Steady-state Boundary Layer Research Articles

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

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

Beyond spreading rate: Controls on the thermal regime of mid-ocean ridges.

The thermal state of mid-ocean ridges exerts a crucial modulation on seafloor spreading processes that shape ~2/3 of our planet's surface. Standard thermal models treat the ridge axis as a steady-state boundary layer between the hydrosphere and asthenosphere, whose thermal structure primarily reflects the local spreading rate. This framework explains the deepening of axial melt lenses (AMLs)-a proxy for the basaltic solidus isotherm-from ~1 to ~3 km from fast- to intermediate-spreading ridges but fails to account for shallow crustal AMLs documented at slow-ultraslow spreading ridges. Here, we show that these can be explained by a numerical model that decouples the potentially transient ridge magma supply from spreading rate, captures the essential physics of hydrothermal convection, and considers multiple modes of melt emplacement. Our simulations show that melt flux is a better thermal predictor than spreading rate. While multiple combinations of melt/dike emplacement modes, permeability structure, and temporal fluctuations of melt supply can explain shallow crustal AMLs at slow-ultraslow ridges, they all require elevated melt fluxes compared to most ridge sections of comparable spreading rates. This highlights the importance of along-axis melt focusing at slow-ultraslow ridges and sheds light on the natural variability of their thermal regimes.

Diffusion analysis of three kinds of species with two salts in two working fluids using Darcy's law using solar radiations

This specific research was carried out with the aim of investigating incompressible Casson fluid and Williamson liquid. Steady-state laminar boundary layer flow involving Brownian diffusion and thermophoretic diffusion is taken over a horizontal penetrating plate saturated with two distinct salts having distinct characteristics. Casson fluid motion was observed with the utilization of Darcy-Forchheimer technique. Whilst, Nanofluid motion and other salts motion induced by wall movement. Solar thermal collectors, Solar thermal systems, Solar cookers, Solar thermal energy, drying, generating electricity, chemical reactions, soil vapor extraction, medication and heat exchange medium. Physical quantities like density, temperature profile and concentration profile were addressed by aiding Bossiness approximation. Whereas the optimization of energy is carried out under the effects of cross-diffusion, regular diffusion and non-Fourier law for two different salt components. Formulation of acquired flow equations in terms of partial differential equations are further transformed into ordinary differential equations using similarity transformations. The numerical solution will be obtained by utilization of FE-method. It was found that the temperature field elevates on increasing solar thermal radiation number, modified Dufour numbers of salt 1 and salt 2. Thickness and width regarding momentum layers for Casson liquid rather than Williamson liquid while temperature field for Williamson liquid is higher than Casson liquid.

Heat flux characteristics of a single droplet splashing on the liquid film obtained with a thermal lattice Boltzmann method

The double-distribution-function thermal lattice Boltzmann method is employed to investigate the heat flux characteristics of single droplet impact on a liquid film above a heated wall. The effects of impact velocity, liquid film thickness, droplet radius, and viscosity coefficient on the average and instant heat flux distribution are analyzed. The droplet impact first breaks the steady-state thermal boundary layer in the impact region, causing the heat flux in the wall impact region to increase. This is because the temperature gradient between the liquid film and the wall increases as the droplet dives downward and expands. The velocity discontinuity at the liquid jet sheet prevents the transfer of the transverse velocity in the liquid film to the static region, yielding a transition region. Convective heat transfer is dominant in the impact and transition regions, while conductive heat transfer is dominant in the static region. Moreover, a large impact velocity promotes the synergy between the temperature and flow velocity fields, enhancing the heat transfer efficiency. The kinetic energy consumption of the droplet increases with the liquid film thickness, which causes the heat flux to decrease. The effect of droplet radius on the heat flux at the wall is minimal. Furthermore, an increased liquid viscosity is not beneficial for wall heat dissipation.

