Magnetite Molybdenum Disulphide Nanofluid of Grade Two: A Generalized Model with Caputo-Fabrizio Derivative

Heat and mass transfer analysis in magnetite molybdenum disulphide nanofluid of grade two is studied. MoS2 powder with each particle of nanosize is dissolved in engine oil chosen as base fluid. A generalized form of grade-two model is considered with fractional order derivatives of Caputo and Fabrizio. The fluid over vertically oscillating plate is subjected to isothermal temperate and species concentration. The problem is modeled in terms of partial differential equations with sufficient initial conditions and boundary conditions. Fractional form of Laplace transform is used and exact solutions in closed form are determined for velocity field, temperature and concentration distributions. These solutions are then plotted for embedded parameters and discussed. Results for the physical quantities of interest (skin friction coefficient, Nusselt number and Sherwood number) are computed in tables. Results obtained in this work are compared with some published results from the open literature

Unsteady newtonian and non-newtonian fluid flows in the circular tube in the presence of magnetic field using caputo-fabrizio derivative

This thesis investigates analytically the magnetohydrodynamics (MHD) transport of Newtonian and non-Newtonian fluids flows inside a circular channel. The flow was subjected to an external electric field for the Newtonian model and a uniform transverse magnetic field for all models. Pressure gradient or oscillating boundary condition was employed to drive the flow. In the first model Newtonian fluid flow without stenotic porous tube was considered and in the second model stenotic porous tube was taken into account. The third model is concerned with the temperature distribution and Nusselt number. The fourth model investigates the non-Newtonian second grade fluid velocity affected by the heat distribution and oscillating walls. Last model study the velocity, acceleration and flow rate of third grade non-Newtonian fluid flow in the porous tube. The non-linear governing equations were solved using the Caputo-Fabrizio time fractional order model without singular kernel. The analytical solutions were obtained using Laplace transform, finite Hankel transforms and Robotnov and Hartley’s functions. The velocity profiles obtained from various physiological parameters were graphically analyzed using Mathematica. Results were compared with those reported in the previous studies and good agreement were found. Fractional derivative and electric field are in direct relation whereas magnetic field and porosity are in inverse relation with respect to the velocity profile in Newtonian flow case. Meanwhile, fractional derivative and Womersely number are in direct relation whereas magnetic field, third grade parameter, frequency ratio and porosity are in inverse relation in third grade non-Newtonian flow case. In the case of second grade fluid, Prandtl number, fractional derivative and Grashof number are in direct relation whereas second grade parameter and magnetic field are in inverse relation. The fluid flow model can be regulated by applying a sufficiently strong magnetic field

Exact solutions on unsteady convective flow of viscous, casson, second grade and maxwell nanofluids

The heat and mass transfer flow of Newtonian and non-Newtonian nanofluids caused by convection has much practical significance, such as in industries, chemicals, cosmetics, pharmaceuticals and engineering. In this thesis, the unsteady convection flows of Newtonian, non-Newtonian and non-Newtonian hybrid nanofluids such as Casson hybrid, second grade and Maxwell nanofluids in a vertical channel or past a vertical plate will be studied. Carbon nanotubes (CNTs), graphene, cobalt, copper and alumina nanoparticles are used for the enhancement of heat transfer rate of fluids in this research work. Nanofluids have a range of applications in automobiles as coolants, microelectronics, microchips in computer, fuel cells and biomedicine. The problem of free and mixed convection flow of nanofluids is studied in a porous as well as non-porous media, with or without magnetohydrodynamics (MHD) influence. Other conditions like oscillating vertical plate, radiation effect and heat generation have been considered. The idea of Caputo time fractional derivative is used in some problems which is a novel topic nowadays. The advantage of fractional derivative is that the range of derivative increases in this case and the derivative of variable are used for a range of numbers. Appropriate non-dimensional variables are used to reduce the dimensional governing equations along with imposed initial and boundary conditions into dimensionless forms. The exact solutions for velocity, temperature and concentration are acquired via Laplace Transform technique and, in some places, regular perturbation technique along with inverse Laplace transform i.e. Zakian technique. The corresponding expressions for skin friction, Nusselt number and Sherwood’s number have been calculated. The outcomes acquired are plotted via computational software MathCAD-15 using the specific thermophysical properties of nanoparticles and base fluids. The graphical outcomes have been discussed to delineate the impact of various embedded parameters such as radiation parameter, Peclet number, Grashof number, fractional parameter and volume fraction of nanoparticles. Throughout the objectives, velocity of the nanofluid is found to be increasing with increasing thermal/solutal Grashof number, radiation parameter while decreasing with volume fraction of nanoparticles. Temperature profile increases with radiation parameter, heat generation and volume fraction. Thermal conductivity and Nusselt number of the nanofluids exhibit significant increment with increasing volume fraction

