Three-dimensional Boundary Layer Flow Research Articles

Detuned secondary instabilities in three-dimensional boundary-layer flow

Detuned secondary instabilities in three-dimensional boundary-layer flow

MHD Darcy–Forchheimer flow and double-diffusive modeling of Maxwell fluid over rotating stretchable surface: A computational study

In this work, the Cattaneo–Christov double diffusion model is used to analyze the three-dimensional boundary layer flow of an upper-convected Maxwell fluid flowing over a bi-directional stretching surface. The model assumes that the fluid’s diffusivity is concentration-dependent, whereas dynamic viscosity and thermal conductivity are temperature-dependent; and the model takes into account the influence of the magnetic field of uniform strength. The problem is formulated using the conservation rules of mass, momentum, and energy as well as the boundary layer approximation. The resulting nonlinear system is then numerically solved using the bvp4c procedure in MATLAB. The obtained results are set forth graphically to illustrate the variations of different parameters. It is contemplated that the increase in thermal relaxation parameter results in a drop in fluid temperature while there is an enhancement in the concentration profile. Also, the temperature field has a direct relationship with the temperature-dependent viscosity. This research has proven its utility in industries where there is a need to analyze fluid flow over surfaces that can stretch in two directions.

Three-dimensional boundary layer flow and heat/mass transfer through stagnation point flow of hybrid nanofluid

This project covers the investigation of the boundary layer flow of a hybrid nanofluid past a biaxial stretching/shrinking sheet. The hybrid nanofluid consists of copper (Cu) and alumina (Al2O3\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${Al}_{2}{O}_{3}$$\\end{document}) nanoparticles, which are diluted into water to form Cu-Al2O3-\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$Cu-{Al}_{2}{O}_{3}-$$\\end{document} water hybrid nanofluid. The governing partial differential equations (PDEs) are derived from Navier-Stokes equations. The system of PDEs is reduced to a system of ordinary differential equations using an appropriate similarity transformation. MATLAB’s bvp4c function is used to numerically solve the resulting system of governing ordinary differential equations. The aim of this study is to gain a comprehensive understanding of the intricate behavior displayed by hybrid nanofluids on the stagnant directed flow of extended/shrunk flat surfaces, considering the effects of Brownian motion, thermophoresis, and various nanoparticles. The generated numerical results of flow profiles, skin friction coefficient, and Nusselt number have been presented graphically and discussed in the relevance of the governing parameters contributing to the flow. The outcomes reveal that the velocity components are reduced with increasing Al2O3-\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${Al}_{2}{O}_{3}-$$\\end{document} water nanofluid volume fraction. A monotonical increase in the parameters stretching/shrinking and suction/injection with a corresponding rise in both nanoparticles volume fraction propels heat gradient rate. An increase in the Schmidt numbers encourages a mass transfer field due to an enhanced boundary viscosity. The validation of numerical results is done with previously published results. Through our results, we have found that the performance of a hybrid nanofluid is more significant than other fluids. In addition, this study enhances the progress of theoretical comprehension by endeavoring to resolve the intricate interplay between fluid dynamics and thermal characteristics through the utilization of numerical approaches.

UTLIZATION OF GENERALIZED HEAT FLUX MODEL ON THERMAL TRANSPORT OF POWELL-EYRING MODEL VIA OHAM WITH HEAT GENEARTION ASPECTS

The focus of this work is on the flow of a spinning Powell-Eyring nanofluid in the boundary layer in three dimensions using magnetohydrodynamics (MHD). The research simulates mass transfer processes and heat transfer processes using non-Fick's mass flux theory and non-Fourier heat flux theory, respectively. Heat transport phenomena are analyzed by the integration of non-linear heat generation/absorption and thermal radiation properties. The boundary layer method is employed to solve a system of nonlinear partial differential equations (PDE) in the mathematical formulation. These equations are converted into nonlinear ordinary differential equations (ODES), and then the optimal OHAM with convergence control parameters is used to solve them. The impact of various physical movement circumstances on concentration and temperature profiles is visually represented through the generation of diagrams. This study provides important new understandings for both applied and scholarly research on complex heat transfer and fluid dynamics mechanisms in the context of three-dimensional MHD boundary layer flows of rotating Powell-Eyring nanofluids.

