Unsteady Boundary Layer Research Articles

A computational study of Eyring‐Powell fluid model over a rotating cone with magnetic field and joule heating effect

AbstractIn this research, we investigate mixed convection transport of mass and heat transfer in the unsteady boundary layer flow of the Eyring‐Powell fluid around a rotating cone in the presence of Brownian and thermophoresis effects. Rotating cones are widely used in conical diffusers, medical devices, Aerospace Engineering and a variety of rheometric and viscosimetry applications. Specifically, we focus on the flow of the Eyring‐Powell fluid around the cone in the presence of magnetohydrodynamics and nanofluid. The modeled momentum, energy, and concentration equations of the problem are transformed into nonlinear dimensionless, nonlinear ordinary equations by utilizing the similarity variables. These nonlinear coupled ordinary differential equations are solved numerically via Bvp4c, and the outcomes for important physical parameters on momentum, energy, and concentration equations are presented graphically. The computational outcomes of physical parameters for skin friction coefficient, local Nusselt number, and Sherwood are also presented in tabular form.

Numerical investigation of an axisymmetric, dissipative, and unstable micropolar fluid flow over a stretched Riga plate incorporating mixed convection and chemical reaction

AbstractThe demand to improve the thermal performance of industrial working fluids and materials for better quality in engineering and household devices has spurred numerous studies on non‐Newtonian viscous fluids under various conditions. Researchers have explored different structures and geometries to understand and enhance the thermal propagation of fluid particles. As such, this research aims to investigate the effects of two‐dimensional unsteady boundary layer flow phenomena of a dissipative micropolar fluid over a radially stretching Riga plate when first‐order slip, thermal and solutal boundary conditions, mixed convection, and thermal radiation are all considered. Ordinary differential equations are the governing equations resulting from converting partial differential equations. The boundary layer conditions are altered and numerically solved using the Runge–Kutta fourth‐order shooting approach. Graphs and tables are used to visually analyze the physical attributes of temperature, concentration, velocity distributions, skin friction, Nusselt number, and Sherwood in relation to various factors. The results reveal significant insights into the impact of mixed convection and chemical reactions on the flow characteristics and dimensions. These findings have important implications for various engineering applications, particularly in enhancing industrial systems' heat and mass transfer processes, providing practical knowledge for improving thermal performance in real‐world applications.

Heat and mass transfer effects on an unsteady MHD boundary layer flow of fractionalized fluid

This research investigates the transient magnetohydrodynamic (MHD) flow of a non-integer Maxwell fluid over a vertical plate, taking into account the effect of diffusion-thermo and parameter of heat absorption. The fractional derivative Caputo-Fabrizio is employed to model the problem. Using the Laplace integral transform technique, we solve the dimensionless governing equations to obtain the profiles of velocity, concentration, and temperature, which are then presented in graphical form for easy comparison and interpretation. The influence of several parameters—specifically, the fractional parameter and heat absorption is thoroughly analyzed and illustrated through a series of graphical representations. Furthermore, a comparison between traditional as well as fractionalized velocity fields is provided. The results show that chemical reactions and magnetic fields reduce the velocity profile, while diffusion-thermo and mass Grashof number increase the fluid velocity.

Unsteady aerodynamic flow control at low Reynolds numbers via internal acoustic excitation

Aerodynamic flow control using internal acoustic excitation holds promise as it combines the simplicity of passive flow control techniques (in terms of added weight and operational complexity) with the control authority of active flow control methods. While previous studies have analyzed the effects of acoustic excitation on steady-wing aerodynamics, the effect of excitation on the unsteady aerodynamics is not known, which is the aim of the current effort. Internally mounted speakers on a symmetric National Advisory Committee for Aeronautics (NACA) 0012 wing are used to excite the unsteady boundary layer at the wing's leading edge as it executes linear pitch motions ranging from quasi-steady (trailing-edge driven stall) to vortex-dominated (mixed leading- and trailing-edge driven stall) motions at freestream Reynolds numbers (Re) of 120 000 and 180 000. Experimental results show that, although acoustic excitation delays stall for quasi-steady motions, it enhances lift in the linear region and increases leading-edge vortex strength for vortex-dominated motions. The degree of change was observed to be a function of the excitation frequency, with lower frequencies (≤ 250 Hz) leading to an increase in aerodynamic efficiency and higher frequencies having a negligible effect. The current work establishes the effects of acoustic flow excitation in unsteady, low-Re wing aerodynamics and provides insights on the path forward to effectively implement the method for active flow control.

