Analysis of entropy generation and Joule heating on curvilinear flow of thermally radiative viscous fluid due to an oscillation of curved Riga surface

This paper investigates the phenomena of heat transfer and entropy generation on time-dependent electro-magnetohydrodynamic boundary layer flow of viscous fluid past a curved oscillatory stretchable Riga surface. Also, the impacts of thermal radiation and Joule heating are accounted for in the energy equation. To develop the flow model in mathematical form, curvilinear coordinates system is followed. The series solution of the governing nonlinear partial differential equations is attained with the help of the homotopy analysis method (HAM). The impacts of various involved parameters like dimensionless radius of curvature, modified magnetic parameter, the proportion of frequency of oscillation of the sheet to its stretchable rate parameter, magnetic parameter, Prandtl number, Eckert number, radiation parameter and Brinkman number on entropy generation, Bejan number, temperature and flow equations are comprehensively examined and results are displayed through graphs. Numerical variation in the magnitude of surface drag force and local Nusselt number under the influence of aforesaid parameters are presented through the tables. Entropy generation is enhanced with an enhancement in a radius of curvature and Brinkman number, while the Bejan number shows opposite behavior for both parameters. The amplitude of velocity distribution shows growing behavior with modified magnetic parameter.

The boundary integral equation for curved solid/liquid interfaces propagating into a binary liquid with convection

The boundary integral method is developed for unsteady solid/liquid interfaces propagating into undercooled binary liquids with convection. A single integrodifferential equation for the interface function is derived using the Green function technique. In the limiting cases, the obtained unsteady convective boundary integral equation (CBIE) transforms into a previously developed theory. This integral is simplified for the steady-state growth in arbitrary curvilinear coordinates when the solid/liquid interface is isothermal (isoconcentration). Finally, we evaluate the boundary integral for a binary melt with a forced flow and analyze how the melt undercooling depends on P\'eclet and Reynolds numbers.

A Computational Analysis for Active Flow and Pressure Control Using Moving Roller Peristalsis

Peristaltic motion arises in many physiological, medical, pharmaceutical and industrial processes. Control of the fluid volume rate and pressure is crucial for pumping applications, such as the infusion of intravenous liquid drugs, blood transportation, etc. In this study, a simulation of peristaltic flow is presented in which occlusion is imposed by pairs of circular rollers that squeeze a deformable channel connected to a reservoir with constant fluid pressure. Naturally, this kind of flow is laminar; hence, the computation occurred in this context. The effect of the number and speed of the pairs of rollers, as well as that of the intrapair roller gap, is investigated. Non-Newtonian fluids are considered, and the effect of the shear-thinning behavior degree is examined. The volumetric flow rate is found to increase with an increase in the number of rollers or in the relative occlusion. A reduction in the Bird–Carreau power index resulted in a small reduction in transport efficiency. The characteristic of the pumping was computed, i.e., the induced pressure as a function of the fluid volume rate. A strong positive correlation exists between relative occlusion and induced pressure. Shear-thinning behavior significantly decreases the developed pressure compared to Newtonian fluids. The immersed boundary method on curvilinear coordinates is adapted and validated for non-Newtonian fluids.

General Fractional Vector Calculus

A generalization of fractional vector calculus (FVC) as a self-consistent mathematical theory is proposed to take into account a general form of non-locality in kernels of fractional vector differential and integral operators. Self-consistency involves proving generalizations of all fundamental theorems of vector calculus for generalized kernels of operators. In the generalization of FVC from power-law nonlocality to the general form of nonlocality in space, we use the general fractional calculus (GFC) in the Luchko approach, which was published in 2021. This paper proposed the following: (I) Self-consistent definitions of general fractional differential vector operators: the regional and line general fractional gradients, the regional and surface general fractional curl operators, the general fractional divergence are proposed. (II) Self-consistent definitions of general fractional integral vector operators: the general fractional circulation, general fractional flux and general fractional volume integral are proposed. (III) The general fractional gradient, Green’s, Stokes’ and Gauss’s theorems as fundamental theorems of general fractional vector calculus are proved for simple and complex regions. The fundamental theorems (Gradient, Green, Stokes, Gauss theorems) of the proposed general FVC are proved for a wider class of domains, surfaces and curves. All these three parts allow us to state that we proposed a calculus, which is a general fractional vector calculus (General FVC). The difficulties and problems of defining general fractional integral and differential vector operators are discussed to the nonlocal case, caused by the violation of standard product rule (Leibniz rule), chain rule (rule of differentiation of function composition) and semigroup property. General FVC for orthogonal curvilinear coordinates, which includes general fractional vector operators for the spherical and cylindrical coordinates, is also proposed.

Fluid Dynamics in Curvilinear Coordinates without Fictitious Forces

The use of curvilinear coordinates is sometimes indicated by the inherent geometry of a fluid dynamics problem, but this introduces fictitious forces into the momentum equations that spoil the strict conservative form. If one is willing to work in three dimensions, these fictitious forces can be eliminated by solving for rectangular (Cartesian) momentum components on a curvilinear mesh. A thoroughly geometric approach to fluid dynamics on spacetime demonstrates this transparently, while also giving insight into a greater unity of the relativistic and nonrelativistic cases than is usually appreciated.

