Narrow Results

The diffusion process of the nanofibers in a nanofluid displays a combination of diffusion and wave characteristics. The wave-like behavior is attributed to the large aspect ratio of the nanofiber, which can be modeled as a bead-spring chain system, exhibiting wave-like properties. In order to describe this mixed diffusion-wave phenomenon, a fractional diffusion-wave equation is proposed, wherein multiple time fractional derivatives are employed. By appropriately regulating the fractional time terms, the model can be transformed into either the traditional diffusion equation or the traditional wave equation, as required. A numerical schedule is developed through the implementation of suitable time and space discretization, and a stability analysis is conducted. The numerical results substantiate the reliability of the numerical schedule and its applicability to other fractional differential equations.

The accurate synthesis of bespoke design requires complicated chemical reactions and high temperature conditions in modern nanomaterial coating techniques. These flow processes are quite complicated, involving not just viscous behavior but also mass and heat transport. Magnetic nanoparticles are utilized by nanocoatings, which are under manipulation by external magnetic fields. Mathematical models offer a low-cost window into the fundamental properties of these coating dynamics processes. This paper proposes a hybrid approach for induction effect in nanoparticle with magneto-convective nanofluid boundary layer. The hybrid technique that is being proposed involves the simultaneous application of Siberian Tiger Optimization (STO) and Multi-Fidelity Deep Neural Network (MFDNN). Hence, it is named as STO-MFDNN technique. The primary goal of this proposed method is to enhance nanoparticle solid volume fraction and minimize error during validation. The proposed technique — STO approach is utilized to optimize the process parameter and the MFDNN approach is utilized to accurately predict the nanoparticle behavior. By then, the MATLAB platform has the proposed approach implemented, and the present method is used to calculate the execution. The proposed technique displays superior outcomes in all existing systems like Wild Horse Optimizer (WHO), Fertile Field Algorithm (FFA) Seagull Optimization Algorithm (SOA). The existing technique displays the errors of 0.24%, 0.21%, 0.18% and the proposed technique displays an error of 0.15% concluding low error when compared to the existing approach.

In this work, a general formulation, which is based on steady boundary layer problems for the Boltzmann equation, of a half-space problem is considered. The number of conditions on the indata at the interface needed to obtain well-posedness is investigated. The solutions will converge exponentially fast “far away” from the interface. For linearized kinetic half-space problems similar to the one of evaporation and condensation in kinetic theory, slowly varying modes might occur near regime transitions where the number of conditions needed to obtain well-posedness changes (corresponding to transition between evaporation and condensation, or subsonic and supersonic evaporation/condensation), preventing uniform exponential speed of convergence. However, those modes might be eliminated by imposing extra conditions on the indata at the interface. Flow velocities at the far end for which regime transitions occur are presented for Boltzmann equations: for monatomic and polyatomic single species and mixtures; as well as bosons and fermions.

We study the applicability of the Lattice Boltzmann Method (LBM) to simulate the 2D laminar boundary layer induced by an oscillating flat plate. We also investigate the transition to the disturbed laminar regime that occurs with a rough oscillating plate. The simulations were performed in two cases: first with a fluid otherwise at rest and second in presence of superimposed current. The generation of coherent vortex structures and their evolution are commented. The accuracy of the method was checked by comparisons with the exact analytical solution of the Navier–Stokes equations for the so-called Stokes' Second Problem. The comparisons show that LBM reproduces this time varying flow with first order accuracy. In the case of the wavy-plate, the results show that a mechanism of vortex-jet formations, low speed-streak and shear instability sustain a systems of stationary vortices outside the boundary layer. The vortex-jet takes place at the end of the decelerating phase whereas the boundary layer turns out to be laminar when the plate accelerates. In the presence of the superimposed current, the vortex-jet mechanism is still effective but the vortices outside the boundary layer are only present during part of the oscillating period. During the remaining part, the flow turns out to be laminar although a wave perturbation in the velocity field is present.

