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Influence of Thermally Radiative Stagnation Point Flow of Casson Nanofluid with Magnetic Field The primary goal of this thesis is to investigate the influence of thermally radiative stagnation point flow of Casson nanofluid with magnetic field. A mathematical model design for physical flow of fluid is in the form of partial differential equation and it Converts partial differential equations (PDEs) into ordinary differential equation (ODEs) by using suitable transformations and employing shooting method to obtain the possible numerical results. For computational work, MATLAB has been used. The graphs show how various parameters affect the non-dimensional velocity, temperature and concentration profiles. Tables also display and examine the numerical values of the Heat generation coefficient, Thermal Grashoff number, Concentration number, Schmidt number, Prandtl number, Eckert number, Nusselt number and Sherwood number.
Influence of Thermally Radiative Stagnation Point Flow of Casson Nanofluid with Magnetic Field The primary goal of this thesis is to investigate the influence of thermally radiative stagnation point flow of Casson nanofluid with magnetic field. A mathematical model design for physical flow of fluid is in the form of partial differential equation and it Converts partial differential equations (PDEs) into ordinary differential equation (ODEs) by using suitable transformations and employing shooting method to obtain the possible numerical results. For computational work, MATLAB has been used. The graphs show how various parameters affect the non-dimensional velocity, temperature and concentration profiles. Tables also display and examine the numerical values of the Heat generation coefficient, Thermal Grashoff number, Concentration number, Schmidt number, Prandtl number, Eckert number, Nusselt number and Sherwood number.
Influence of Thermally Radiative Stagnation Point Flow of Casson Nanofluid with Magnetic Field The primary goal of this thesis is to investigate the influence of thermally radiative stagnation point flow of Casson nanofluid with magnetic field. A mathematical model design for physical flow of fluid is in the form of partial differential equation and it Converts partial differential equations (PDEs) into ordinary differential equation (ODEs) by using suitable transformations and employing shooting method to obtain the possible numerical results. For computational work, MATLAB has been used. The graphs show how various parameters affect the non-dimensional velocity, temperature and concentration profiles. Tables also display and examine the numerical values of the Heat generation coefficient, Thermal Grashoff number, Concentration number, Schmidt number, Prandtl number, Eckert number, Nusselt number and Sherwood number.
Decision Analysis of General Linguistic Interval Valued Intuitionistic Fuzzy Soft Expert Sets The 2-Dimensional Linguistic Intuitionistic Fuzzy Variables (2-DLIFVs) add a subjective estimation of the trustworthiness of the evaluated results provided by experts, so 2-Dimensional Linguistic Intuitionistic Fuzzy Variables (2-DLIFVs) are very valuable instruments for describing uncertain or fuzzy information. This work extends the notion of 2-DLIVs by introducing General Linguistic Interval-Valued Intuitionistic Fuzzy Soft Expert Sets (GLIVIFSESs) in which the two terms are contained, the first term describes the subjective estimation of the objects under observation or discussions, second term describes the subjective evaluations of the reliability of the valuated results provided by experts. In this thesis we construct few operations on the structure (GLIVIFSESs) and then defines operational laws, scores, and accuracy functions for GLIVIFSESs. We illustrate some examples for the described operations. Further, we progress some arithmetical and geometrical aggregation operators for aggregating GLIVIFSE information and prove so many important properties related with them.
Characteristics of Chemically Reactive Casson Nanofluid Flow with Mixed Convection This detailed research of chemically reactive Casson nanofluid with mixed convection is being covered in this thesis. It examines how radiation affects magnetohydrodynamic Casson fluid flow on an exponentially stretchable sheet. The effects of frictional heating and viscous dissipation on heat transfer are taken into consideration. The governing partial differential equations are transformed into ordinary differential equations using proper similarity transformation. We obtained confluent hypergeometric solutions to the heat and mass transport equations as well as zero-order analytical solutions to the momentum equation. The accuracy of analytical solutions is confirmed by numerical results obtained using a shooting strategy and the bvp4c integration scheme. Momentum, heat, and pressure are affected by the radiation parameter, the magnetic parameter, the Gebhart, Grashof, Prandtl, Eckert, and Schmidt numbers.