Numerical study of dissipative SW/MWCNT-nanofluid coating flow from a stretching wall to a porous medium with shape factor effects

A mathematical model is developed for incompressible steady-state dissipative CNT-aqueous nanofluid boundary layer flow from a stretching sheet to a saturated isotropic porous medium. Three different CNT shapes (spheres, blades and platelets) are considered. Both single-walled (SWCNT) and multi-walled (MWCNT) carbon nanotubes are examined. A Darcy-Brinkman model is adopted for the porous medium and a modified viscous dissipation formulation is considered which features porous media influence in the energy conservation equation. Appropriate expressions are deployed for the CNT-modified nanofluid viscosity, density, specific heat capacity, thermal conductivity and CNT shape factor. Via similarity transformations, the governing conservation equations for mass, momentum and energy with associated boundary conditions are normalized to generate a coupled nonlinear ordinary differential boundary value problem. A numerical solution is presented with the robust MATLAB-based bvp4c method and 4th order Runge-Kutta shooting scheme. Validation with previous studies is included. Velocity, temperature, skin friction and Nusselt number are computed for a range of selected parameters. The computations show that elevation in CNT volume fraction parameter accelerates the boundary layer flow whereas increment in the Darcian (inverse permeability) parameter induces strong deceleration. MWCNTs produce higher velocities than SWCNTs. Temperature and thermal boundary layer thickness are found to be enhanced with increasing Eckert number, Darcian (inverse permeability) parameter, CNT volume fraction and CNT shape factor. Significantly greater temperatures are computed for MWCNTs.

High-speed measurements and conditional analysis of boundary-layer flows at engine speeds up to 2500 rpm in a motored IC engine

The importance of near-wall processes in internal combustion engines, such as near-wall heat transfer, will increase with the current trend toward engine downsizing. Engine boundary layers have been shown to differ from canonical steady-state turbulent boundary layers. A comprehensive understanding of the structure and behaviour of engine boundary layers is required, especially for predictive wall models used in numerical simulations.In the present study, the boundary layer flow over the piston surface in an optically accessible spark ignition engine was investigated using high-resolution, high-speed particle tracking velocimetry. To resolve the phase-averaged viscous sublayer for technically relevant engine speeds up to 2500 rpm, a vector resolution of up to 5 µm perpendicular to the wall was implemented. During compression, the conventionally phase-averaged flow relative to the piston surface resembles canonical flows over a flat plate. However, the results show that no logarithmic layer is present even at higher engine speeds and Reynolds numbers, extending the findings of previous studies. At 2500 rpm and 0.95 bar intake load, the viscous sublayer (y+=5) gets as thin as 30 µm. Additionally, the outer layer is small, as the bulk flow already starts at a wall-scaled distance of y+=30−90, which has to be considered when applying wall models in numerical simulations.A conditional analysis revealed flow modes that differ substantially from the conventional phase-average. Furthermore, a strong impact of temporal flow evolution and horizontal position on the boundary layer was found. Even in the case of wall-parallel flows, a strong acceleration and deceleration of the flow can be observed, which affects the adherence of boundary layer profiles to the law-of-the-wall. Another dominant flow mode is the impingement on the piston, where the degree of boundary layer development increases with distance from the stagnation point. These results show a striking similarity to classical channel flows with impinging wall jets.

Numerical analysis of the effect of attack angle on the boundary layer flow along an archery bare shaft arrow

The velocity boundary layer, formed on an archery bare-shaft arrow, is computed by using two kinds of finite difference codes; an axisymmetric code and a three-dimensional code. Two types of arrow point, i.e., bullet point and streamlined point, are attached to a cylindrical arrow shaft. The Reynolds number, based on the shaft diameter, is varied in a range 10, 000 ≤ Re ≤ 20, 000, and the attack angle, α, is fixed at α = 0.0°. Critical assessment is performed on the grid dependency of velocity profiles, the difference in velocity profiles between axisymmetric and 3D computations, the effect of interpolation method on the interpolants by comparing the spline and the tri(bi)-cubic interpolations. The results of assessment indicates that the effect of varying the number of grid points, simulation codes and the interpolation method, considered in the present study, is reasonably small for the steady state boundary layers.

Haar wavelet scrutinization of heat and mass transfer features during the convective boundary layer flow of a nanofluid moving over a nonlinearly stretching sheet

In this study, we investigate steady-state convective boundary layer fluid flow of heat and mass transfer features of a nanofluid moving over a nonlinearly stretching sheet in detail. The nanofluid physical model of the problem comprises with effects of thermophoresis and Brownian motion. The mathematical model scrutinizes mass, momentum and heat transfer equations are reduced to ordinary differential equations over infinite domain using suitable similarity variables. Haar wavelet collocation method is used to solve the resulting coupled nonlinear ordinary differential equations with an infinite domain. The obtained results are validated with available numerical findings and the solutions are more efficient which confirm and verify the wavelet method. The impact of several interesting physical aspects viz. thermophoresis parameter, stretching parameter, Brownian motion and Schmidt number on nanoparticle volume fraction and temperature profile curves are graphically demonstrated. The derived quantities of various parameters on the rate of heat and mass transfer are depicted in tabular forms. It predicts that the increase in Brownian motion and thermophoresis parameter reduces the local Nusselt number. The local Sherwood number increases with an increase in the parameters of Brownian motion and thermophoresis. For both temperature and volume fraction profiles decreases due to an increase in the Schmidt number.