The symmetry group of MHD boundary layer flow and heat transfer of a non-Newtonian power-law fluid over a stretching surface under the effects of variable fluid properties is investigated. The similarity equations with the corresponding boundary conditions are solved numerically by using a shooting method with the fourth order Runge–Kutta integration scheme. Comparisons of the numerical method with the existing results in the literature are made and obtained an excellent agreement. It is observed that the heat transfer rate diminishes with an increase in magnetic parameter and variable thermal conductivity parameter. Further, the opposite influence is found with an increase in variable viscosity parameter.

This work aims to numerically simulate the dynamics of a channel flow with an obstruction since the moment we inject a fluid with an homogeneous velocity profile. The simulations uses the open source tools of the OpenFOAM platform, the pisoFoam and the LES turbulence model, describing in detail the velocity profiles of laminar and turbulent flows. We also perform a boundary layer mapping in the presence of an obstacle. We used three different domains to follow the evolution of the velocity profile while the fluid progresses downstream and passes the obstruction. The results reproduce the well-known results of laminar flow in a channel, as well as the average velocity profile in the turbulent regime and the occurrence of attachments by the obstruction. These preliminary results are used to validate the solvers and the mesh used. Next, an analysis of the velocity profile dynamics resulted in determining an exponential decay of the root mean square deviations of the homogeneous to the parabolic, and to the turbulent regime in the channel.

The nanofluids are a recent challenging task in a nanotechnology field used in heat transfer enhancement for base fluids. The major purpose of this research is to examine the influences of Hall current on the non-Newtonian power-law nanofluid on an exponentially extending surface. Implementation in the Cattaneo–Christov heat flux and the free stream is performed to analyze the thermal relaxation features. Entropy generation evaluation and Bejan number during the convection flow are investigated. The Runge–Kutta–Fehlberg method is employed to resolve the transformed governing nonlinear equations. The impacts of the key physical factors on the profiles of primary and secondary velocities, temperature and entropy generation are discussed across the graphs. The local skin-friction coefficients, Nusselt and Sherwood numbers are demonstrated in a tabular form under the impacts of key physical parameters. Two different types of power-law indicators including pseudoplastic fluid $(n=0.7)$ and dilatant fluid $(n=1.2)$ are conducted. The results indicated that the flow speed decreases at dilatant fluid compared to pseudoplastic fluid due to higher viscosity. Increasing Hall current parameter powers the axial and secondary velocity profiles. Thermophoresis parameter powers the profiles of the temperature, nanoparticle volume fraction and local entropy generation. The dilatant fluid $(n=1.2)$ gives higher values of $C_{fx},C_{fz},{\mathrm{\text{Nu}}}_x$ and ${\mathrm{\text{Sh}}}_x$ compared to the pseudoplastic fluid $(n=0.7)$.

It is of great importance to reveal the refrigeration mechanism at low-temperature around 4 K in pulse tube for improvement of the cooling performance in 4 K pulse tube crycoolers (PTCs). In this paper, the thermo-physical process in 4 K pulse tube was studied analytically from microscopic viewpoint using CFD simulation. The thermodynamic cycles of different gas parcels throughout the pulse tube were investigated. It was found that the real gas characteristics of the helium at the pulse tube cold end manifest more apparently from the central part nearer to the wall outside the boundary layer. Furthermore, it was revealed that boundary layer has the weakened heat loss or helpful effect on refrigeration in phase-shifting 4 K pulse tube operating at low frequency. This research newly provides intensified understanding of the inherent characteristics of 4 K GM-type pulse tube.

The novelty of this paper is examining the impacts of Hall currents on Sisko nanofluid slip flow generated by an exponentially stretching sheet in the existence of entropy generation. Entropy generation assessment, Brownian, thermophoresis and Bejan numbers during convection flow are explored in the presence of the Hall effect. The pertinent parameters are Hall parameter m, a magnetic field parameter M, Brownian motion parameter $Nb$, thermophoresis parameter $Nt$, generalized thermal Biot number ${\gamma }_1$, generalized velocity slip parameter $\lambda$ and material parameter of Sisko fluid A. The changes in pertinent parameters on principal and secondary velocities, entropy generation and temperature are discussed. The coefficients of local skin friction, Brownian, thermophoresis and Nusselt/Sherwood numbers are expressed in a tabular structure. Two different kinds of power-law nanofluid, Pseudoplastic $(n=0.7)$ and dilatant fluid $(n=1.5)$ are considered. The current results exposed that growth in magnetic field parameter diminishes the nanofluid axial velocity and boosts the profiles of temperature, secondary nanofluid velocity and nanoparticle volume fraction. The coefficients of local skin friction are enhanced according to a growth in the magnetic field factor. The Pseudoplastic fluid supports the velocity, temperature and nanoparticle volume fraction profiles compared to the dilatant fluid. The local entropy generation number, Bejan number, local skin friction coefficients and local Nusselt/Sherwood numbers are influenced by the pertinent parameters.