Structural aspects of the attached turbulent boundary layer flow over a hill

Three-dimensional turbulent boundary layers under strong pressure gradients and curvature are the rule in real-world flow applications but are typically not well predicted by turbulence models due to isotropic eddy viscosity or equilibrium assumptions. Validation-quality data in complex 3D flows is necessary for continued efforts to improve simulation accuracy. The Benchmark Validation Experiments for RANS/LES Investigations (BeVERLI) Hill bump model, designed specifically for validation experiments, was tested in the Virginia Tech Stability Wind Tunnel to collect validation experiment data on the three-dimensional (3D) boundary layer flow over a 3D hill. Laser Doppler velocimetry measurements on the bump model were used to study the mean flow and turbulence structure and evaluate the impact of pressure gradient and curvature upon the total shear stress in the boundary layer and evaluate the impact of pressure gradient and curvature upon the total shear stress behavior in the near-wall region. From analysis of the BeVERLI Hill flow, including the boundary layer just upstream of the hill, and comparison with the 3D flow around a wing-body junction of Ölçmen et al. (Exp Fluids 31:219–228, 2001), it is shown that none of the stations studied exhibit a constant shear stress region over any significant region of the boundary layer.Graphical abstract

Non-ideal gas behavior matters in hydrodynamic instability

Hydrodynamic instability, the foundation for flow’s laminar-turbulent transition and various predicting models, has been helping to understand the physics and shape the design of aerodynamic devices. While for hypersonic flow it is clear that thermodynamic/-chemical effects need be accounted for due to the high temperatures occurring, this letter unveils that also for low-speed flow at ambient temperatures non-ideal, i.e. real-gas effects can play a strong role—a feature missed by the classic theory for Newtonian fluids. By considering a three-dimensional low-speed boundary-layer flow in different thermodynamic regimes—subcritical, supercritical and transcritical—we show the importance of coupling thermodynamics by sensitivity studies of the perturbation growth rate to various inputs of the full stability equations. High sensitivities are found, and not only the transition-onset location but also the transition mechanism may be concerned.

Effect of Coriolis and buoyancy forces on three-dimensional flow of chemically reactive tangent hyperbolic fluid subject to variable viscosity

Thermophoresis effect has wide range of applications in electro-static precipitators and in biology for calculating single biological macro molecules, such as genomic-length DNA and HIV virus in the micro channels. Current study deal with effects of Coriolis and buoyancy forces on the three-dimensional boundary layer flow of tangent hyperbolic fluid with thermo-migration and haphazard motion of nano-sized particles. Arrhenius kind of chemical reaction is taken along an exponentially stretchable surface. The main focus of current exploration is to execute shear thinning nano-liquid flow past an exponentially rotating stretchable surface under the influence of variable viscosity, mixed convection and activation energy. We are motivated to explore the features of three-dimensional shear thinning model combined under the features of mixed convention, variable viscosity, and activation energy. The mathematical model is designed to generate PDEs and converted them into ODEs by employing fractious transformation. The numerical outcomes are exhibited via graphs by employing Bvp4c numerical technique whereas the values of skin friction coefficient are calculated by monopolizing shooting method. Characteristics of the parameters appearing in modeling like the viscosity parameter, power-law index, local Weissenberg number, mix convection parameter, rotation parameter, Prandtl number and chemical reaction parameter are comprehensively analyzed through graphical behavior. The impact of governing parameters on skin friction, heat and mass transfer rates is illustrated through tables. The detail analysis anticipates that the elevation in Weissenberg number and porosity caused decline in velocity. Further, the temperature behaves doppositely analogous to development Prandtl besides the thermophoresis parameter.

A computational study of three-dimensional laminar boundary layer flow and forced convective heat transfer in a porous medium

A computational study of three-dimensional laminar boundary layer flow and forced convective heat transfer in a porous medium

Instabilities in three-dimensional boundary-layer flows with a highly non-ideal fluid