Similarity solutions of a class of unsteady laminar boundary layer

The study of laminar unsteady boundary layer flows is essential for understanding the transition from laminar to turbulent flow, as well as the origins of turbulence. However, finding solutions to this phenomenon poses significant challenges. In this study, we introduce a novel method that employs a similarity transformation to convert the two-dimensional unsteady laminar boundary layer equations into a single partial differential equation with constant coefficients. By applying this transformation, we successfully derive similarity solutions for flat plate boundary layer flow, expressed in terms of Kummer functions. For convergent boundary layer flow, we derive an approximate analytical solution that includes both shock wave and soliton wave solutions. The superposition of these solutions provides evidence for the existence of solitons or soliton-like coherent structures (SCS) within boundary layers. Additionally, this paper explores two- and three-dimensional laminar flows, as well as three-dimensional turbulent flow equations, revealing that they all incorporate third-order derivatives with respect to spatial coordinates. This finding suggests that all viscous fluid motions have the potential to exhibit solitons/like coherent structures (SCS).

Influence of Time-Varying Freestream Conditions on the Dynamics of Unsteady Boundary-Layer Separation

Unsteady flow separation of a turbulent boundary layer under dynamic pressure gradients is investigated using the Large-Eddy Simulation technique. The unsteadiness is introduced by prescribing an oscillating freestream vertical-velocity profile at the top boundary of the domain. Although previous studies, including Ambrogi et al. (Journal of Fluid Mechanics, Vol. 945, Aug. 2022, p. A10) and Ambrogi et al. (Journal of Fluid Mechanics, Vol. 972, Oct. 2023, p. A36), focused on the kinematics of the flow and the effects of the oscillation frequency on flow separation, the goal of this paper is to analyze the effects of three time-varying freestream-forcing profiles while the oscillation frequency is kept the same for all Cases. Whereas in Case A the freestream-velocity profile changes from suction–blowing to blowing–suction in a complete cycle, Cases B and C are both suction–blowing only and the strength of the adverse pressure gradient is modulated in time. Moreover, the boundary layer in Case B never approaches a zero-pressure gradient condition. A closed separation bubble is formed for all Cases; however, its dimensions change depending on the far-field forcing. The time evolution of turbulent kinetic energy (TKE) reveals an advection mechanism of turbulent structures out of the domain for all Cases. Whereas in Case A and C the high-TKE region, generated in the separated shear layer, is washed out of the domain as a rigid body, in Case B the separation bubble remains present and the advection mechanism of TKE is characterized by a breathing pattern.

Asymptotic analysis of MHD chemically reacting boundary layer flow of Jeffrey hybrid nanofluid