Development of Ostrowski Type of Inequalities for Fractional Integral In this thesis, first of all various types of convex functions and fractional integrals, their applications and various related identities and well-known inequalities are discussed. Then a new identity for differentiable, GA-convex function is established. Using this identity, Ostrowski type inequalities for fractional integral are developed. Then, two versions of Ostrowski type inequality for GA-convex differentiable and bounded function for Hadamard fractional integral are developed. Consequently, Ostrowski type inequalities for GA-convex nth differentiable bounded function for Hadamard fractional integral version-I and version-II are generalized. Accordingly, some applications to special means, such as arithmetic-, geometric-, logarithmic and p-logarithmic means in subsequent sections are also provided. Further, Ostrowski type inequalities for first time differentiable and n-time differentiable GA-convex function via fractional integral are established using power mean inequality. At the end, some conclusions and recommendations for further research work are provided.
Investigation of Distinct Roots of Nonlinear Equations using Modified Root Finders In this research, derivative free and with memory iterative methods involving self-accelerating parameters have proposed for the solution of distinct roots of single variable non-linear equations. The technique of obtaining self-accelerating parameters is based on forth order iterative methods developed by Wang and Fan [16]. A very simple strategy has been used to construct two iterative methods using self-accelerating parameters which improve the convergence order from four to six. Numerical test examples show that the newly proposed methods are efficient, more accurate and robust in computation.
Characteristics of Melting Heat Transfer in Hybrid Nanofluid Flow with Joule Heating Hybrid nanofluids are accepted as more useful fluids than traditional nanofluids. There is no doubt that the hybrid nanofluids’ mixed properties of two or more nanoparticles respond to better thermal conductivity. The concept is beneficial for improving the properties of the advanced kind of nanofluids than those made out of a single nanoparticle. The present study examines the magnetohydrodynamic hybrid nanofluid flow near a stagnation point over a stretching sheet of variable thickness. The heat transfer phenomenon is analyzed in the presence of Joule heating, melting heat transfer, viscous dissipation and heat generation/absorption. The fluid model is presented in the form of partial differential equations and in order to convert these partial differential equations into ordinary differential equations, appropriate similarity transformations are used. Bvp4c method, a numerical technique is employed to solve the ordinary differential equations and through this method, the effects of influential parameters on velocity, skin friction coefficient, temperature and Nusselt number are examined. A graphical comparison of basefluid (Gasoline oil), nanofluid (SWCNTs, gasoline oil), and hybrid nanofluid (SWCNTs, Ag and gasoline oil) is also carried out which provides the evidence of hybrid nanofluids’ improved performance.
Impact of Mixed Convection on Williamson Nanofluid Flow over a Stretching Surface This research work deals with the mixed convection flow of a shear thinning nanofluid over a stretching surface. The surface is assumed to be porous and stretching exponentially. Two different cases of heat transfer, i.e., prescribed exponential surface temperature (PEST) and prescribed exponential heat flux (PEHF) are used for the analysis. Moreover, an inclined magnetic field is applied to the flow and the effects of chemical reaction, heat generation/absorption and viscous dissipation are considered. The boundary layer theory is applied to the fluid model and the resultant system of differential equations are presented and simplified with the help of useful similarity transformations. Homotopy analysis method is used to solve the governing nonlinear system using Mathematica Software. The velocity, temperature and concentration profiles are graphically analyzed under the influence of various flow parameters. From the results, it is found that increased values of local grashof number increases the velocity profile while the opposite behaviour is seen for the temperature profile. An enhanced temperature profile corresponds to enhanced Eckert number and the enhanced chemical reaction parameter reduces the concentration profile. The friction drag, Nusselt number and Sherwood number are studied for varying dimensionless parameters. A comparison with the existing literature is also performed.