This work investigates a non-Newtonian MHD Carreau nanofluid over a stretched vertical cylinder of an incompressible boundary layer with mobile microorganisms. The flow exists in permeable media and follows the modified Darcy’s law. An unchanged normal magnetic strength to the walls saturates the system. Ohmic dissipation, heat source, modified chemical reaction with activation energy properties, heat, volumetric nanoparticles fraction as well as microorganism profiles are covered. Thermal conductivity and mass diffusivity are taken as functions of heat and nanoparticle concentration, correspondingly. The fundamental governing system of nonlinear partial differential equations (PDEs) is converted into nonlinear ordinary differential equations (ODEs) by employing appropriate similarity transforms. The latter system is numerically analyzed through fourth-order Runge–Kutta (RK-4) simultaneously with the shooting process. The numerical outcomes showed that the curvature coefficient, magnetism and chemically activated energy perform a significant role in the velocity, heat, nanoparticle and chemical organism distributions. The impacts of several physical restrictions are tested and portrayed in a group of graphs. It is observed that the presence of microbes and nanoparticles, which are described in buoyancy terms, causes the flow to decay and slow down. By lowering the buoyancy and bio-convection characteristics, this infection can be prevented. With the development of all heat-related elements, heat transfer is enhanced, which is a significant feature associated with the current flow. These insights are important and useful in various physical and engineering fields.

The application of nanofluids has exploded in recent decades to improve the local number, mean Nusselt number, and rate of heat transfer. However, boundary layer equations of nanofluid across a flat plate with radiation have not been studied, and therefore this paper studies them mathematically for the first time. For water-based copper and aluminum oxide nanofluids, a similarity solution is presented in this study, and the subsequent system of the ordinary differential equation (ODE) is numerically solved by the Runge–Kutta method in MATLAB. Two different hydraulic boundary conditions are used in the simulations. In the first, the flow across a moving plate and the direction of the flow are analyzed, while in the second, the flow over a nonlinearly moving plate in a still fluid is investigated. The nanoparticle’s boundary layer thickness is found less than the thermal and hydraulics boundary layers. The local Nusselt number and friction factor of both the nanofluids are calculated and compared with the base fluid. The results demonstrate that the friction coefficient is high and the Nusselt number is low for nanoparticles with a high volume fraction. It also revealed that the friction factor for water–aluminum oxide is 16% greater than that for the water–CuO whereas the local Nusselt number for water–aluminum oxide is only 5% more than that for the water–CuO.

Nonparallel stability of the compressible boundary layers for three-dimensional configurations having large curvature variation on the surface is investigated by using the parabolic stability equations, which are derived from the Navier-Stokes equations in the curvilinear coordinate system. The difference schemes with fourth-order accuracy can be used in the entire computational regions. The global method is combined with the local method using a new iterative formula, thus more precise eigenvalues are obtained, and fast convergences are achieved. Computed curves of the amplification factor and shape functions of disturbances show clearly variable process of the flow stability, and agree well with other available results.

This study deals with the active control of T-S (Tollmien-Schlichting) wave in a two-dimensional boundary layer over a flat plate using a neural network and a flapping actuator. The flapping actuator consists of a thin aluminum plate and a piezoelectric element bonded together. Microphones were used as sensors to measure the pressure fluctuation in the boundary layer. A neural network was used to control the piezoelectric actuator based on the pressure signals from the sensors. The experimental results shows that the T-S wave in the boundary layer can be successfully suppressed even when its phase, amplitude and frequency change with time.

