Time-dependent Boundary Layer Flow Research Articles

Fractal Numerical Investigation of Mixed Convective Prandtl-Eyring Nanofluid Flow with Space and Temperature-Dependent Heat Source

Fractal Numerical Investigation of Mixed Convective Prandtl-Eyring Nanofluid Flow with Space and Temperature-Dependent Heat Source

Capturing features of turbulent Ekman–Stokes boundary layers with a stochastic modeling approach

Abstract. Atmospheric boundary layers (ABLs) exhibit transient processes on various time scales that range from a few days down to seconds, with a scale separation of the large-scale forcing and the small-scale turbulent response. One of the standing challenges in modeling and simulation of ABLs is a physically based representation of complex multiscale boundary layer dynamics. In this study, an idealized time-dependent ABL, the so-called Ekman–Stokes boundary layer (ESBL), is considered as a simple model for the near-surface flow in the mid latitudes and polar regions. The ESBL is driven by a prescribed temporal modulation of the bulk–surface velocity difference. A stochastic one-dimensional turbulence (ODT) model is applied to the ESBL as standalone tool that aims to resolve all relevant scales of the flow along a representative vertical coordinate. It is demonstrated by comparison with reference data that ODT is able to capture relevant features of the time-dependent boundary layer flow. The model predicts a parametric enhancement of the bulk–surface coupling in the event of a boundary layer resonance when the flow is forced with the local Coriolis frequency. The latter reproduces leading order effects of the critical latitudes. The model results suggest that the bulk flow decouples from the surface for high forcing frequencies due to a relative increase in detached residual turbulence.

Numerical analysis of thermal transportation in nanodiamond and silver-based nanofluid using the Cattaneo–Christov heat flux model

Background and Purpose: Studying the effects of suction and injection on heat transportation in nanofluids for time-dependent boundary layer flow is a key topic in fluid dynamics. Aerodynamics and the sciences of space both make extensive use of these types of flow. In this research, nanodiamond and silver nanoparticles in water-type base-fluid nanofluids flow are analyzed under the effects of thermal radiation and non-Fourier theory.Methodology: A mathematical system having certain physical variations of the flow model is converted to a non-dimensional ordinary differential equation system via suitable similarity transformation variables. Then the flow model is numerically solved by RK4 and a shooting technique to describe the dynamics of the nanofluids under varied flow conditions. RK4 with the shooting approach gives a rapid result with high convergence accuracy. The relevant characteristics of physical quantities evaluated by an inclusive numerical scheme are observed for flow pattern, temperature distribution, and nanofluids concentration variations in the presence of suction and injection fluxes.Finding: According to the findings, both ND-H2O and Ag-H2O have outstanding thermal performance characteristics. The Ag-based nanofluid, however, has a better heat transfer capability. To validate the analysis, a graphical and tabular comparison is presented under specified assumptions. The key finding is that, with the injection effect, the heat flow rate is larger than with the suction effect. The unsteadiness parameter causes a drop in the velocity profile, whereas energy distribution rises with this parameter.

Analytical simulation of time dependent electromagneto-hydrodynamic flow of Williamson fluid due to oscillatory curved convectively heated Riga surface with variable thermal conductivity and diffusivity

The main objective of the present article is to provide an analytical simulation for time dependent boundary layer flow of non-Newtonian Williamson fluid due to stretchable curved oscillatory Riga surface. Also the characteristics of heat and mass transport are studied under the influence of variable thermal conductivity and diffusivity along with convective heat and mass boundary conditions. Additionally, energy equation is also characterized with the impact of heat production. Curvilinear coordinate scheme is followed to attain the boundary layer expressions for the flow model. The governing nonlinear partial differential equations are solved analytically via homotopy analysis method (HAM). Graphs are plotted to examine comprehensively the consequences of various concerned parameters like modified magnetic parameter and radius of curvature, Williamson fluid parameter, relation of the surface's oscillating frequency to its stretching rate constant, Prandtl number, variable conductivity and heat production parameters, Schmidt number and variable diffusivity parameter on concentration, temperature, pressure and velocity profile. Also the outcomes of afore said variables on surface drag force, rate of temperature and mass transmission (Nusselt and Sherwood numbers) are shown in tabular form. The liquid velocity amplitude is enhanced with modified magnetic parameter and shows opposite behavior for Williamson fluid parameter.