Design & Optimization of Large Cylindrical Radomes with Subcell and Non-Orthogonal FDTD Meshes Combined with Genetic Algorithms

The word radome is a contraction of radar and dome. The function of radomes is to protect antennas from atmospheric agents. Radomes are closed structures that protect the antennas from environmental factors such as wind, rain, ice, sand, and ultraviolet rays, among others. The radomes are passive structures that introduce return losses, and whose proper design would relax the requirement of complex front-end elements such as amplifiers. The radome consists mostly in a thin dielectric curved shape cover and sometimes needs to be tuned using metal inserts to cancel the capacitive performance of the dielectric. Radomes are in the near field region of the antennas and a full wave analysis of the antenna with the radome is the best approach to analyze its performance. A major numerical problem is the full wave modeling of a large radome-antenna-array system, as optimization of the radome parameters minimize return losses. In the present work, the finite difference time domain (FDTD) combined with a genetic algorithm is used to find the optimal radome for a large radome-antenna-array system. FDTD uses general curvilinear coordinates and sub-cell features as a thin dielectric slab approach and a thin wire approach. Both approximations are generally required if a problem of practical electrical size is to be solved using a manageable number of cells and time steps in FDTD inside a repetitive optimization loop. These approaches are used in the full wave analysis of a large array of crossed dipoles covered with a thin and cylindrical dielectric radome. The radome dielectric has a thickness of ~λ/10 at its central operating frequency. To reduce return loss a thin helical wire is introduced in the radome, whose diameter is ~0.0017λ and the spacing between each turn is ~0.3λ. The genetic algorithm was implemented to find the best parameters to minimize return losses. The inclusion of a helical wire reduces return losses by ~10 dB, however some minor changes of radiation pattern could distort the performance of the whole radome-array-antenna system. A further analysis shows that desired specifications of the system are preserved.

Tractography in Curvilinear Coordinates

Coordinate invariance of physical laws is central in physics, it grants us the freedom to express observations in coordinate systems that provide computational convenience. In the context of medical imaging there are numerous examples where departing from Cartesian to curvilinear coordinates leads to ease of visualization and simplicity, such as spherical coordinates in the brain's cortex, or universal ventricular coordinates in the heart. In this work we introduce tools that enhance the use of existing diffusion tractography approaches to utilize arbitrary coordinates. To test our method we perform simulations that gauge tractography performance by calculating the specificity and sensitivity of tracts generated from curvilinear coordinates in comparison with those generated from Cartesian coordinates, and we find that curvilinear coordinates generally show improved sensitivity and specificity compared to Cartesian. Also, as an application of our method, we show how harmonic coordinates can be used to enhance tractography for the hippocampus.

Combined Effects of Binary Chemical Reaction/Activation Energy on the Flow of Sisko Fluid over a Curved Surface

In this study, a modified Sisko fluid with Buongiorno model effects over a curved surface was considered. The MHD was applied normally to the flow direction, and the effects of chemical reacted and active energy at the curved surface is also discussed. We chose this pertinent non-Newtonian fluid model since it best represents blood composition, and thus helps us venture into complex blood flow problems. Since the flow is discharged over a curved shape, we therefore commissioned curvilinear coordinates to best portray our envisaged problem. We were also required to define various sundry parameters to make our mathematical equations easily solvable. Mathematical modelling was completed by considering traditional assumptions, including boundary layer approximation. Numerical simulation was conducted using MATLAB solver bvp4c. Several numerical tests were conducted to select the best blend of the linked parameters. We noticed thermal flux upsurged when the chemical reaction parameter was increased with the magnetic indicator parameter caused the flow to slow down, while an increasing amount of activation energy enhanced the concentration of the fluid. The numerical results and impacts of assorted parameters on different profiles are elaborated with the help of graphs and a table.

Modelling and numerical computation for flow of micropolar fluid towards an exponential curved surface: a Keller box method

The numerical analysis of MHD boundary layer non-Newtonian micropolar fluid due to an exponentially curved stretching sheet is developed in this study. In the energy equation effects of viscous dissipation are included. For the mathematical description of the governing equations curvilinear coordinates are used. By utilizing exponential similarity variables, the modelled partial differential equations (PDEs) are reduced into ordinary ones. The resultant non-linear ODEs are numerically solved with two methods shooting and Keller box method. The study reveals that the governing parameters, namely, radius of curvature, material parameter, magnetic parameter, Prandtl number and Eckert number have major effects on the fluid velocity, micro-rotation velocity, surface friction, couple stress and heat transfer rate. The results indicate that the magnetic field diminishes the fluid velocity inside the hydrodynamics boundary layer whereas it enhances the temperature inside the thermal boundary layer. Microrotation profile decreases near the surface, as the magnetic parameter and radius of curvature increases but far away behavior is opposite. The material parameter enhances the velocity and microrotation profile whereas, opposite behaviors is noticed for the temperature distribution. Obtained outcomes are also compared with the existing literature and the comparison shows a good agreement with existing studies.