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In this paper, the computational examination is carried out on the heat generation, Soret and Dufour’s influence on the unsteady MHD convection flow of an incompressible viscous fluid with chemical reaction. It is due to the exponentially accelerated vertical porous plate embedded in a permeable medium with ramped wall temperature together with surface concentration and also with thermal radiation impacts. The basic governing set of the equations of the fluid dynamics to the flow is converted into nondimensional form by inserting suitable nondimensional parameters and variables. In addition, the resultant equations are solved computationally with the efficient Crank–Nicolsons implicit finite difference methodology. The influences for several imperative substantial parameters for the model on the velocity, temperature and concentration for the fluids, the skin friction coefficient, Nusselt and Sherwood number for together thermal situations have been explored with the help of graphical profiles and tabular forms. It is found that, the increasing quantities of the Dufour, temperature generation and thermal radiation parameters, the fluid temperature as well as velocity enhances. Similarly, it is noted that an escalating Soret parameter causes the fluid’s velocity and concentration whereas the chemical reaction parameter notifies reversal outputs. [ABSTRACT FROM AUTHOR]

A few basic, intuitive, properties of the Navier–Stokes system of equations for incompressible fluid flows are discussed in this paper. We present a rephrased interpretation of the Navier–Stokes equation in a space having an arbitrary number of dimensions. We then derive spatially periodic solutions for the velocity and pressure fields that span an unbounded domain in three and four dimensions, given a smooth solenoidal initial velocity vector field. In these solutions all velocity components depend non-trivially on all coordinate directions. [ABSTRACT FROM AUTHOR]

Microscopic active droplets are able to swim autonomously in viscous flows. This puzzling feature stems from solute exchanges with the surrounding fluid via surface reactions or their spontaneous solubilization and from the interfacial flows resulting from these solutes' gradients. Contrary to asymmetric active colloids, these isotropic droplets swim spontaneously by exploiting the nonlinear coupling of solute transport with self-generated Marangoni flows; such coupling is also responsible for secondary transitions to more complex individual and collective dynamics. Thanks to their simple design and their sensitivity to physico-chemical signals, these droplets are fascinating to physicists, chemists, biologists, and fluid dynamicists alike in analyzing viscous self-propulsion and collective dynamics in active-matter systems, developing synthetic cellular models, or performing targeted biomedical or engineering applications. I review here the most recent and significant developments of this rapidly growing field, focusing on the mathematical and physical modeling of these intriguing droplets, together with their experimental design and characterization. [ABSTRACT FROM AUTHOR]

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A rotational version of the fluid-mechanical sewing machine (FMSM) is investigated experimentally. A thin thread of silicon oil was dispensed at a constant flow rate Q from a height H and fell on a table rotating at an angular speed ω , at a distance R from the axis. In all experimental runs, the values of Q and H were kept constant while the radius R was changed manually after each full rotation. Preliminary results show that the usual stitching patterns ensue as the local linear speed V = ω R approaches the critical transition speeds seen in the FMSM scenario but with subtle asymmetries introduced by rotational (centrifugal) effects. In some instances, arcs and loops of the traces were noticeably more pronounced when directed outward compared to those pointing toward the axis of rotation. Moreover, we observed stitching patterns not reported before. Overall, the symmetry-breaking features, while clearly visible, were rather subtle. Their morphological characteristics, such as differences in local curvature of traces relative to those in FMSM, are estimated to be below 10% in most cases. [ABSTRACT FROM AUTHOR]

The effects of roughness parameters, including height, diameter, and spacing of the cylindrical roughness elements, on turbulent transition are investigated in a three-dimensional boundary layer using direct numerical simulation. There are two types of transition process, classified as gradual and forced. The former is caused by a linear development of crossflow vortices and their secondary instability, while the latter is an immediate breakdown to turbulence behind the roughness without any crossflow vortex. These processes are only demarcated by the roughness height. The diameter and the spacing affect the initial creation processes of the crossflow vortex as well as the onset of the secondary instability in the gradual transition. With a fixed roughness volume, the greater height induces larger initial disturbances and causes earlier transition than a larger diameter. The aforementioned observations apply when the most unstable crossflow mode is induced. When the unstable mode is absent or is secondarily induced, the disturbance decays or the transition point shifts downstream. Therefore, when considering the critical parameter between the gradual and forced transitions, only the height is crucial. However, for a gradual transition, roughness parameters affect the transition point and we should consider the flow alternation caused by the roughness. [ABSTRACT FROM AUTHOR]