The present work investigates the linear instability of three-dimensional boundary layers in thermodynamically non-ideal regimes. As a representative fluid, we consider carbon dioxide at supercritical pressure (80 bar). The flow set-up is matched to the redesigned DLR (German Aerospace Center) experiment on cross-flow instability, with identical pressure-coefficient distribution (accelerating the flow), sweep angle and Reynolds number, at a low Mach number. The flow temperature relative to the Widom line – also known as the pseudocritical line – thus characterises the non-ideality of the flow. We consider supercritical (gas-like), subcritical (liquid-like) and transcritical (pseudoboiling) regimes, where the flow temperature remains above, below or crosses the Widom line. The stability analyses of the parabolised Navier–Stokes baseflows indicate that wall heating destabilises the flow in the supercritical regime while wall cooling stabilises both effects similar to the ideal-fluid situation but being stronger. On the contrary, wall heating/cooling exhibits reversed effects in the subcritical regime, like for an ideal liquid. In the transcritical regime, with its sharp gradients of the thermodynamic and transport properties, wall heating stabilises the flow. Most substantially, however, wall cooling provokes a changeover of the leading instability mechanism: the accelerated streamwise flow attains inflectional wall-normal profiles, and the invoked inviscid Tollmien–Schlichting instability prevails with growth rates up to one order of magnitude larger than those of the cross-flow mode. We establish a two-fold mathematical relation from the momentum equation that explains the consequence of non-ideality and wall heating/cooling. The streamwise perturbation patterns of the flows in their linear instability regime are shown by mimicking wave trains emanating from virtual point-disturbance sources. From the viewpoint of keeping laminar flows, the transcritical thermodynamic state with a cooling wall must be avoided.

Trajectory and effectiveness of film cooling in endwall crossflow

The crossflow, one of the most important flow structures in the turbine endwall, has significant effects on the endwall film cooling. However, there is a lack of quantitative analysis on it due to the complexity of the endwall flow field. In the current study, a turning channel is utilized to generate the crossflow free from vortex structures. Experiments are conducted and numerical results are utilized to supplement flow-field details. Effects of the momentum ratio (I), crossflow intensity, and main-flow Reynolds number (ReD) are analyzed. Theories of three-dimensional boundary layer flow are introduced to help reveal underlying mechanisms. It is observed that coolant trajectories obey linearity in the cylindrical coordinate. Then, the deflection of coolant can be quantified using the straight-line slope, and I is demonstrated to well scale the coolant migration under the crossflow, which guides predictions on coolant trajectories. Reversely, the disturbance of cooling injections on the crossflow is non-negligible, mainly suppressing the crossflow development. Besides, the crossflow enhances the coolant spreading, and improves the cooling performance. ReD has non-negligible effects on the cooling performance by altering the crossflow profile in the boundary layer. Lower ReD leads to a distorted coolant spatial distribution, resulting in a severer main gas/coolant mixture.

MHD 3D flow of powell eyring fluid over a bidirectional non-linear stretching surface with temperature dependent conductivity and heat absorption/generation

The Present work addresses the MHD three-dimensional boundary layer flow of Powell Eyring fluid over a bidirectional non-linear stretching surface in the presence of thermal radiation and heat generation/absorption. We also considered the temperature dependent thermal conductivity. The governing flow partial differential equations are transmuted into ordinary differential equations with the help of suitable similarity transformations. The resultant non-linear coupled system is solved numerically by the shooting technique. This article presents the novel exploration of radiative heat transport of Powell Eyring fluid by considering temperature dependent conductivity over a bidirectional non- linear stretching sheet. The effects of various pertinent parameters on the present flow are presented graphically and explained in detail. We noticed that the velocity and temperature fields can be reduced by applying a strong magnetic field. The progress in Prandtl number condenses the temperature field but it improves the rate of heat transfer. Further, it is concluded that the large values of Powell Eyring fluid parameters enhance the skin friction.

Effect of heating on the stability of the three-dimensional boundary layer flow over a rotating disk

The effect of heating on the stability of the laminar three-dimensional boundary layer flow over a rotating disk was experimentally investigated. Local convective heat transfer coefficients were obtained at different running speeds and heating rates by means of an electrically heated disk apparatus placed in a large water tank. The accuracy of the method was assessed by comparison with predictions of the analytical self-similarity solution for laminar flow, and an excellent agreement was found. By means of local heat transfer measurements, the critical Reynolds number corresponding to the onset of vortices was determined as a function of the wall temperature difference and Prandtl number. A substantial increase of the critical Reynolds number with higher wall temperature difference was observed for the three-dimensional flow. The observed stabilizing effect due to heating of three-dimensional water flows was comparable with the predictions of perturbation analyses conducted for two-dimensional flows.