AbstractFluids with enhanced heat transport characteristics are essential for efficient convection heat transportation. Hybrid nanofluids have demonstrated their effectiveness as viable substitutes for conventional heat transport fluids. This study explores the heat and mass exchange occurring within a chemically reactive, unsteady boundary layer flow of a copper oxide‐multi‐walled carbon nanotubes (CuO‐MWCNTs)/ethylene glycol Jeffrey hybrid nanofluid. Additionally, the influence of heat source/sink effects in a hydromagnetic environment is carefully added. The study employs a non‐Newtonian flow model and incorporates the Arrhenius activation energy for analysis. The hybrid nanofluid consists of a base fluid, ethylene glycol, enriched with copper oxide nanoparticles and multi‐walled carbon nanotubes. The governing coupled non‐linear partial differential equations are transformed into ordinary differential equations using similarity transformations, considering appropriate free stream, and wall boundary conditions; then, the Shooting method is employed to solve the resulting ordinary differential equations (ODEs) in MATLAB. The graphical and numerical outcomes are studied for various parameter combinations. The graphs illustrate the numerical results for the CuO‐MWCNTs/ethylene glycol hybrid nanofluid. These results are comprehensively discussed to analyze the influence of different thermo‐fluidic parameters on the Jeffrey hybrid nanofluid's heat, mass, and flow characteristics. The skin friction, Nusselt number, and Sherwood number are provided in a numerical table that displays the alterations of these parameters across various parameter values. As the Jeffrey fluid parameter rises, the Nusselt number and skin friction escalate, while the Sherwood number diminishes. Conversely, as the Deborah number rises, the Nusselt number and skin friction decline, but the Sherwood number increases. A comparative analysis with published results confirms the consistency of the present results.

Magnetohydrodynamics flow and heat transfer of novel generalized Kelvin–Voigt viscoelastic nanofluids over a moving plate

In this work, the unsteady magnetohydrodynamics boundary layer flow and heat transfer of novel generalized Kelvin–Voigt viscoelastic nanofluids over a moving plate are investigated. The classical Kelvin–Voigt constitutive relation is generalized to incorporate a time-fractional derivative to characterize the fluid behavior, which is proved to be of significance and physically justified. The newly developed fractional Kelvin–Voigt constitutive correlation and a dual-phase-lagging constitutive equation are applied to the momentum and energy equations, respectively, for a nanofluid model over a moving plate. The formulated integrodifferential velocity and thermal boundary layer equations are solved using the finite difference method together with a fast algorithm, which reduces the consumed central processing unit time significantly. Several numerical examples are presented to illustrate the influence of the critical parameters on the nanofluid motion and thermal characteristics. Compared to the fractional Maxwell nanofluid model, the velocity boundary layer for the fractional Kelvin–Voigt nanofluid model is thinner. Although the fractional indexes show similar effects on the velocity boundary layer, the impacts of the relaxation parameters are in contrast. This work provides valuable insights into the feasibility of using the fractional Kelvin–Voigt viscoelastic model to depict the fluid flow and heat transfer characteristics of nanofluids.

Group Classification of the Unsteady Axisymmetric Boundary Layer Equation

Unsteady equations of flat and axisymmetric boundary layers are considered. For the unsteady axisymmetric boundary layer equation, the problem of group classification is solved. It is shown that the kernel of symmetry operators can be extended by no more than four-dimensional Lie algebra. The kernel of symmetry operators of the unsteady flat boundary layer equation is found and it is shown that it can be extended by no more than a five-dimensional Lie algebra. The non-existence of the unsteady analogue of the Stepanov–Mangler transformation is proved.

Numerical Investigation of Three-Dimensional Magnetohydrodynamic Flow of Ag 􀀀 H2O Nanofluid Over an Oscillating Surface in a Rotating Porous Medium

Objective: To investigate the three-dimensional flow of a nanofluid (Ag-water) over a stretchable vertical oscillatory sheet. This study involves considering fluctuating temperatures on the sheet and comparing them to the free stream temperature. The formulation of the unsteady boundary layer equations leading to the flow of nanofluid also takes into consideration the occurrence of the heterogeneous-homogeneous chemical reaction and thermal radiation. Method: The governing equations and the boundary conditions have been derived in a dimensionless form by using the appropriate transformations, and they are then solved using an EFDS (Explicit Finite Difference Scheme) in Matlab software. The Von-Neumann stability analysis is used to determine the method’s stability requirements for constant sizes of the grid. Findings: The physical factors impact on the concentration fields, temperature distribution, and velocity distribution were obtained and are studied by graphs and described in extensive detail. Convergence and stability requirements are attained in order to achieve accurate solutions. Novelty: In this study fluctuations in the temperature and stretching velocity of sheet on three-dimensional magnetohydrodynamic flow of Ag − H2O nanofluid over an oscillating surface through rotating porous are taken into account. Impacts of porous media permeability, velocity slip, magnetic fields, nanoparticle volume fraction, heat radiation, rotation, and homogeneous and heterogeneous chemical reaction parameters had all been attempted to be determined. Keywords: Oscillatory Surface, Heat transmission, Nonlinear PDE, Explicit Finite Difference Scheme, Nanoparticle

