Incompressible Research Articles

A numerical investigation of the two-dimensional magnetohydrodynamic water-based hybrid nanofluid flow composed of Fe3O4 and Au nanoparticles over a heated surface

Abstract In this research article, the viscous, steady, and incompressible two-dimensional hybrid nanofluid flow composed of Fe3O4 and Au nanoparticles on an extending sheet has been presented. An inclined magnetic field impact is used for evaluating the impacts of various factors in that case. Furthermore, the influences of porosity, Brownian motion, thermophoresis, thermal and space-dependent heat sources, and thermal radiation factors are also used in this work. The numerical analysis is done by using the bvp4c technique. Validation of the present results confirms that the present analysis is valid. The outcomes show that the higher magnetic factor reduces velocity distribution while increasing the frictional force at the surface due to Lorentz forces which oppose the fluid flow. The friction force at the sheet’s surface is higher when the sheet stretches as compared to the case when the sheet shrinks. Increase in the magnetic factor increases the skin friction of sheet’s surface which consequently increases the rate of thermal transmission at the surface along with thermal distribution. The higher values of thermal radiation and thermal-dependent heat source increase the thermal transportation rate of sheet’s surface. Insights from this investigation can improve electronics cooling systems, vital for devices prone to overheating. Optimizing heat transfer with magnetohydrodynamic water-based hybrid nanofluids containing Fe3O4 and Au nanoparticles ensures efficient heat dissipation, enhancing device performance and longevity.

Optimal wall shapes and flows for steady planar convection

We compute steady planar incompressible flows and wall shapes that maximize the rate of heat transfer ( $Nu$ ) between hot and cold walls, for a given rate of viscous dissipation by the flow ( $Pe^2$ ), with no-slip boundary conditions at the walls. In the case of no flow, we show theoretically that the optimal walls are flat and horizontal, at the minimum separation distance. We use a decoupled approximation to show that flat walls remain optimal up to a critical non-zero flow magnitude. Beyond this value, our computed optimal flows and wall shapes converge to a set of forms that are invariant except for a $Pe^{-1/3}$ scaling of horizontal lengths. The corresponding rate of heat transfer $Nu \sim Pe^{2/3}$ . We show that these scalings result from flows at the interface between the diffusion-dominated and convection-dominated regimes. We also show that the separation distance of the walls remains at its minimum value at large $Pe$ .

Data-driven model for Lagrangian evolution of velocity gradients in incompressible turbulent flows

Velocity gradient tensor, $A_{ij}\equiv \partial u_i/\partial x_j$ , in a turbulence flow field is modelled by separating the treatment of intermittent magnitude ( $A = \sqrt {A_{ij}A_{ij}}$ ) from that of the more universal normalised velocity gradient tensor, $b_{ij} \equiv A_{ij}/A$ . The boundedness and compactness of the $b_{ij}$ -space along with its universal dynamics allow for the development of models that are reasonably insensitive to Reynolds number. The near-lognormality of the magnitude $A$ is then exploited to derive a model based on a modified Ornstein–Uhlenbeck process. These models are developed using data-driven strategies employing high-fidelity forced isotropic turbulence data sets. A posteriori model results agree well with direct numerical simulation data over a wide range of velocity-gradient features and Reynolds numbers.

NUMERICAL SIMULATION OF TURBULENT FLOW AROUND DARRIEUS AND SAVONIUS ROTORS

The study of unsteady processes during the flow around the rotors of vertical-axis wind turbines was carried out based on the Navier-Stokes equations. General definition of the coupled problem on vertical-axis wind turbines rotors aerodynamics and dynamics is formulated. The solution to the system of initial equations is obtained using an implicit finite-volume numerical algorithm based on the method of artificial compressibility and multi-block structured grids. A code for the calculation of vertical-axis wind turbines rotors aerodynamic and power characteristics is developed on the base of Reynolds averaged Navier-Stokes equations for incompressible fluids. Two types of Darrieus and Savonius rotors with different geometric parameters and number of blades were calculated. The influence of Reynolds numbers, tip-speed-ratios and solidity on the power characteristics of the rotors has been established.

