Boundary Layer Growth Research Articles

Modeling nonlinear acoustic damping due to flow separation

Nonlinear acoustic damping has been observed in many high-amplitude acoustic systems as a result of flow separation and shear layer vortical motion, eventually transforming some of the acoustical energy into heat. The amount of nonlinear acoustic damping helps determine the nonlinear limit cycle amplitude, e.g., damping caused by baffle blades in a liquid rocket engine to reduce combustion instabilities. The damping mechanism is dependent on both the location and phase of flow separation. Identifying the flow separation is a function of both the boundary layer growth and the acoustically imposed pressure gradient. When the acoustic pressure gradient is adverse, the boundary layer is more prone to separation. Using this as a basis, a model can be created that is applicable to general geometry, which will then be used to approximate the nonlinear acoustic damping in various situations. The constructed model will be compared to established cases, such as an orifice in a duct, to validate the model.

Evaluating the Response of Diurnal Variations in Surface and Air Temperature to Evaporative Conditions across Vegetation Types in FLUXNET and ERA5

Abstract The diurnal variations of surface and air temperature are closely related, but their different responses to evaporative conditions can inform us about land–atmosphere interactions. Here, we evaluate the responses of the diurnal ranges in surface (ΔTs) and air (ΔTa) temperature to evaporative fraction at 160 FLUXNET sites and in the ERA5 reanalysis. We show that the sensitivity of ΔTs to evaporative fraction depends on vegetation type, whereas ΔTa does not. On days with low evaporative fraction, ΔTs in FLUXNET is enhanced by up to ∼20 K (∼30 K in ERA5) in short vegetation, but only by up to ∼10 K (∼10 K in ERA5) in forests. Note that ΔTa responds rather similarly to evaporative fraction irrespective of vegetation type (∼5 K in FLUXNET, ∼10 K in ERA5). We find a systematic bias in ERA5’s ΔT response to evaporative conditions, showing a stronger sensitivity to evaporative fraction than in FLUXNET. We then demonstrate with a simple atmospheric boundary layer (SABL) model that the weak response of ΔTa to evaporative fraction can be explained by greater boundary layer growth under dry conditions, which increases the heat storage capacity and reduces the response of air temperature to evaporative fraction. Additionally, using a simplified surface energy balance (SSEB) model we show that ΔTs mainly responds to solar radiation, evaporative fraction, and aerodynamic conductance. We conclude that the dominant patterns of diurnal temperature variations can be explained by fundamental physical concepts, which should help us to better understand the main controls of land–atmosphere interactions. Significance Statement Generally, air temperature is used more widely than the surface temperature, and often they are assumed to be equivalent. However, we show that their responses to changes in vegetation type and evaporative conditions are quite different. Using FLUXNET observations, ERA5 reanalysis, and two simple physical models, we found that these responses are much stronger in surface temperature, especially in short vegetation, and relatively weaker in air temperature. Despite being measured just 2 m above the surface, air temperature carries lesser imprints of evaporation and vegetation than the surface temperature because of boundary layer dynamics. These findings suggest the importance of coupled land–atmosphere processes in shaping surface and air temperature differently and provide insights on their distinctive responses to global changes.

Heat gain in an internally dimpled tube heat exchanger - a numerical investigation

Many researchers have looked at heat transfer improvement methods utilizing circular dimpled pipes, surfaces, and other methods in the past. The size and position of dimples, for example, have a major influence on the pipe's flow and thermal properties. Five internally dimpled pipe configurations were analyzed in this computational research. The flow was simulated using ANSYS Fluent 16, with water as the working fluid and steel pipes with internal dimples. The effect of dimple number and diameter on flow and thermal parameters was studied with the five different internal dimple configurations and compared them with plain tube heat exchanger thermal performance under similar conditions. Internal dimples (inside protrusions in tube heat exchanger) resulted in a larger pressure drop in the path of flow from entry to exit. It was discovered that dimples increased the pipe heat exchanger's heat transfer coefficient when compared to the plain tube heat exchanger. A higher pressure loss than plain pipe heat exchangers (HE) was found although the thermal performance was more than that for a plain pipe. The Reynolds number of flows was changed as a result of the pressure drop. When the Reynolds number was lower, the friction factor was found to be higher, resulting in increased heat exchange in the experiment. The results of the numerical analysis for the tube HE with dimples indicate that dimples help mixing of flow in the tube HE and a growth of thermal boundary layer which enhance heat between the hot fluid and cold fluid through the tube HE wall.