RETRACTED: Aqueous aluminium–copper hybrid nanofluid flow past a sinusoidal cylinder considering three-dimensional magnetic field and slip boundary condition

We analyzed the problem of the steady general three-dimensional magnetohydrodynamics stagnation-point boundary layer flow past an impermeable wavy circular cylinder considering aluminium–copper/water hybrid nanofluid as the working fluid and velocity slip as well as temperature jump boundary conditions. The induced magnetic field effect was also taken into account. The analytical procedure is based on the model that implements the nanoparticles and base fluid masses to formulate the equivalent volume fraction, equivalent density, and equivalent specific heat at constant pressure which is then substituted in the chosen single-phase thermophysical properties. Then, the foregoing relations were used in basic governing PDEs (partial differential equations), according to Tiwari–Das nanofluid scheme. It is worth mentioning that the bvp4c code from MATLAB software that is a famous finite-difference method has been exploited for solving the final similarity ODEs (ordinary differential equations). Results demonstrate that the developed mass-based model can be successfully employed with great confidence to study the flow and heat transfer of hybrid nanofluid in other similar problems. Moreover, it is proved that the nodal stagnation points possess higher values of skin friction coefficients and local Nusselt numbers relative to those for the saddle stagnation points. Besides, enhancing the second nanoparticle's mass leads to increase in all parameters of engineering interest including skin friction coefficients along x and y directions as well as local Nusselt number.

Heat transfer in generalized Carreau fluid flow near a radioactive heated rotating disk

A theoretical study is examined to investigate the effects of enthalpy and radioactive heat transfer in generalized Newtonian fluid flow due to an inclined rotating disk. In order to examine the shear thickening phenomenon, Carreau fluid model is utilized. Here for the first time, Carreau fluid model under the enthalpy, thermophoretic effect, binary mixture and solar radiation effects are examined near an inclined rotating disk. In this study, the fluid flow does not give an analytical solution of the Navier–Stokes equations, except for the limit case, that is for high Reynolds number. The flow inside three-dimensional boundary layer flow is determined by the von Kármán transformations. The boundary layer equations are converted into system of ordinary differential equations by using von Kármán inequalities and solved numerically by employing shooting method. The effects of shear thinning and shear thickening fluids show a increase behaviour for base flow profiles. Thermal conductivity and mass diffusivity increases the temperature and concentration distributions. The azimuthal velocities increases by increasing values of and parameters. We present the numerical solutions for different physical parameters and discussed them for radial and azimuthal velocities and for heat and mass transfer profiles through graphs and tables.

Numerical investigation of three-dimensional nanofluid flow with heat and mass transfer on a nonlinearly stretching sheet using the barycentric functions

Purpose The purpose of this paper is to investigate a three-dimensional boundary layer flow with considering heat and mass transfer on a nonlinearly stretching sheet by using a novel operational-matrix-based method. Design/methodology/approach The partial differential equations that governing the problem are converted into the system of nonlinear ordinary differential equations (ODEs) with considering suitable similarity transformations. A direct numerical method based on the operational matrices of integration and product for the linear barycentric rational basic functions is used to solve the nonlinear system of ODEs. Findings Graphical and tabular results are provided to illustrate the effect of various parameters involved in the problem on the velocity profiles, temperature distribution, nanoparticle volume fraction, Nusselt and Sherwood number and skin friction coefficient. Comparison between the obtained results, numerical results based on the Maple's dsolve (type = numeric) command and previous existing results affirms the efficiency and accuracy of the proposed method. Originality/value The motivation of the present study is to provide an effective computational method based on the operational matrices of the barycentric cardinal functions for solving the problem of three-dimensional nanofluid flow with heat and mass transfer. The convergence analysis of the presented scheme is discussed. The benefit of the proposed method (PM) is that, without using any collocation points, the governing equations are converted to the system of algebraic equations.

A new similarity solution with stability analysis for the three-dimensional boundary layer of hybrid nanofluids

Purpose The purpose of this study is to implement a new class of similarity transformation in analyzing the three-dimensional boundary layer flow of hybrid nanofluid. The Cu-Al2O3/water hybrid nanofluid is formulated using the single-phase nanofluid model with modified thermophysical properties. Design/methodology/approach The governing partial differential equations are reduced to the ordinary (similarity) differential equations using the proposed similarity transformation. The resulting equations are programmed in Matlab software through the bvp4c solver to obtain their solutions. The features of the reduced skin frictions and the velocity profiles for different values of the physical parameters are analyzed and discussed. Findings The non-uniqueness of the solutions is observed for certain physical parameters. The dual solutions are perceived for both permeable and impermeable cases and being the main agenda of the work. The execution of stability analysis proves that the first solution is undoubtedly stable than the second solution. An increase in the mass transpiration parameter leads to the uniqueness of the solution. Oppositely, as the injection parameter increase, the two solutions remain. However, no separation point is detected in this problem within the considered parameter values. The present results are decisive to the pair of alumina and copper only. Originality/value The present findings are original and can benefit other researchers particularly in the field of fluid dynamics. This study can provide a different insight of the transformation that is applicable to reduce the complexity of the boundary layer equations.