On the Motion Past a Slip-Stick Sphere and a Shear Free Sphere in a Viscous Fluid

The theoretical development of the complex fluid flows such as more than one obstacle with different shapes have great interest for scientists to understand flow phenomena and verify the model or approximate solution. The complex physical properties due to a uniform streaming motion past two fixed spheres is investigated having one with shear stress and another being shear stress-free. This study concerns analytical technique of a steady incompressible viscous fluid past to two fixed spheres. The Gegenbaur function and associated Legendre polynomials is used to derive the solution that simplify the process of the theoretical calculations. The mathematical expression for the flow fields are obtained in terms of stream functions by Gegenbaur function and associated Legendre polynomials. The physical properties of interest such as the Stokes stream function, the stress and its drag are calculated. It is understandable that for the uniform streaming motion around a sphere with the stress and its drag are affected owing to the presence of another stress-free are analyzed. The present result can be considered as a generalized by making other established results as a corollary of this solution. This theoretical study helps to the numerical or computational work for the verification of their approximated results of interest.

Computational Analysis of the Dissipative Casson Fluid Flow Originating from a Slippery Sheet in Porous Media

This research paper examines the characteristics of a two-dimensional steady flow involving an incompressible viscous Casson fluid past an elastic surface that is both permeable and convectively heated, with the added feature of slip velocity. In contrast to Darcy’s Law, the current model incorporates the use of Forchheimer’s Law, which accounts for the non-linear resistance that becomes significant at higher flow velocities. The accomplishments of this study hold significant relevance, both in terms of theoretical advancements in mathematical modeling of Casson fluid flow with heat mass transfer in engineering systems, as well as in the context of practical engineering cooling applications. The study takes into account the collective influences of magnetic field, suction mechanism, convective heating, heat generation, viscous dissipation, and chemical reactions. The research incorporates the consideration of fluid properties that vary with respect to temperature or concentration, and solves the governing equations by employing similarity transformations and the shooting approach. The heat transfer process is significantly affected by the presence of heat generation and viscous dissipation. Furthermore, the study illustrates and presents the impact of various physical factors on the dimensionless temperature, velocity, and concentration. From an engineering perspective, the local Nusselt number, the skin friction, and local Sherwood number are also depicted and provided in graphical and tabular formats. In the domains of energy engineering and thermal management in particular, these results have practical relevance in improving our understanding of heat transmission in similar settings. Finally, the thorough comparison analysis reveals a significant level of alignment with the outcomes of the earlier investigations, thus validating the reliability and effectiveness of our obtained results.

High order asymptotic inequalities for some dissipative systems

We obtain some important fundamental inequalities concerning the long time behavior of high order derivatives for solutions of some dissipative systems in terms of their algebraic L2 decay. Some of these inequalities have not been observed in the literature even for the fundamental Navier–Stokes equations. To illustrate this new approach, we derive bounds for the asymmetric incompressible fluids equations, where improved inequalities were established for the micro-rotational field w. Finally, we show how this technique can be applied to other dissipative systems.

Numerical solutions for magneto-convective boundary layer slip flow from a nonlinear stretching sheet with wall transpiration and thermal radiation effects

A mathematical model is presented for magnetohydrodynamic viscous incompressible flow of an electrically conducting Newtonian polymeric fluid from a moving permeable horizontal stretching sheet with variable magnetic field, momentum and thermal slip boundary conditions. The emerging nonlinear ordinary differential boundary value problem is solved numerically by the Runge-Kutta-Fehlberg fourth-fifth order numerical method in Maple symbolic software. The effects of the governing parameters on the dimensionless stream function, dimensionless flow velocity and the dimensionless temperature have been investigated, displayed graphically and discussed. It is found that greater momentum slip and magnetic field parameters reduce the dimensionless velocity. It is further observed that higher values of Prandtl number, thermal slip, and conductionradiation parameter (weaker radiation contribution) reduce the dimensionless temperature whilst stronger magnetic field increases the temperature due to the supplementary work expended in dragging the polymer against the action of the magnetic field which is dissipated as heat. Comparisons of numerical results with previous published results show an excellent agreement. The study finds applications in electro-conductive polymer (ECP) processing systems.

A robust algorithm for computational floating body dynamics.