Symmetric mhd channel flow of nonlocal fractional model of btf containing hybrid nanoparticles

A nonlocal fractional model of Brinkman type fluid (BTF) containing a hybrid nanostructure was examined. The magnetohydrodynamic (MHD) flow of the hybrid nanofluid was studied using the fractional calculus approach. Hybridized silver (Ag) and Titanium dioxide (TiO2) nanoparticles were dissolved in base fluid water (H2O) to form a hybrid nanofluid. The MHD free convection flow of the nanofluid (Ag-TiO2-H2O) was considered in a microchannel (flow with a bounded domain). The BTF model was generalized using a nonlocal Caputo-Fabrizio fractional operator (CFFO) without a singular kernel of order α with effective thermophysical properties. The governing equations of the model were subjected to physical initial and boundary conditions. The exact solutions for the nonlocal fractional model without a singular kernel were developed via the fractional Laplace transform technique. The fractional solutions were reduced to local solutions by limiting α→1 . To understand the rheological behavior of the fluid, the obtained solutions were numerically computed and plotted on various graphs. Finally, the influence of pertinent parameters was physically studied. It was found that the solutions were general, reliable, realistic and fixable. For the fractional parameter, the velocity and temperature profiles showed a decreasing trend for a constant time. By setting the values of the fractional parameter, excellent agreement between the theoretical and experimental results could be attained

MHD effects on Casson fluid flow squeezing between parallel plates

We introduce this work by studying the non-Newtonian fluids, which have huge applications in different science fields. We decided to concentrate on taking the time-dependent Casson fluid, which is non-Newtonian, compressed between two flat plates. in fractional form and the magnetohydrodynamic and Darcian flow effects in consideration using the semi-analytical iterative method created by Temimi and Ansari, known as TAM, this method is carefully selected to be suitable for studying the Navier-Stokes model in the modified form to express the studied case mathematically. To simplify the partial differential equations of the system to the nonlinear ordinary differential equation of order four the similarity transformations suggested by Wang (1976) are used. The TAM approach demonstrates a high degree of accuracy, efficiency, and convergence when applied to the resolution of both linear and nonlinear problems, and the results in this article are used to study the effect of the related factors like squeeze number Sq, Casson parameterβ, magnetohydrodynamic parameter Mg and permeability constant Mp and examining the skin friction coefficient effect. The velocity profile is studied numerically, which is tabulated and graphically represented to show and confirm the theoretical study. We can conclude that the success of the proposed method in studying time-dependent Casson fluid, which is non-Newtonian, compressed between two flat plates provides opportunities for additional study and advancements in fluid mechanics using the techniques

Numerical approximations of fractional differential equations: a Chebyshev pseudo-spectral approach.

Doctoral Degree. University of KwaZulu-Natal, Pietermaritzburg.This study lies at the interface of fractional calculus and numerical methods. Recent studies suggest that fractional differential and integral operators are well suited to model physical phenomena with intrinsic memory retention and anomalous behaviour. The global property of fractional operators presents difficulties in fnding either closed-form solutions or accurate numerical solutions to fractional differential equations. In rare cases, when analytical solutions are available, they often exist only in terms of complex integrals and special functions, or as infinite series. Similarly, obtaining an accurate numerical solution to arbitrary order differential equation is often computationally demanding. Fractional operators are non-local, and so it is practicable that when approximating fractional operators, non-local methods should be preferred. One such non-local method is the spectral method. In this thesis, we solve problems that arise in the ow of non-Newtonian fluids modelled with fractional differential operators. The recurrent theme in this thesis is the development, testing and presentation of tractable, accurate and computationally efficient numerical schemes for various classes of fractional differential equations. The numerical schemes are built around the pseudo{spectral collocation method and shifted Chebyshev polynomials of the first kind. The literature shows that pseudo-spectral methods converge geometrically, are accurate and computationally efficient. The objective of this thesis is to show, among other results, that these features are true when the method is applied to a variety of fractional differential equations. A survey of the literature shows that many studies in which pseudo-spectral methods are used to numerically approximate the solutions of fractional differential equations often to do this by expanding the solution in terms of certain orthogonal polynomials and then simultaneously solving for the coefficients of expansion. In this study, however, the orthogonality condition of the Chebyshev polynomials of the first kind and the Chebyshev-Gauss-Lobatto quadrature are used to numerically find the coefficients of the series expansions. This approach is then applied to solve various fractional differential equations, which include, but are not limited to time{space fractional differential equations, two{sided fractional differential equations and distributed order differential equations. A theoretical framework is provided for the convergence of the numerical schemes of each of the aforementioned classes of fractional differential equations. The overall results, which include theoretical analysis and numerical simulations, demonstrate that the numerical method performs well in comparison to existing studies and is appropriate for any class of arbitrary order differential equations. The schemes are easy to implement and computationally efficient