An Innovative Neuroevolutionary Approach for Heart Beat Analysis with ANN The prominence of artificial neural networks (ANNs) is rising in a variety of applications. Most mathematical models have a form of differential equations (DEs), and recent research work has demonstrated that neural networks (NN) can be used to solve differential equations (DEs). In this thesis, we present a new neuroevolutionary approach called hybrid fractional particle swarm optimization (FO-PSO) to solve a differential equation (DE). Here we find an approximate solution to a 2nd order non-linear ordinary differential equation (ODE), known as the Van der Pol (VdP) heartbeat model (HBM), utilizing artificial neural networks (ANNs) with feed-forward (FF), and also examine the effectiveness of our technique and approach. Fractional order particle swarm optimization (FO-PSO) is a hybrid technique for the fractional order velocity of the particle swarm optimization algorithm. For this thesis, we considered two problems: One of the problems contains a forcing term, while the other does not. Each problem has two scenarios, and each scenario has four cases. These cases arise because of some variations in parameters. We make a comparison of our proposed hybrid FO-PSO–ASA technique’s results with the hybrid genetic algorithm with the interior point technique’s results. 100 independent runs have been performed. In terms of mean absolute deviation, root-mean-square error, and Nash–Sutcliffe efficiency, statistical analyses demonstrate its application, efficacy, and dependability.
Modification of Gruss Type Inequalities Via Conformable Fractional Integral In this thesis, Grüss type integral inequalities were established for conformable fractional integral given by Katugampola [11]. Grüss type integral provides the estimation of a function to its integral mean. It is useful in error estimations of the quadrature rules in numerical analysis. Grüss type integral inequality to weighted Ostrowski-Grüss type inequality are modified for differentiable mapping in terms of the upper and lower bounds of the first derivative via Katugampola conformable fractional integral. The inequality is then applied to numerical integration. Afterward, the application to numerical integration of modified Grüss type inequality to weighted Ostrowski-Grüss inequality via conformable fractional integral for fractional differentiable mapping is described.
Features of Slip Phenomenon in Double Stratified Fluid Flow with Viscous Dissipation The dissertation investigates the steady motion of an incompressible viscous fluid on a sheet caused by a stretching phenomenon under the influence of magnetic field. The porous medium effects are also retained in the analysis. Here, features of mass and heat transport are described in terms of viscous dissipation, joule heating and double stratification phenomena. The slip conditions (i.e. velocity, thermal and solutal) are accounted in the current analysis. The governing equations are made dimensionless by implementing suitable variables. The convergent solutions are acquired by utilizing a homotopic technique. Surface heat transfer rate and drag force are elaborated to corresponding few important parameters. As conclusion, it is depicted that dominant stratification phenomenon decays both temperature and concentration fields.
Numerical Investigation of Stagnation Point Flow of Non- Newtonian Fluid with Thermal Radiation The main objective of this dissertation is to focus on a numerical investigation of stagnation point flow of non- Newtonian fluid with thermal radiation. A mathematical model has been constructed for governs the physical flow condition. A similarity transformation set is used to transform the governing partial differential equations (PDEs) into non-linear ordinary differential equations (ODEs). With the help of the software MATLAB, the shooting technique was employed to produce numerical results. The influence of the governing parameters on the dimensionless velocity, temperature and concentration profile as well as the Biot numbers, Schmidt number and Prandtl number are analyzed. The influence of physical parameters such as Permeable parameter, Stagnation point, Magnetic parameter, Space dependent heat generation parameter, Eckert number, Prandtl number, Radiation parameter, Thermophoresis and Brownian motion parameter, Non-linear chemical reaction parameter, Grashof ratio parameter on the velocity profile, temperature distribution, concentration profile. Skin friction, Nusselt number and Sherwood number coefficient are presented in graphical and tabular forms.
Characteristics of Thermally Stratified Casson Fluid Flow with Convective Boundary Conditions This dissertation focuses on the stretching flow of Casson fluid through horizontal sheet. The study is carried out to analyze the characteristics of velocity slip and hydromagnetic phenomena. Features of heat are elaborated with viscous dissipation, thermal radiation and nonlinear stratification. Sheet surface is subjected to convective boundary condition. The governing educations are made dimensionless by implementing suitable variables. The problem is analyzed analytically via homotopic technique. The upshots of several pertinent parameters upon the dimensionless profiles of velocity and temperature are scrutinized. Results found that Biot number intensifies the temperature field.