Investigation of Velocity Profile in Time Dependent Boundary Layer Flow of a Modified Power-Law Fluid of Fourth Grade

This paper deals with the investigation of time dependent boundary layer flow of a modified power-law fluid of fourth grade on a stretched surface with an injection or suction boundary condition. The fluid model is a mixture of fourth grade and power-law fluids in which the fluid may display shear thickening, shear thinning or normal stress textures. By using the scaling and translation transformations which is a type of Lie Group transformation, time dependent boundary layer equations are reduced into two alternative ordinary differential equations systems (ODEs) with boundary conditions. During this reduction, special Lie Group transformations are used for translation, scaling and combined transformation. Numerical solutions have been carried out for the ordinary differential equations for various fluids and boundary condition parameters. As a result of numerical analysis, it is observed that the boundary layer thickness decreases as the power-law index value increases. It was also observed that for the fourth-grade fluid parameter, as the parameter increases, the boundary layer thickness decreases while the velocity in the <i>y</i> direction increases.

Heat and mass transfer analysis in unsteady flow of tangent hyperbolic nanofluid over a moving wedge with buoyancy and dissipation effects

In this study, a convective heat and mass transfer phenomena in a time-dependent boundary layer flow of tangent hyperbolic nanofluid over a permeable stretching wedge has been examined with respect to some pertinent thermo-physical parameters. Convenient similarity transformation is used to reformulate the dimensional partial differential equations into dimensionless system of ordinary differential equations. The reduced set of equations is solved by the homotopy analysis method implemented in Mathematica environment. The effects of the relevant parameters on velocity, temperature and concentration profiles were examined in detail. The impacts of the parameters on the rates of momentum, heat and mass transfer are also analyzed quantitatively in terms of the wall friction coefficient, local Nusselt number and Sherwood number, respectively. Analysis of the results reveals that the increase in the buoyancy ratio parameter facilitates the flow velocity and the increase in the dissipation parameter maximizes the temperature distribution and nanoparticle concentration near the surface of the wedge. Moreover, the analytic approximations obtained by implementing the homotopy analysis method are found in excellent agreement with some previously published results.

Time Dependent Boundary Layer Flow and Heat Transfer of Jeffrey Nanofluid with Viscous Dissipation Effects

Time Dependent Boundary Layer Flow and Heat Transfer of Jeffrey Nanofluid with Viscous Dissipation Effects

Rheological Effects Due to Oscillating Field on Time Dependent Boundary Layer Flow of Magnetic Nanofluid Over a Rotating Disk

This study presents the rheological effects on unsteady flow of an incompressible, electrically non-conducting magnetic nanofluid due to an oscillating magnetic field. Shliomis theory has been employed to formulate the governing equations for nanofluid flow due to a disk rotation. The governing nonlinear coupled partial differential equations with the boundary conditions are transformed into a set of ordinary differential equations which are then solved by Newton’s method in MATLAB. The influences of low oscillating field with different values of effective magnetization parameter and nanoparticle-size volume fraction on the velocity profiles are computed. It has been observed that the effective magnetization parameter creates an additional resistance on the axial velocity provided the applied magnetic field and vorticity of the flow are not collinear. This additional resistance becomes maximal when the applied magnetic field is perpendicular to the vorticity of the flow. Further, the axial velocity depends on the distance from the plate and not on the distance from the axis. The results are very useful in understanding the effects of viscosity variation due to the applied magnetic field and volume fraction on magnetic nanofluid based electronic devices such as damping systems, and needs further practical investigations.

Variable Viscosity Effects on Time Dependent Magnetic Nanofluid Flow past a Stretchable Rotating Plate

Abstract An attempt has been made to describe the effects of geothermal viscosity with viscous dissipation on the three dimensional time dependent boundary layer flow of magnetic nanofluids due to a stretchable rotating plate in the presence of a porous medium. The modelled governing time dependent equations are transformed a from boundary value problem to an initial value problem, and thereafter solved by a fourth order Runge-Kutta method in MATLAB with a shooting technique for the initial guess. The influences of mixed temperature, depth dependent viscosity, and the rotation strength parameter on the flow field and temperature field generated on the plate surface are investigated. The derived results show direct impact in the problems of heat transfer in high speed computer disks (Herrero et al. [1]) and turbine rotor systems (Owen and Rogers [2]).