Applicability of Two-Parameter Turbulence Models to Simulation of the Interaction of Near-Wall Flows with Blowing and Suction on Permeable Surfaces

The applicability of two-parameter turbulence models to investigation of the impact of free-stream high-intensity turbulence on the characteristics of near-wall flow and heat- and mass-transfer in the steady-state and unsteady boundary layers under the conditions of blowing and suction through permeable surface sections is analyzed. The calculated results obtained in specifying a constant relative mass flow rate parameter in the cases of blowing and suction through permeable sections are compared with the experimental data. The mechanisms of the interaction of blowing and suction of a gas of homogeneous constitution with the flow on two permeable sections upstream and downstream of these sections in the near-wall zone of turbulent boundary layer are studied on the basis of numerical solutions. The calculated results obtained in specifying a time-dependent flow-rate parameter on two permeable surface sections are given.

Numerical Solution of MHD Nanofluid Over a Stretching Surface with Chemical Reaction and Viscous Dissipation

The main objective of this paper is to focus on a numerical study of chemical reaction and viscous dissipation effects on the steady state boundary layer flow of MHD nanofluid past the horizontally stretching sheet with the existence of nanoparticles. A proper similarity transformation is utilized to convert the boundary layer equations into the nonlinear and coupled ordinary differential equations. These ODEs are sorted out numerically by applying the shooting mechanism. Graphical representations are also included to explain the effect of evolving parameters against the above-mentioned distributions. Significance of different physical parameters on dimensionless velocity, temperature and concentration are elaborated through graphs and tables. For increasing values of Eckert number, the temperature profile increases whereas the chemical reaction parameter increases, the boundary layer thickness decreases.
 Chemical Engineering Research Bulletin 21(2019) 36-45

Steady-State Large-Eddy Simulations of Convective and Stable Urban Boundary Layers

A comprehensive investigation is carried out to establish best practice guidelines for the modelling of statistically steady-state non-neutral urban boundary layers (UBL) using large-eddy simulation (LES). These steady-state simulations enable targeted studies under realistic non-neutral conditions without the complications associated with the inherently transient nature of the UBL. An extensive set of simulations of convective and stable conditions is carried out to determine which simplifications, volumetric forcings, and boundary conditions can be applied to replicate the mean and turbulent (variance and covariance) statistics of this intrinsically transient problem most faithfully. In addition, a new method is introduced in which a transient simulation can be ‘frozen’ into a steady state. It is found that non-neutral simulations have different requirements to their neutral counterparts. In convective conditions, capping the boundary-layer height h with the top of the modelled domain to h/5 and h/10 (which is common practice in neutral simulations) reduces the turbulent kinetic energy by as much as 61% and 44%, respectively. Consistent with the literature, we find that domain heights l_z ge 5 |L| are necessary to reproduce the convective-boundary-layer dynamics, where L is the Obukhov length. In stably stratified situations, the use of a uniform momentum forcing systematically underestimates the mechanical generation of turbulence over the urban canopy layer, and therefore leads to misrepresentations of both the inner- and outer-layer dynamics. The new ‘frozen-transient’ method that is able to maintain a prescribed flow state (including entrainment at the boundary-layer top) is shown to work well in both stable and convective conditions. Guidelines are provided for future studies of the capped and uncapped convective and stable UBL.

Thermal energy statistics for Jeffery fluid flow regime: A generalized Fourier’s law outcomes

This paper is about Jeffery fluid with thermal stratification effects at a stagnation point. The thermal energy and heat transfer is studied through Cattaneo–Christov heat flux model. The flow is induced by the stretching cylinder. The homogeneous–heterogeneous chemically reactive species are taken into account. The homogeneous reaction is provided by isothermal cubic autocatalytic kinetics and the heterogeneous reaction by first order kinetics. The steady state boundary layer flow is discussed in case when both reactants and auto-catalyst have equal diffusion coefficients. The concerned mathematical problem is developed by laws of conservation of mass, momentum and energy which provides a coupled partial differential equations. The order of these equations is reduced through similarity transformation. Later on, the set of reduced coupled equations are sorted out numerically by means of Runge–Kutta Fehlberg technique with shooting algorithm. The fluid velocity is decreasing at Deborah number. The influence of thermal relaxation parameter and thermal stratification parameter on fluid temperature trend is decreasing. The numerical values for skin friction coefficient is examined and found excellent match with existing literature.