We present a non-iterative algorithm, FloatStepper, for coupling the motion of a rigid body and an incompressible fluid in computational fluid dynamics (CFD) simulations. The purpose of the algorithm is to remove the so-called added mass instability problem, which may arise when a light, floating body interacts with a heavy fluid. The idea underlying the presented coupling method is to precede every computational time step by a series of prescribed probe body motions in which the fluid response is determined, thus revealing the decomposition of the net force and torque into two components: (i) an added mass contribution proportional to the instantaneous body acceleration and (ii) all other forces and torques. The algorithm is implemented and released as an open-source extension module to the widely used CFD toolbox, OpenFOAM, as an alternative to the existing body motion solvers. The accuracy of the algorithm is investigated with several single-phase and two-phase flow benchmark cases. The benchmarks demonstrate excellent stability properties, allowing simulations even with massless bodies. They also highlight aspects of the implementation, such as the mesh motion method, where it can be improved to further enhance the flexibility and predictive capabilities of the code.

The principle of minimum pressure gradient: An alternative basis for physics-informed learning of incompressible fluid mechanics

Recent advances in the application of physics-informed learning in the field of fluid mechanics have been predominantly grounded in the Newtonian framework, primarily leveraging Navier–Stokes equations or one of their various derivatives to train a neural network. Here, we propose an alternative approach based on variational methods. The proposed approach uses the principle of minimum pressure gradient combined with the continuity constraint to train a neural network and predict the flow field in incompressible fluids. We describe the underlying principles of the proposed approach, then use a demonstrative example to illustrate its implementation, and show that it reduces the computational time per training epoch when compared to the conventional approach.

A hydrodynamic model of capillary flow in an axially symmetric tube with a non-slowly-varying cross section and a boundary slip

The capillary flow of a Newtonian and incompressible fluid in an axially symmetric horizontal tube with a non-slowly-varying cross section and a boundary slip is considered theoretically under the assumption that the Reynolds number is small enough for the Stokes approximation to be valid. Combining the Stokes equation with the hydrodynamic model assuming the Hagen–Poiseulle flow, a general formula for the capillary flow in a non-slowly-varying tube is derived. Using the newly derived formula, the capillary imbibition and the time evolution of meniscus in tubes with non-uniform cross sections such as a conical tube, a power-law-shaped diverging tube, and a power-law-shaped converging tube are reconsidered. The perturbation parameters and the corrections due to the non-slowly-varying effects are elucidated, and the new scaling formulas for the time evolution of the meniscus of these specific examples are derived. Our study could be useful for understanding various natural fluidic systems and for designing functional fluidic devices such as a diode and a switch.

Physics-constrained and flow-field-message-informed graph neural network for solving unsteady compressible flows

With the increasing use of deep neural networks as surrogate models for accelerating computational simulations in mechanics, the application of artificial intelligence in computational fluid dynamics has seen renewed interest in recent years. However, the application of deep neural networks for flow simulations has mainly concentrated on relatively simple cases of incompressible flows. The strongly discontinuous structures that appear in compressible flows dominated by convection, such as shock waves, introduce significant challenges when approximating the nonlinear solutions or governing equations. In this work, we propose a novel physics-constrained, flow-field-message-informed (FFMI) graph neural network for spatiotemporal flow simulations of compressible flows involving strong discontinuities. To enhance the nonlinear approximation capability of strong discontinuities, a shock detector method is leveraged to extract the local flow-field messages. These messages are embedded into the graph representation to resolve the discontinuous solutions accurately. A new FFMI sample-and-aggregate-based message-passing layer, which aggregates the edge-weighted attributes with node features on different hop layers, is then developed to diffuse and process the flow-field messages. Furthermore, an end-to-end paradigm is established within the encoder–decoder framework to transform the extracted information from the flow field into latent knowledge about the underlying fluid mechanics. Finally, a variety of one- and two-dimensional cases involving strong shock waves are considered to demonstrate the effectiveness and generalizability of the proposed FFMI graph neural network.

Quasi all-speed schemes for magnetohydrodynamic flows in a wide range of Mach numbers

We present novel numerical schemes for ideal magnetohydrodynamic (MHD) simulations aimed at enhancing stability against numerical shock instability and improving the accuracy of low-speed flows in multidimensions. Stringent benchmark tests confirm that our scheme is more robust against numerical shock instability and is more accurate for low-speed, nearly incompressible flows than conventional shock-capturing schemes. Our scheme is a promising tool for tackling MHD systems, including both high and low Mach number flows.