Modelling the downstream development of a turbulent boundary layer following a step change of roughness

In this study, we develop an analytical model to predict the turbulent boundary layer downstream of a step-change in the surface roughness where upstream flow conditions are given. We first revisit the classical model of Elliott (Trans. Am. Geophys. Union, vol. 39, 1958, pp. 1048–1054), who modelled the velocity distribution within and above the internal layer with a simple piecewise logarithmic profile, and evolved the velocity profile using the streamwise momentum equation. Elliott's model was originally developed for an atmospheric surface layer, and to make the model applicable to a spatially developing turbulent boundary layer with finite thickness, we propose a number of more physical refinements, including adding a wake function to the velocity profile, considering the growth of the entire boundary layer in the streamwise direction, and using a more realistic shear stress profile in the momentum equation. In particular, we implement the blending model (Li et al., J. Fluid Mech., vol. 923, 2021, p. A18) to account for the deviation of the mean flow within the internal layer from a canonical velocity profile based on the local wall condition. These refinements lead to improved agreement between the prediction and the measurement, especially in the vicinity of the rough-to-smooth change.

Aerosol–stratocumulus interactions: towards a better process understanding using closures between observations and large eddy simulations

Abstract. We carried out a closure study of aerosol–cloud interactions during stratocumulus formation using a large eddy simulation model UCLALES–SALSA (University of California Los Angeles large eddy simulation model–sectional aerosol module for large applications) and observations from the 2020 cloud sampling campaign at Puijo SMEAR IV (Station for Measuring Ecosystem–Atmosphere Relations) in Kuopio, Finland. The unique observational setup combining in situ and cloud remote sensing measurements allowed a closer look into the aerosol size–composition dependence of droplet activation and droplet growth in turbulent boundary layer driven by surface forcing and radiative cooling. UCLALES–SALSA uses spectral bin microphysics for aerosols and hydrometeors, and incorporates a full description of their interactions into the turbulent-convective radiation-dynamical model of stratocumulus. Based on our results, the model successfully described the probability distribution of updraught velocities and consequently the size dependency of aerosol activation into cloud droplets, and further recreated the size distributions for both interstitial aerosol and cloud droplets. This is the first time such a detailed closure is achieved not only accounting for activation of cloud droplets in different updraughts, but also accounting for processes evaporating droplets and drizzle production through coagulation–coalescence. We studied two cases of cloud formation, one diurnal (24 September 2020) and one nocturnal (31 October 2020), with high and low aerosol loadings, respectively. Aerosol number concentrations differ more than 1 order of magnitude between cases and therefore, lead to cloud droplet number concentration (CDNC) values which range from less than 100 cm−3 up to 1000 cm−3. Different aerosol loadings affected supersaturation at the cloud base, and thus the size of aerosol particles activating to cloud droplets. Due to higher CDNC, the mean size of cloud droplets in the diurnal high aerosol case was lower. Thus, droplet evaporation in downdraughts affected more the observed CDNC at Puijo altitude compared to the low aerosol case. In addition, in the low aerosol case, the presence of large aerosol particles in the accumulation mode played a significant role in the droplet spectrum evolution as it promoted the drizzle formation through collision and coalescence processes. Also, during the event, the formation of ice particles was observed due to subzero temperature at the cloud top. Although the modelled number concentration of ice hydrometeors was too low to be directly measured, the retrieval of hydrometeor sedimentation velocities with cloud radar allowed us to assess the realism of modelled ice particles. The studied cases are presented in detail and can be further used by the cloud modellers to test and validate their models in a well-characterized modelling setup. We also provide recommendations on how increasing amount of information on aerosol properties could improve the understanding of processes affecting cloud droplet number and liquid water content in stratiform clouds.