The Effect of Variable Heat Flux on Unsteady Laminar MHD Boundary Layer Flow and Heat Transfer Due to a Stretching Sheet

The purpose of this research is to look into the solution technique for obtaining MHD velocity and temperature profiles. In the presence of a changing heat flux, the unsteady laminar boundary layer flow and heat transfer of a viscous incompressible fluid across a stretching sheet are numerically investigated. The unsteadiness is thought to be generated by a sudden increase in the surface temperature and a time-dependent stretching velocity. The flow and heat transfer partial differential equations were numerically solved using an implicit finite difference scheme and a quasi-linearization technique. Both velocity and temperature rise with time and magnetic field, according to the findings. The computed results are compared to previous work that has been published. Variable heat flux (VHF) conditions have also been taken into account.

Calculation and Selection of Airfoil for Flapping-Wing Aircraft Based on Integral Boundary Layer Equations

The flight of a migratory bird-like flapping-wing aircraft is characterized by a low Reynolds number and unsteadiness. The selection of airfoil profiles is critical to designing an efficient flapping-wing aircraft. To choose the suitable airfoil for various wing sections, it is necessary to calculate the aerodynamic forces of the unsteady two-dimensional airfoil with a Reynolds number in the range of 105. While accurate, calculating this by solving the Navier–Stokes equations is impractical for early design stages due to its high consumption of computing resources and time. The computational demands for extending it to 3D aerodynamic calculations are even more prohibitive. In this paper, a relatively simple method is proposed. The two-dimensional unsteady panel method is utilized to derive the inviscid flow field, the unsteady integral boundary layer method is utilized to solve the boundary layer viscous flow, and the eN transition model is adopted to predict the position of the transition. These models are coupled with the semi-inverse interaction method to solve the aerodynamics of the unsteady low-Reynolds-number two-dimensional airfoil. The unsteady aerodynamics of the symmetric and cambered airfoils at different wing sections are calculated respectively by the proposed method. Mechanism analysis of the calculation results is conducted, and a symmetrical airfoil or a slightly cambered airfoil is recommended for the wing tip, a moderately cambered airfoil is suggested for the outer-wing section, and a highly cambered airfoil is suggested for the inner-wing section.

THERMAL DIFFUSION AND RADIATION ABSORPTION IMPACTS ON CHEMICALLY REACTIVE AND RADIATIVE NANOFLUID FLOW PAST AN EXPONENTIALLY ACCELERATED VERTICAL POROUS PLATE

The role of thermal diffusion (Soret) and radiation-absorption influences on the unsteady MHD boundary layer flow for Silver (Ag) and Copper (Cu) water-based nanofluid over an accelerated exponentially vertical porous plate has been investigated. The varying temperature and concentration at the plate are also considered. The governing equations of the flow are numerically resolved to employ the finite-difference system of the implicit Crank-Nicolson method. Fluid velocity, f luid temperature, and species concentration were all plotted for meaningful physical parameters. For both nanofluids, non-dimensional metrics such as the friction factor, Nusselt number, and Sherwood number at the surface are tabulated. The data obtained from the literature provide strong validation for the findings. The f inding of the study is that both nanofluids’ velocities rise with increases in Soret and radiation absorption parameters. For increased values of Soret and radiation absorption parameters, the friction factor and Nusselt number increase. Sherwood numbers drop for the Soret parameter and rise for the radiation absorption.