This paper presents a Lagrangian vortex method combined with iterative Brinkman penalization for the simulation of incompressible flow past a complex geometry. In the proposed algorithm, particle and penalization domains are separately introduced. The particle domain is for the computation of particle convection and diffusion, while the penalization domain is the enforcement of the wall boundary conditions. In iterative Brinkman penalization, the no-slip boundary condition is enforced by applying penalization force in multiple times within each time step. This enables large time step size reducing computational cost and maintains the capability in handling complex geometries. The method is validated for benchmark problems such as an impulsively started flow past a circular cylinder, normal to a flat plate, and a symmetric airfoil at Reynolds numbers ranging from 550 to 1000. The vorticity and streamline contours, drag, and lift coefficients show a good agreement with those reported in literature. [ABSTRACT FROM AUTHOR]

A rotational version of the fluid-mechanical sewing machine (FMSM) is investigated experimentally. A thin thread of silicon oil was dispensed at a constant flow rate Q from a height H and fell on a table rotating at an angular speed ω, at a distance R from the axis. In all experimental runs, the values of Q and H were kept constant while the radius R was changed manually after each full rotation. Preliminary results show that the usual stitching patterns ensue as the local linear speed V=ωR approaches the critical transition speeds seen in the FMSM scenario but with subtle asymmetries introduced by rotational (centrifugal) effects. In some instances, arcs and loops of the traces were noticeably more pronounced when directed outward compared to those pointing toward the axis of rotation. Moreover, we observed stitching patterns not reported before. Overall, the symmetry-breaking features, while clearly visible, were rather subtle. Their morphological characteristics, such as differences in local curvature of traces relative to those in FMSM, are estimated to be below 10% in most cases.

Resonant three-dimensional nonlinear sloshing in a square-base basin is analysed numerically to investigate swirling instability. The aim of this research is based on understanding how viscosity influences this instability. Four different fluids at increasing Reynolds number were considered in a tank forced to oscillate in a horizontal motion. The present study investigates the tight relation between the energy dissipation and this instability, showing that water tends to dissipate more energy during its rotating motion than the other three liquids characterised by higher viscosity. This aspect is strictly linked to the occurrence of free-surface fragmentation and liquid impacts. The numerical solutions are provided using an enhanced version of the Smoothed Particle Hydrodynamics (SPH) model called δ -LES-SPH model which proved to be suitable for the simulation of violent free-surface flows. [ABSTRACT FROM AUTHOR]

The Hagen-Poiseuille equation for gas flow had never been derived theoretically; it is rather a simple analogy of the same for liquid flow, and "gas viscosity" is a measure for overall resistance to flow. In this work, experimental flow data for different gases through capillaries and porous media, reported in literature by different groups, including those measured and treated by Knudsen are treated with Hagen-Poiseuille equation, but taking "gas viscosity" as an adjustable parameter. It is found that, at constant temperature, there exists an unambiguous relation between the viscosity (µ) of a given gas, and the product of average pressure (P av ) and capillary diameter (D). In addition, for P av * D < 0.01, a universal linear relation exists between µ/M 0.5 (where M is molecular mass) for different gases and the parameter P av * D. The new interpretation of gas viscosity avoids the differentiation of regimes into "Knudsen" and "viscous" flow as it is frequently done in literature. The concept can be applied to obtain a reliable data base for gas viscosities in different fields of applications, for example in microfluidic systems or the analysis of pore size distributions of filters and membranes by gas flow porometry., (© 2023 The Authors. Small published by Wiley-VCH GmbH.)

Within the framework of natural configurations developed by Rajagopal and Srinivasa, evolution within continuum thermodynamics is formulated as evolution of a natural configuration linked with the current configuration. On the other hand, withing the General Equation for Non-Equilibrium Reversible–Irreversible Coupling (GENERIC) framework, the evolution is split into Hamiltonian mechanics and (generalized) gradient dynamics. These seemingly radically different approaches have actually a lot in common and we show their compatibility on a wide range of models. Both frameworks are illustrated on isotropic and anisotropic rate-type fluid models. We propose an interpretation of the natural configurations within GENERIC and vice versa (when possible). • Equilibrium thermodynamics is considered to be a closed theory • Non-equilibrium thermodynamics, on the contrary, is not • In many frameworks an intensive research has been conducted separately • However, less attention is paid to their relation and general understanding • We compare the Natural Configuration framework and GENERIC on particular models [ABSTRACT FROM AUTHOR]