A canonical Hamiltonian formulation of the Navier–Stokes problem

This paper presents a novel Hamiltonian formulation of the isotropic Navier–Stokes problem based on a minimum-action principle derived from the principle of least squares. This formulation uses the velocities $u_{i}(x_{j},t)$ and pressure $p(x_{j},t)$ as the field quantities to be varied, along with canonically conjugate momenta deduced from the analysis. From these, a conserved Hamiltonian functional $H^{*}$ satisfying Hamilton's canonical equations is constructed, and the associated Hamilton–Jacobi equation is formulated for both compressible and incompressible flows. This Hamilton–Jacobi equation reduces the problem of finding four separate field quantities ( $u_{i}$ , $p$ ) to that of finding a single scalar functional in those fields – Hamilton's principal functional ${S}^{*}[u_{i},p,t]$ . Moreover, the transformation theory of Hamilton and Jacobi now provides a prescribed recipe for solving the Navier–Stokes problem: find ${S}^{*}$ . If an analytical expression for ${S}^{*}$ can be obtained, it will lead via canonical transformation to a new set of fields which are simply equal to their initial values, giving analytical expressions for the original velocity and pressure fields. Failing that, if one can only show that a complete solution to this Hamilton–Jacobi equation does or does not exist, that will also resolve the question of existence of solutions. The method employed here is not specific to the Navier–Stokes problem or even to classical mechanics, and can be applied to any traditionally non-Hamiltonian problem.

Integration of vorticity–velocity formulation in a lattice Boltzmann method for porous media

A lattice Boltzmann method (LBM) is proposed to address the two-dimensional macroscopic equations of velocity–vorticity for porous media in incompressible flows. The macroscopic equations of two-dimensional porous media using the representative element volume scale approach, employing various models, are shown. The momentum equations are transformed and presented in the velocity and vorticity format. Additionally, the energy and concentration equations are thoroughly examined. Subsequently, the LBM is presented to restore the dimensional macroscopic equations of the velocity–vorticity format for various porous models, accounting for external forces. The paper provides proof and derivations of the equations for the LBM, which are then demonstrated and discussed. The suggested approach is evaluated across a variety of well-established benchmark examples within the realm of fluid flow, heat, and mass transfer in porous media. Importantly, the LBM approach significantly reduces computational time compared to previous methods in the field by eliminating pressure in the momentum equation, thereby reducing the number of unknown variables and transforming the equation into a convection–diffusion form. This modification leads to a linear equilibrium distribution function and a noteworthy decrease in computational costs.

Computation of hydromagnetic tangent hyperbolic non-Newtonian flow from a rotating non-isothermal cone to a non-Darcy porous medium with thermal radiative flux

A theoretical and numerical study is conducted on nonlinear, steady-state thermal convection boundary layer flow of a magnetized incompressible Tangent Hyperbolic non-Newtonian fluid from a rotating cone to a non-Darcy porous medium. Power-law variation in temperature on the cone surface is considered and thermal radiation heat transfer is also present. The Brinkman-Darcy-Forchheimer model is deployed for the porous medium. The study is motivated by rotational (spin) coating with new emerging magnetic rheological polymers, a process which often utilizes filtration media and high temperatures. The transformed non-dimensional conservation equations are solved numerically subject to physically appropriate boundary conditions using a second-order accurate implicit finite-difference Keller Box technique. The numerical code is validated with previous studies. Extensive visualization of axial, tangential velocity components and temperature distributions with variation in key parameters including Rosseland radiative number, Darcy number, Forchheimer number (non-Darcy inertial parameter), magnetic interaction parameter, tangent-hyperbolic non-Newtonian power-law index and Weissenberg (non-Newtonian) number is included. Additionally, axial and tangential (circumferential) skin friction and Nusselt number values are tabulated for variation in key control parameters. With increasing Weissenberg number, axial velocity is depleted near the cone surface, tangential velocity is suppressed throughout the boundary layer regime and temperature is strongly enhanced. Axial flow is strongly decelerated further from the cone surface with increasing tangent-hyperbolic power-law index and there is also a significant depletion in tangential (swirl) velocity. Temperature is however boosted throughout the boundary layer transverse to the cone surface with a rise in tangent-hyperbolic power-law index. Both tangential and axial velocity are suppressed with increment in magnetic interaction parameter whereas temperature and thermal boundary layer thickness are enhanced. With larger Darcy number (i.e. greater permeability), axial velocity is strongly increased near the cone surface with no tangible modification further from the cone; However tangential velocity is consistently elevated throughout the boundary layer with greater Darcy number whereas temperature is depleted. An increase in Forchheimer number substantially damps both axial and tangential velocity whereas it elevates temperature. Increasing radiative flux strongly energizes the magnetic polymer and elevates temperature but suppresses the axial and tangential velocities. With elevation in non-isothermal wall exponent, axial skin friction is suppressed whereas Nusselt number are elevated at the cone vertex. Further along the cone surface a similar response is observed but there is also a reduction in magnitudes of tangential skin friction.