Numerical Study of Unsteady Boundary Layer Flow through A Vertical Surface with Convective Boundary Conditions

In the present-day paper the effort is to see the properties of heat allocation over a vertical flat surface for an unsteady mixed, boundary layer convective flow. The non-linear partial differential equations of the present model are transformed in to ordinary differential equations by means of suitable similar transformations. The consequent ordinary differential equations are resolved mathematically by means of MATLAB program bvp4c and discussed the effects of skin friction, suction and injection for temperature and velocity.

Unsteady numerical study of film cooling and heat transfer on turbine blade squealer tip with coolant jet

Cooling performance of blade squealer tip with film holes in its cavity was investigated numerically under unsteady condition, and the effects of blowing ratio (BR), cavity depth, and tip clearance were comprehensively discussed. Results show that flow inside tip gap periodically fluctuates and affects the outlet pressure, BR, and jet characteristics of film hole, resulting in unsteady tip cooling effectiveness which could not be observed in steady condition. Average cooling effectiveness on 40-70% axial chord of tip changes the most over time. In comparison to steady result, unsteady time-average cooling effectiveness of tip and its region before 40% axial chord is lower while it is relatively higher in the region after 40% axial chord. Coolant from tip hole located in the flow area of rolling vortex is strongly mixed with rolling vortex, leading to high heat transfer coefficient downstream of that hole. Unsteady leakage flow and boundary layer flow cause stronger heat transfer on squealer rim than steady result. Small BR under unsteady condition could result in insufficient coolant supply and high temperature gas intrusion in tip holes located in 40-70% axial chord of tip. Increasing cavity depth brings longer normal jet distance and higher momentum of coolant, leading to coverage deterioration on floor with a drop in tip average cooling effectiveness of 11.6-34.7%. Large tip clearance causes the distribution of BR to become more uneven, and then more coolant flows out from trailing region, resulting in decrease tendency of average cooling efficiency with change in the range of −23.4%∼6.1% over time compared to base design.

Unsteady Boundary Layer Heat and Mass Transfer Flow of Nanofluid Over Porous Stretching Sheet with Non-Uniform Heat Generation/Absorption and Double Stratification

The influence of thermal radiation and stratification process on unsteady MHD flow over stretching sheet embedded in “nanofluid saturated porous medium with non-uniform heat source/sink was analyzed numerically in the present analysis. Proper similarity transformations reduce the nonlinear partial differential equations into ordinary differential equations and are solved numerically by using Galerkin Finite element method. Impact of different parameters, such as, magnetic parameter (0.1–1.0), buoyancy ratio parameter (0.1–4.5), radiation parameter (0.5–1.7), Rayleigh number (0.1–0.7), thermophoresis parameter (0.4–1.5), thermal stratification parameter (0.01–1.0), Brownian motion parameter (1.0–2.0), solutal stratification parameter (0.01–1.0), unsteadiness parameter (0.1–0.4), space–dependent (-0.5–0.4) and temperature dependent (-0.5–0.2) heat source/sink parameters on velocity, temperature and concentration profiles is calculated and are illustrated graphically. Skin-friction coefficient, Nusselt and Sherwood number are calculated and the results are shown in tabular form. It is found that the thermal stratification parameter deteriorates the temperature of the fluid. The concentration of the fluid diminishes with rising values of solutal stratification parameter. The thermal boundary layer thickness elevates” with higher values of Brownian motion and thermophoresis parameters.