Time-fractional Caputo derivative versus other integro-differential operators in generalized Fokker-Planck and generalized Langevin equations

Fractional diffusion and Fokker-Planck equations are widely used tools to describe anomalous diffusion in a large variety of complex systems. The equivalent formulations in terms of Caputo or Riemann-Liouville fractional derivatives can be derived as continuum limits of continuous time random walks and are associated with the Mittag-Leffler relaxation of Fourier modes, interpolating between a short-time stretched exponential and a long-time inverse power-law scaling. More recently, a number of other integro-differential operators have been proposed, including the Caputo-Fabrizio and Atangana-Baleanu forms. Moreover, the conformable derivative has been introduced. We here study the dynamics of the associated generalized Fokker-Planck equations from the perspective of the moments, the time averaged mean squared displacements, and the autocovariance functions. We also study generalized Langevin equations based on these generalized operators. The differences between the Fokker-Planck and Langevin equations with different integro-differential operators are discussed and compared with the dynamic behavior of established models of scaled Brownian motion and fractional Brownian motion. We demonstrate that the integro-differential operators with exponential and Mittag-Leffler kernels are not suitable to be introduced to Fokker-Planck and Langevin equations for the physically relevant diffusion scenarios discussed in our paper. The conformable and Caputo Langevin equations are unveiled to share similar properties with scaled and fractional Brownian motion, respectively.Comment: 26 pages, 7 figures, RevTe

Recent Trends in Coatings and Thin Film–Modeling and Application

Over the past four decades, there has been increased attention given to the research of fluid mechanics due to its wide application in industry and phycology. Major advances in the modeling of key topics such Newtonian and non-Newtonian fluids and thin film flows have been made and finally published in the Special Issue of coatings. This is an attempt to edit the Special Issue into a book. Although this book is not a formal textbook, it will definitely be useful for university teachers, research students, industrial researchers and in overcoming the difficulties occurring in the said topic, while dealing with the nonlinear governing equations. For such types of equations, it is often more difficult to find an analytical solution or even a numerical one. This book has successfully handled this challenging job with the latest techniques. In addition, the findings of the simulation are logically realistic and meet the standard of sufficient scientific value

Computational Fluid Dynamics 2020

This book presents a collection of works published in a recent Special Issue (SI) entitled “Computational Fluid Dynamics”. These works address the development and validation of existent numerical solvers for fluid flow problems and their related applications. They present complex nonlinear, non-Newtonian fluid flow problems that are (in some cases) coupled with heat transfer, phase change, nanofluidic, and magnetohydrodynamics (MHD) phenomena. The applications are wide and range from aerodynamic drag and pressure waves to geometrical blade modification on aerodynamics characteristics of high-pressure gas turbines, hydromagnetic flow arising in porous regions, optimal design of isothermal sloshing vessels to evaluation of (hybrid) nanofluid properties, their control using MHD, and their effect on different modes of heat transfer. Recent advances in numerical, theoretical, and experimental methodologies, as well as new physics, new methodological developments, and their limitations are presented within the current book. Among others, in the presented works, special attention is paid to validating and improving the accuracy of the presented methodologies. This book brings together a collection of inter/multidisciplinary works on many engineering applications in a coherent manner

Current Perspective on the Study of Liquid-Fluid Interfaces: From Fundamentals to Innovative Applications

Fluid interfaces are promising candidates for confining different types of materials - e.g., polymers, surfactants, colloids, and even small molecules - and for designing new functional materials with reduced dimensionality. The development of such materials requires a deepening of the Physico-chemical bases underlying the formation of layers at fluid interfaces, as well as on the characterization of their structures and properties. This is of particular importance because the constraints associated with the assembly of materials at the interface lead to the emergence of equilibrium and dynamics features in the interfacial systems, which are far from those conventionally found in the traditional materials. This Special Issue is devoted to studies on fundamental and applied aspects of fluid interfaces, trying to provide a comprehensive perspective on the current status of the research field