Numerical study on magnetic control of boundary layers in non-Newtonian flows over stretching cylinders using Keller box analysis

This article presents an analysis of the magnetic field’s effects on two-dimensional, two-directional, incompressible, and steady third-grade fluid flow over a stretched circular cylinder. A mathematical model describing the behavior of third-grade fluid in the cylindrical coordinate system is developed, accounting for nonlinear differential conditions. To simplify the analysis, appropriate transformations are applied to convert the fractional differential conditions into ordinary differential conditions. The resulting nonlinear differential framework is solved using the Keller Box method. The influences of several novel parameters on the velocity are depicted and examined. Furthermore, the expression for the skin-friction coefficient is computed and provided. The comparison of the obtained results with existing literature is made and found in good accordance. Through comprehensive numerical simulations and analytical derivations, this study contributes to the understanding of magnetic field control in boundary layers of third-grade fluid over stretching cylinders, with implications for a wide range of practical applications in engineering and fluid dynamics. The stronger influence of the magnetic field, indicating an increase in the Hartmann number, corresponds to suppression of thermal and solutal transport, thereby leading to a decrease in the temperature and concentration gradients. Conversely, the velocity profile exhibits an increase, indicating enhanced fluid motion under the influence of the magnetic field. This behavior is consistent with the magnetohydrodynamic effects, where the Lorentz force induced by the magnetic field alters the fluid flow, resulting in changes in the velocity distribution while impacting temperature and concentration gradients.

Study of pulse wave phenomena associated with blood flow model in human viscoelastic artery

Cardiac output monitoring has proven to be a promising hemodynamic management tool especially for critically ill patients. Pulse wave analysis is a noninvasive method used to quantify cardiac output continuously with respect to time. In this article, we have proposed a novel methodology to quantify the contribution of pulse waves to further study the role of arterial wall relaxation with respect to time. The relaxation time can further help in the diagnosis of disease. The pulse wave velocity component is derived by transforming governing fluid flow equations into hyperbolic equations for laminar incompressible blood flow in an artery of viscoelastic walls. The viscoelastic behavior of the wall is analogously modeled by the modified Zener model that has the capability to measure creep, stress relaxation, and hysteresis. The derived model equations are solved numerically by the multiderivative Runge–Kutta implicit–explicit time integration method with a weighted, essentially non-oscillatory, discretization scheme. The results are well validated with clinical trial-based Riemann problems for the case of elastic walls. It is observed that the proposed modified Zener model is well suitable to identify the location of arterial stiffness where the pulse wave manifests various types of phenomena like discontinuity and reflection.

Design of short Venturi flow meters for incompressible and isothermal flow applications

The Venturi flow meter offers a range of measurement options for liquids, gas, steam, and slurries in piped systems. The main criteria for assessing Venturi performance include permanent pressure loss, discharge coefficient, relative pressure loss coefficient, and measurement accuracy. However, the extended length of Venturis, relative to other flow rate measuring instruments, can present limitations in some applications. Furthermore, the manufacturing of shorter Venturis requires less material and energy. This study addresses the challenge by developing shorter Venturi meters that adhere to established performance standards. Previous studies show that cone angles, the ratio of throat diameter to inlet diameter (β-ratio), and the throat length impact the performance of a Venturi. The scope of this research considers single-phase, incompressible and isothermal flows. The investigation focuses on the effect of cone angles for flows with Reynolds numbers ranging from 5000 to 10,000,000. Two axisymmetric Venturis, with a β-ratio of 0.7, were designed and evaluated against an ISO-5167 classical Venturi with the same β-ratio. Despite the ISO-5167 Venturi outperforming the others across the key criteria, a Venturi designed with a 40-degree convergent cone angle and a 10-degree divergent cone angle was 24.9 % shorter than the classical design and demonstrated similar performance to the ISO-5167 Venturi across Reynolds numbers from 100,000 to 10,000,000.

Numerical Investigation of Three-Dimensional Incompressible Fluid Flow in Curved Elastic Tube

Numerical Investigation of Three-Dimensional Incompressible Fluid Flow in Curved Elastic Tube