Systematic error and correction of intensity-based I-PLIF for local pH and concentration measurements in unsteady boundary layers

Systematic error and correction of intensity-based I-PLIF for local pH and concentration measurements in unsteady boundary layers

Heat transfer modification in an unsteady laminar boundary layer subject to free-stream traveling waves

A laminar, thermal boundary layer was forced computationally by free-stream, traveling-wave velocity fluctuations and the effects on the wall heat flux and skin friction were measured as a function of the phase speed of the disturbances and the streamwise location along the developing flow. The heat flux modification due to the flow forcing was significantly higher than the corresponding skin friction enhancement, and the dependence of these two transport properties on the phase speed was qualitatively different. The skin friction modification exhibited a maximum at an optimal phase speed, which was explained in terms of the overlap of two distinct viscous layers within the boundary layer. The heat flux modification did not exhibit this maximum, although evidence was found to suggest such a maximum may occur with sufficient boundary layer development. Because the magnitude of the wall heat-flux modification scales quadratically with wave amplitude, traveling wave disturbances pose significant challenges for thermal transport measurements in periodically perturbed environments, like turbomachinery, but also new opportunities for the control of heat transfer.

Application of Heat and Mass Transfer to Convective Flow of Casson Fluids in a Microchannel with Caputo–Fabrizio Derivative Approach

It has been demonstrated that fractional derivatives exhibit a range of solutions that are helpful in the engineering, medical, and manufacturing sciences. Particularly in analytical research, investigations on using fractional derivatives in fluid flow are still in their infancy. Therefore, it is still being determined whether fractional derivatives may be represented geometrically in the mechanics of the flow of fluids. However, theoretical research will be helpful in supporting upcoming experimental research. Therefore, the aim of this study is to showcase an application of Caputo–Fabrizio toward the Casson fluid flowing in an unsteady boundary layer. Mass diffusion and heat radiation are taken into account while analyzing the PDEs that governed the problem. Dimensionless governing equations are formed from the fractional PDEs by utilizing the necessary dimensionless variables. Once the equations have been transformed into linear ODEs, the solution may then be found by applying the Laplace transform technique. Inverting Laplace transforms by Stehfest’s and Tzou’s Algorithm is then used to retrieve the original variables and the solutions as concentration, temperature, and velocity fields. Graphical illustrations sketched using the Mathcad program are used to show how physical parameters affect temperature, velocity, and concentration profiles. Findings show that the velocity, temperature, and concentration profiles have been improved by thermal radiation, mass diffusion, and fractional parameters. The fractional derivative is a more general derivative due to its nonlocal and flexible nature the flow model that is formulated by applying the fractional derivative is suitable to address the memory effect. The present fractionalized results of velocity, concentration, and temperature are more general and applicable to the wide range of orders of fractional derivatives.

Direct Numerical Simulation of a High-Pressure Turbine Stage: Unsteady Boundary Layer Transition and the Resulting Flow Structures

Abstract In the present study, we investigate the unsteady boundary layer transition based on the direct numerical simulation database of a high-pressure turbine (HPT) stage (Zhao and Sandberg, 2021, High-Fidelity Simulations of a High-Pressure Turbine Stage: Effects of Reynolds Number and Inlet Turbulence, ASME Turbo Expo 2021, Paper No. GT2021-58995), focusing on the transition mechanisms on the rotor blade, affected by the incoming periodic wakes and the background freestream turbulence (FST). On the basis of the fully resolved flow fields, we provide detailed analysis of the flow structures responsible for the transition, and two distinctive transition paths have been identified. The first path is the typical bypass transition via the instability of Klebanoff streaks, which happens when the transition region is not directly affected by the wake. The suction-side boundary layer is disturbed at the leading edge, resulting in the formation of streamwise streaks. These streaky structures endure varicose instability in the region with adverse pressure gradient (APG), then quickly break down into turbulent spots, which then evolve into fully turbulent flow. The other transition path is a consequence of the direct interaction between the wake structures and the blade boundary layer, when the wake apex starts to affect the transitional region. To be specific, the wake structures directly interact with the separation bubble in the APG region, causing sudden breakdown into turbulence. A calmed region is found to follow the wake-induced turbulent boundary layer. It is observed that the recovery to a calmed region can be impacted by the FST, as the calmed region in case with no FST is much longer compared to cases with stronger FST.