The influence of MHD and heat generation/absorption in a Newtonian flow field manifested with a Cattaneo–Christov heat flux model

The purpose of this report is to emphasize magnetohydrodnamics, heat generation/absorption and slip effects over a Newtonian fluid flow with homogeneous–heterogeneous chemical reactions induced by the rotating disk. The homogeneous reaction is provided by isothermal cubic autocatalytic kinetics and the heterogeneous reaction by first order kinetics. The concerned steady state boundary layer flow is discussed in the case when both reactants and auto-catalyst have equal diffusion coefficients. The Cattaneo–Christov approach is proposed to derive the energy equation and heat transfer phenomena. The consequential partial differential equations descend to ordinary differential equations by using similarity transformation. Further, these equations are sorted numerically using the Runge–Kutta–Fehlberg technique with a shooting scheme. The influences of arising parameters on fluid velocity, temperature and concentration are observed through graphs. Further, the numerical results for the skin friction coefficient and local Nusselt number are examined and compared with existing literature.

Rethinking Craig and Gordon's approach to modeling isotopic compositions of marine boundary layer vapor

Abstract. We develop a one-dimensional (1-D) steady-state isotope marine boundary layer (MBL) model that includes meteorologically important features missing in models of the Craig and Gordon type, namely height-dependent diffusion and mixing, lifting to deliver air to the free troposphere, and convergence of subsiding air. Kinetic isotopic fractionation results from this height-dependent diffusion that starts as pure molecular diffusion at the air–water interface and increases with height due to turbulent eddies. Convergence causes mixing of dry, isotopically depleted air with ambient air. Model results fill a quadrilateral in δD–δ18O space, of which three boundaries are defined by (1) vapor in equilibrium with various sea surface temperatures (SSTs), (2) mixing of vapor in equilibrium with seawater and vapor in subsiding air, and (3) vapor that has experienced maximum possible kinetic fractionation. Model processes also cause variations in d-excess of MBL vapor. In particular, mixing of relatively high d-excess descending and converging air into the MBL increases d-excess, even without kinetic isotope fractionation. The model is tested by comparison with seven data sets of marine vapor isotopic ratios, with excellent correspondence. About 95 % of observational data fall within the quadrilateral predicted by the model. The distribution of observations also highlights the significant influence of vapor from nearby converging descending air on isotopic variations within the MBL. At least three factors may explain the ∼5 % of observations that fall slightly outside of the predicted regions in δD–δ18O and d-excess–δ18O space: (1) variations in seawater isotopic ratios, (2) variations in isotopic composition of subsiding air, and (3) influence of sea spray.

A boundary layer flow analysis of a magnetohydrodynamic fluid over a shrinking sheet

A steady-state boundary layer flow analysis of a non-Newtonian magnetic fluid over a shrinking sheet was studied. The boundary layer thickness and the velocity distribution in the layer were studied under the conditions of a uniform magnetic field normal to the shrinking sheet and/or a vertical uniform mass suction across the sheet. The similarity transformation method was used to transform the governing partial differential equations to ordinary differential equations. The shooting method with Newton’s algorithm and Runge–Kutta integration method were used to obtain the solutions of the equations. The results showed that the variation of the flow velocity profiles in the boundary layer was significant, the thickness of the boundary layer was thinner, and the skin friction coefficient was bigger for either shear thinning or shear thickening magnetic fluids under the conditions of a stronger magnetic field or a larger mass suction effect.

