn, Tn and Dn. We did same for line graph of these convex polytopes.Item Mixed convection flows of non-Newtonian fluid subject to Newtonian heating under the effect of fractional Fourier’s and Fick’s laws(UMT Lahore, 2021) Tanzila AslamThe purpose of this study is to obtain some fixed point theorems for more generalized multivalued contractions mappings on metric spaces. The metric preserving function is a real valued function. The function whose composition with metric gives another metric is known as metric preserving function in the literature. We study the conditions of metric preserving functions and related fixed point theorems for the sake of convenience. We extend the notion of local radial contraction to local radial h contraction mapping for metric preserving function, where h is a non expansive mapping.Item Radiative heat and mass transfer analysis in main stream velocity which oscillates without reversing(UMT Lahore, 2021) Khushbakht NaseerWithin recent work the phenomenon of mixed convective heat and mass exchange/transfer in free stream which oscillates without turning over the semi-endless vertical heated plate ( y = 0 , x ≥ 0) within the sight of thermal radiation is investigated.fluid under consideration is viscous, incompressible and optically dense grey. The temperature of the plate is uniform and greater than that of oncoming fluid. In this analysis the free stream velocity is of the form U (x, t) = Uo(x)V (ωt) = Uo(x)(1 + α1sinωt), where 0 ≤ α1 < 1 is the amplitude parameter, Uo(x) ∝ xn, and 0 ≤ n < 1. Three cases for n = 0 (level plate), n = 1 3 (wedge of semi-vertex angle 1 4 π) and n = 1 (stagna- tion point) are discussed. A gathering of transformations is introduced to decrease the boundary layer equations to advantageous form of the equations for integration . The solutions of the transformed model are obtained by employing the asymptotic expansions for the small and large values of the frequency parameter 1 = ωx Uo(x) . The effect of involved dimensionless parameters such as Richardson number, Mod- ified Richardson number, Prandtl number and Schmidt number is analyzed. Main aim of this study is to analyze the composite matching of inner and outer solutions to observe the behaviour of radiative heat and mass transfer in free stream which oscillates without reversing.Item Topological indices of chemical and metallic frameworks(UMT Lahore, 2021) DilawaizTopological index is a numerical coding of the molecular graphs that predict the physico-chemical, natural, toxicological, and primary properties of the synthetic mixtures that are straightforwardly connected with the molecular graphs. Kekulene is a donut-like formed polycyclic fragrant hydrocarbon comprising consistently showed benzene rings. Face-centered cubic lattice FCC(n) has gotten broad thought lately, inferable from its perceived properties and non-noxious nature, insignificant exertion, wealth, and essential creation measure. There are numerous topological files that have valuable properties to contemplate the molecular atoms. In this thesis, we examine different types of topological indices to study the chemical and metallic structure including first Zagreb connection index, second Zagreb connection index, forgotten index, redefined Zagreb index, general Randic index and symmetric division degree index. We explain the generalized Zagreb indices and Zagreb connection indices of the concealed non-kekulean benzenoid hydrocarbons and face-centered cubic lattice. In the end, the outcomes are registered with the help of mathematical quantities and their 3D plots.Item Role of Magnet, Thermal Radiation and Chemical Reaction on the Parabolic Unsteady Flow of Viscous Fluid in the Presence Of Power-Law, Exponential and Mittag-Leffler Kernels(UMT Lahore, 2021) Muhammad Mohsin ZiaIn this thesis, our purpose is to investigate the outcomes of thermal radiation and chemical reaction on the unsteady free convection flow, heat, and mass transfer properties in an electrically conducting parabolic and viscous incompressible fluid past an infinite vertical plate with variable temperature when there is a magnetic field present. The problem is ruled by coupled partial differential equations with or without singular kernels that use fractional derivative operators. To be compatible with physical processes, the fractional parameter’s value that characterizes the presence of fractional structures in the system must fall within a unit interval. The dimensionless equation of the problem has been obtained by the Laplace transform technique. By bringing the limit of the fractional parameter closer to unity, the classical cases can be retrieved. Moreover, we can use graphical diagrams to evaluate and compare the behavior of the model with various fractional operator descriptions. Furthermore, flow variables are addressed quantitatively using velocity field, temperature field, and concentration field graphs.Item On significance of bioconvection and chemical reaction for time dependent MHD flow of Williamson nanofluid due to extending permeable sheet(UMT Lahore, 2021) Muhammad ZahidEnhancement in heat transfer can be suitably managed with nanofluids movement due to time dependent stretched sheet. The concentration and settling of the nano-particles in the base fluid are addressed to consider non-Newtonian Williamson fluid and the bioconvection of microorganisms. In this scenario, the fluid flow occurs in the presence of normal and uniform magnetic field, thermal radiation and chemical reaction are taken into account. For the two dimensional flow with heat and mass transfer five dependent variables and three independent variables constitutes system of partial differential equations, where the coupling and non-linearity urges for the numerical solution. For this purpose, similarity functions are involved to transmute these equations to corresponding ordinary differential equations. Then Runge-Kutta method with shooting technique is hired to evaluate the desired findings with utilization of MATLAB script. The fluid velocity becomes slow against strength of magnetic parameter and it boosts with mixed convection. The temperature rises with parameter of Brownian motion and thermophoresis. The bioconvection Rayleigh number diminishes the velocity field. In the results, a satisfactory concurrence is observed when compared with existing literature.Item Influence of slip over an exponentially moving vertical plate with constant proportional Caputo-time fractional(UMT Lahore, 2021) Saqib Ali ShahIn this article, the influence of an MHD is analyzed on a viscous fluid accompanying double convection, due to the transfer included by temperature and focus gradients with the slip at the line. More, influences of chemical reaction and heat producers are also reaching into account. The idea of non-integer constant proportional Caputo time-fractional derivative is used for a common viscous fluid model comprising three PDEs of momentum, heat, and mass transfer provided initial and line restrictions. The Laplace Transform art and Stefest’s algorithm and Tzou’s algorithm are obtained to use the wanted results of velocity, temperature, and concentration. The effect of physical parameters and fluid is clear examined through computational MATHCAD software. The results obtained as special matters are also wonderfully accepted along with the broadcast outcomes from the literature. Finally, it has been looked that the mounting values of the slip a numerical quantity deduces the fluid velocity. This entitled the influence of slip at the line on the fluid flow.