Unsteady boundary layer flow and heat transfer of Oldroyd-B nanofluid towards a stretching sheet with variable thermal conductivity

This paper presents a time dependent boundary layer flow and heat transfer of an incompressible Oldroyd-B nanofluid past an impulsively stretching sheet. Heat transfer analysis is carried out by taking thermal conductivity as a function of temperature. The non-dimensionalized partial differential equations are solved using bivariate spectral quasi-linearization method). The employs the concept of quasi-linearization to obtain a linear system of partial differential equations which is subsequently solved using a spectral collocation method that uses bivariate Lagrange interpolating polynomials as basic functions. This method is found to converge rapidly and is very effective in yielding accurate results. Numerical results have been presented graphically to illustrate the details of flow and heat transfer characteristics and their dependence on some of the physical parameters.

On series solution for unsteady boundary layer equations in a special third grade fluid

Analytic solution for the time-dependent boundary layer flow over a moving porous surface is derived by using homotopy analysis method (HAM). A special third grade fluid model has been used in the problem formulation. The obtained HAM solution is also compared with the numerical solution and a reasonable agreement is noted.

Free convection fluctuating flow on a horizontal magnetized plate

The free convection flow of electrically conducting fluid along a semi-infinite horizontal magnetized plate is analysed, when the plate temperature oscillates about a constant mean. The basic steady flow is purely buoyancy induced, while the oscillations in the plate temperature cause a time-dependent boundary layer flow and heat transfer. The unsteady boundary layer equations are linearized and the first two approximations are considered. Two separate solutions valid for high and low frequency ranges are obtained by series expansion method in terms of frequency parameters. For very high frequencies, the oscillatory flow pattern is of ‘shear-wave’ type unaffected by the mean flow. The skin friction in the very high frequency solution has a phase lag of 45° while the phase of heat transfer oscillations is ahead of the plate temperature fluctuations by π/4.

Fluctuating boundary layer on a heated horizontal plate

The paper deals with the boundary layer flow and heat transfer on a horizontal plate whose temperature differs from that of ambient fluid. The basic flow is purely induced by buoyancy which is caused by the difference of temperature in the plate and the fluid. The oscillation in the plate temperature causes a time dependent boundary layer flow and heat transfer. Two separate solutions for high and low frequency ranges are developed. The velocity and temperature fields are obtained with the help of Karman-Pohlhausen method in the low frequency range while for high frequencies we have employed a series expansion method in terms of frequency parameters. For very high frequencies, the oscillatory flow pattern is of ‘shear wave’ type unaffected by the mean flow and predicts a phase lead of π/4 in the local rate of heat transfer fluctuations while the skin friction has a phase lead of π/2.

Free convection effects on fluctuating boundary layer from a horizontal plate

The paper deals with the combined free and forced convection flows when the free stream and the plate temperature both fluctuate about non-zero mean. The basic flow is nothing but steady state combined free and forced convection flow past a horizontal plate while the oscillations in the free stream and plate temperature cause a time-dependent boundary layer flow and heat transfer. Two separate methods are applied for high and low frequency ranges. It is found that when the frequency of oscillations is extremely low, the boundary layer behaviours can be predicted well with the steady state theory based on instantaneous velocity and temperature distributions. For the very high frequency, the amplitude of the skin friction increases with ω and its phase is ahead of that of the imposed oscillations by 90° while the amplitude of the rate of heat transfer increases as\(V\bar \omega \) and its phase has a lead of 45°.

The Effect of Plate Oscillations on Horizontal Free Convection Flow

The free convection flow along a semi-infinite horizontal plate oscillating in its own plane is analysed The basic flow is purely buoyancy induced, while the oscillations in the plate cause a time-dependent boundary layer flow and heat transfer. The boundary layer equations are linearized and the first two approximations are considered. Two separate solutions valid for high and low frequency ranges are obtained by a series expansion in terms of frequency parameters. The skin friction and the rate of heat transfer are studied for both frequency ranges. For very high frequencies, the oscillatory flow pattern is of a 'shear-wave' type, unaffected by the mean flow. It is found that the phase of the skin friction at the plate lags that of the plate oscillations by in and the rate of heat transfer has a phase lag of 1/2n.

Fluctuating free convection boundary layers

The free convection flow along a horizontal plate whose temperature oscillates about a non-zero mean is analysed. The basic flow is purely buoyancy induced while the oscillation in the plate temperature causes a time dependent boundary layer flow and heat transfer. Two separate solutions valid for high and low frequency ranges are developed. The velocity and temperature are obtained by a series expansion in terms of frequency parameters. For very high frequencies, the oscillatory flow pattern is of “Shear Wave” type unaffected by the mean flow and predicts a phase lead of π/4 in the local rate of heat transfer fluctuations while the skin friction has a phase lag of π/2.