Numerical Study of Three-dimensional Boundary-layer Flow over a Wedge: Magnetic Field Analysis

The magnetohydrodynamic flow of a viscous fluid over a constant wedge in three- dimensional boundary-layer has been analyzed both numerically and asymptotically. The magnetic field is applied normal to the flow. The mainstream flows aligned with wedge surface are assumed to be proportional to the power of the coordinate distances. The system is described using three-dimensional MHD boundary-layer equations which are converted to couple nonlinear ordinary differential equations using similarity transformations. The resulting equations are solved numerically using the Keller-box method which is second-order accurate and asymptotically for far-field behavior. Both numerical and asymptotic solutions give good agreement in predicting the velocity behaviors and wall shear stresses. The effects of Hartmann number, pressure gradient and shear-to- strain-rate on the velocity fields are studied. Particularly, it is shown that the solutions of three-dimensional boundary-layer for variable pressure gradient exist, its effects are important on the boundary-layer flow. Results show that there are new families of solutions for some range of shear-to-strain-rate and there exists a threshold value of it beyond which no solutions exist. For some range of parameters, there is a reverse flow at which our boundary-layer assumptions are no longer valid. Various results for the velocity profiles, wall-shear stresses and displacement thicknesses are also obtained. The physical mechanisms behind these results are discussed.

Cattaneo–Christov heat flux model for three-dimensional flow of a viscoelastic fluid on an exponentially stretching surface

ABSTRACT In this article, we explore the three-dimensional boundary-layer flow over an exponentially stretching surface in two parallel ways. Constitutive equations of a second-grade fluid are used. Instead of classical Fourier’s law, Cattaneo–Christov heat flux model is employed for the formulation of the energy equation. This model can predict the effects of thermal relaxation time on the boundary layer. The resulting partial differential equations are reduced into ordinary differential equations by similarity transformations. Homotopy Analysis Method (HAM) is employed to solve the non-linear problem. Physical impact of emerging parameters on the momentum and thermal boundary-layer thickness are studied.

Three-dimensional mixed convection flow with variable thermal conductivity and frictional heating

In this article, three-dimensional mixed convection flow over an exponentially stretching sheet is investigated. Energy equation is modelled in the presence of viscous dissipation and variable thermal conductivity. Temperature of the sheet is varying exponentially and is chosen in a form that facilitates the similarity transformations to obtain self-similar equations. Resulting nonlinear ordinary differential equations are solved numerically employing the Runge–Kutta shooting method. In order to check the accuracy of the method, these equations are also solved using bvp4c built-in routine in Matlab. Both solutions are in excellent agreement. The effects of physical parameters on the dimensionless velocity field and temperature are demonstrated through various graphs. The novelty of this analysis is the self-similar solution of the three-dimensional boundary layer flow in the presence of mixed convection, viscous dissipation and variable thermal conductivity.

NUMERICAL SIMULATION OF THREE-DIMENSIONAL FLOW OF RADIATING GRAY NANOFLUID THROUGH POROUS MEDIUM SUBJECTED TO VIBRATIONAL ROTATIONS AND SLIP AT LIQUID-SHEET INTERFACE

We present a numerical scheme based on explicit finite difference approximation to handle the three-dimensional boundary layer flow of absorbing, emitting, and electrically conducting grey nanofluid over a flat surface. Nanofluid is designed by suspending iron-oxide nanoparticles (IONPs) in the base fluid. The flow field is assumed to be embedded in the porous medium, which executes vibrational rotations. To maintain the flow, velocity slip is introduced at the liquid-sheet interface. The governing equations are reduced to nondimensional form using dimensionless parameters and variables. The stability and convergence criteria have also been discussed to elaborate the validity of results. The hydromagnetic and convective heat transfer characteristics of magnetite nanofluid have been exhibited through graphs and tables for different related parameters. Substantial influences of oscillations and rotations have been noticed on the velocity profiles, temperature profiles, skin-friction coefficients, and Nusselt number.