An experiment was performed to investigate the onset of turbulence in a flat plate boundary layer. The correlation dimension was calculated from the experimental data by means of chaos dynamics and the existence of the strange attractor was shown in the transitional processes. Therefore, the transitional processes to turbulence have been classified by not only the instability theory but also the nonlinear chaotic analysis. The relationship between the correlation dimension and the streamwise positions implies a natural connection between chaos dynamics and the onset of turbulence in a plate boundary layer, so transition is linked to the chaotic motion.

The energy gradient method is used to analyze the turbulent generation in the transition boundary layer flow. It is found that the maximum of the energy gradient function occurs at the wall for the Blasius boundary layer flow. At this location under a sufficiently high Reynolds number, even a low level of free-stream disturbance can cause the turbulent transition and sustain the flow to be in a state of turbulence. This is an excellent explanation of the physics of self-sustenance of wall turbulence. The mechanism of receptivity for boundary layer flow can also be understood from the energy gradient criterion. That is, the free-stream disturbance can propagate towards the wall by the "energy gradient" process to cause turbulent transition, and the transition point in boundary layer can be moved forward towards the leading edge when the level of external disturbance increases.

The flow field past the rotating blade of a horizontal axial wind turbine has been modeled with a full 3–D steady–RANS approach. Flow computations have been performed using the commercial finite–volume solver Fluent. The NREL phase VI wind turbine blade sections from the 3–D rotating geometry were chosen and the corresponding 2–D flow computations have been carried out for comparison with different angles of attack and in stalled conditions. The simulation results are analyzed. The main features of the boundary layer flow are described, for both the rotating blade and the corresponding 2–D profiles. Computed pressure distributions and aerodynamic coefficients show evidence of less lift losses after separation in the 3–D rotating case, mostly for the inward sections of the blade and the highest angles of attack, which is in agreement with the literature.

The flow of the laminar boundary layer on a flat plate is studied with the simulation of Navier–Stokes equations. The mechanisms of flow instability at external edge of the boundary layer and near the wall are analyzed using the energy gradient theory. The simulation results show that there is an overshoot on the velocity profile at the external edge of the boundary layer. At this overshoot, the energy gradient function is very large which results in instability according to the energy gradient theory. It is found that the transverse gradient of the total mechanical energy is responsible for the instability at the external edge of the boundary layer, which induces the entrainment of external flow into the boundary layer. Within the boundary layer, there is a maximum of the energy gradient function near the wall, which leads to intensive flow instability near the wall and contributes to the generation of turbulence.

Plasma-based flow control is one of the most promising techniques for aerodynamic problems, such as delaying the boundary layer transition. The boundary layer’s characteristics induced by AC-DBD plasma actuators and applied by the actuators to delay the boundary layer transition on airfoil at Ma = 0.3 were experimentally investigated. The PIV measurement was used to study the boundary layer’s characteristics induced by the plasma actuators. The measurement plane, which was parallel to the surface of the actuators and 1 mm above the surface, was involved in the test, including the perpendicular plane. The instantaneous results showed that the induced flow field consisted of many small size unsteady vortices which were eliminated by the time average. The subsequent oil-film interferometry skin friction measurement was conducted on a NASA SC(2)-0712 airfoil at Ma = 0.3. The coefficient of skin friction demonstrates that the plasma actuators successfully delay the boundary layer transition and the efficiency is better at higher driven voltage.

This note proposes a non-inertial similarity solution for the classic von Kármán swirling flow as perceived from the rotational frame. The solution is obtained by implementing non-inertial similarity parameters in the non-inertial boundary layer equations. This reduces the partial differential equations to a set of ordinary differential equations that is solved through an integration routine and shooting method.

We give the formulation of the boundary layer problem of triple deck type with a known displacement in von Mises variables. The condition associated with the displacement is transformed into a nonlocal condition. We introduce an appropriate method to prove the existence of a solution. It relies on a semi-discrete problem in which the pressure gradients are considered as a parameter. We prove the existence of a solution of the von Mises problem for Lipschitzian nondecreasing displacements. We can apply the inverse von Mises transform using an original expression of y and we prove that the functions u, v, p satisfy the system in physical variables except v(x, 0) = 0 because of a lack of regularity. We obtain all the asymptotic behaviors when y → +∞.