Convective conditions and dissipation on Tangent Hyperbolic fluid over a chemically heating exponentially porous sheet

Abstract In this present analysis we investigated the steady-state magnetohydrodynamic boundary layer flow of tangent hyperbolic fluid over an exponentially stretching surface in the presence of heat source and chemical reaction. The chemical reaction with combination of exponential surface has significance in many industrial and manufacturing systems. The partial nonlinear differential equations are transformed into ordinary differential equations by using the similarity conversion and the accomplished boundary layer ordinary differential equations are elucidated numerically by using Shooting technique. The effects of numerous non-dimensional governing factors on velocity, temperature and concentration profiles were depicted graphically and analyzed in detail. The numerically computed results of Skin friction factor, Nusselt and Sherwood numbers are presented in tabular form for suction and injection cases separately.Heat transfer rate at the surface increases with increasing values of power law of index and whereas it declines with the magnetic field, heat source and chemical reaction parameters. It observed that Biot number enhances the skin friction, Nusselt number and decrease the Sherwood number.Heat transfer rate and mass transfer rate increases and skin friction decreases with increasing Eckert number.

Numerical Study of Viscoelastic Micropolar Heat Transfer from a Vertical Cone for Thermal Polymer Coating

Abstract A mathematical model is developed to study laminar, nonlinear, non-isothermal, steady-state free convection boundary layer flow and heat transfer of a micropolar viscoelastic fluid from a vertical isothermal cone. The Eringen model and Jeffery’s viscoelastic model are combined to simulate the non-Newtonian characteristics of polymers, which constitutes a novelty of the present work. The transformed conservation equations for linear momentum, angular momentum and energy are solved numerically under physically viable boundary conditions using a finite difference scheme (Keller Box method). The effects of Deborah number (De), Eringen vortex viscosity parameter (R), ratio of relaxation to retardation times (λ), micro-inertia density parameter (B), Prandtl number (Pr) and dimensionless stream wise coordinate (ξ) on velocity, surface temperature and angular velocity in the boundary layer regime are evaluated. The computations show that with greater ratio of retardation to relaxation times, the linear and angular velocity are enhanced whereas temperature (and also thermal boundary layer thickness) is reduced. Greater values of the Eringen parameter decelerate both the linear velocity and micro-rotation values and enhance temperatures. Increasing Deborah number decelerates the linear flow and Nusselt number whereas it increases temperatures and boosts micro-rotation magnitudes. The study is relevant to non-Newtonian polymeric thermal coating processes.

Modelling of the Interaction of Unsteady High-Intensity Turbulence Flow with Heat- and Mass-Transfer in the Boundary Layer on the Surface

The dynamic and thermal characteristics of unsteady near-wall flows are investigated numerically on the basis of two-parameter turbulence models under conditions of high-turbulence free stream and impact of perturbing heat- and mass-transfer factors in the boundary layer. The effect of mass-transfer parameters considered on the permeable section on the development of dynamic and thermal processes in the steady-state turbulent boundary layer is studied and the boundary layer structure along the surface is investigated. The mutual action of time harmonic oscillations of the velocity of outer inviscid free stream and the heat-transfer parameters on wall on the development of time-dependent heat-transfer characteristics in turbulent flow is analyzed. The numerical results are compared with experimental and theoretical data.

Mathematical Modeling of Natural Convection in a Third-Grade Viscoelastic Micropolar Fluid from an Isothermal Inverted Cone

A mathematical model is developed to investigate the nonlinear, isothermal steady-state free convection boundary layer flow in an incompressible third-grade viscoelastic micropolar fluid from a vertical isothermal cone. The non-Newtonian fluid exhibits both viscoelastic and micro-structural characteristics and is representative of certain polymers. The transformed conservation equations for mass, linear momentum, angular momentum and heat are solved numerically subject to realistic boundary conditions using the second-order accurate implicit finite-difference Keller-box method. The numerical code is validated with previous studies and also with a Nakamura tridiagonal method. Detailed interpretation of the computations is included. The present simulations are of interest in chemical engineering systems and solvent and low density polymer materials processing.

Effect of microtexturing on powder boundary layer: An experimental study based on laser microscopy and profilometry measurements

AbstractPowder lubrication can effectively reduce friction under extreme conditions, but powder filling and storage are yet to be improved. In this study, the evolution of the powder boundary layer on microtextured surfaces is investigated. The effect of load and speed on the friction properties of the microtexutured surface is also revealed by using a multifunctional friction and wear tester. Interrupted laser microscopy and profilometry measurements of the friction surface show 4 evolution stages of the powder boundary layer development: localised formation, complete formation, local spalling, and large scuffing of the boundary layer. The steady state boundary layer is characterised with many tadpole‐shaped units and exhibits better lubricity under high load and speed, which effectively delay the damage and improve the life of frictional samples. The present work may provide some new insights to engineers and researchers in designing surface micro/nanotextures with better lubricity and wear resistance.