On the use of twisting technique to enhance the performance of helically coiled heat exchangers

This paper introduces an idea to enhance the thermal performance of helically coiled heat exchangers by integrating the effect of using a tube with an elliptical cross section shape with the effect of tube twisting. Numerical simulations showed that the combination of these two effects resulted in disrupting the growth of hydrodynamic and thermal boundary layers leading to better distributions of temperature, velocity, and turbulent kinetic energy compared with the untwisted model with a circular cross section. The Nusselt number was found to be increased significantly by decreasing the aspect ratio of the elliptical tube shape along with increasing the number of tube twisting turns. The average Nusselt number was increased by 29.24% when using aspect ratio of 0.3 with a twist ratio of 0.0327 m. The enhancement in the thermal performance is accompanied with an increase in the pressure drop due to the increased turbulence levels. Findings of this research reveal that this technique is promising in raising the performance of helically coiled heat exchangers. Detailed analysis provided may be useful for future researches on this topic.

Interaction between the turbulent boundary layer flow of superheated vapor and the velocity field induced by liquid vaporization

We consider the heat and mass transfer in the turbulent boundary layer flow over a stationary but evaporating liquid surface via direct numerical simulations. We investigate the influence of the vaporization of a static liquid pool at its saturation temperature on a fully developed turbulent boundary layer of superheated vapor, where the vaporization mass flux is treated as a boundary condition for the wall-normal velocity. It is found that the vaporization enhances the boundary layer growth whilst the friction coefficient and the Stanton number are reduced. Turbulent production is shifted further away from the wall and increased in the logarithmic layer whereas the near-wall dissipation rate is decreased in the viscous sub-layer due to the presence of non-vanishing velocity fluctuations. Spectral analysis showed an associated increase in the cross velocity energy spectrum due to vaporization as well as a shift of the peaks towards smaller wavelengths. A similar behavior is observed for the wall-normal turbulent heat flux spectra. The streamwise velocity energy spectrum decreases in the viscous sub-layer and increases in the logarithmic layer.

Experimental observations on turbulent boundary layers subjected to a step change in surface roughness

Based on experimental data acquired with particle image velocimetry, we examine turbulent boundary layers that are subjected to an abrupt change in wall roughness in the streamwise direction. Three different sandpapers (P24, P36 and P60) together with a smooth wall are used to form a number of different surface transition cases, including both R $\rightarrow$ S (where upstream surface is rough and second surface is either smooth or smoother compared with the upstream surface) and S $\rightarrow$ R (where upstream surface is smoother compared with the downstream surface; both surfaces are rough). This enables us to investigate the effect of the surface transition strength ( $M = \ln [y_{02}/y_{01}]$ , where $y_{01}$ and $y_{02}$ are the roughness lengths of the upstream and downstream surfaces, respectively) on the growth of the internal boundary layer (IBL) and the corresponding flow structure. The results show that for each surface transition group (i.e. R $\rightarrow$ S and S $\rightarrow$ R), the thickness of the IBLs is proportional to the strength of the surface transition, and that the IBLs are thicker for the S $\rightarrow$ R cases compared with their R $\rightarrow$ S counterparts for similar $|M|$ , when normalised by the initial boundary layer thickness ( $\delta _0$ ). The results also show that the growth rates of the IBLs could be represented by a power law, consistent with the previous studies. However, despite a wide range of scatter in the literature for the power-law exponent, an average value of $0.75$ (varies between $0.71$ and $0.8$ with no clear trend) is obtained in the present study considering all the surface transition cases. The pre-factor for the power-law fit, on the other hand, is found to be related to the strength of the surface transition. In addition to the variations in the velocity defect and diagnostic plots with the growth of the IBLs, sweep and ejection events appear to differ significantly (depending on the type of the step change). Two-point spatial correlations, moreover, show that the structure is more elongated in the wall-normal and streamwise directions, as the flow accelerates over the downstream surface (i.e. R $\rightarrow$ S cases). For the reverse transition cases (i.e. S $\rightarrow$ R, where the flow decelerates over the downstream rougher surface), however, the correlation coefficients shrink in size in both directions.

The impact of heat and inflow wind variations on vertical transport around a supertall building – The One Vanderbilt field experiment

The impact skyscrapers have on wind flow remains poorly characterized, thus affecting atmospheric dispersion predictions in dense urban centers. A new mobile observatory equipped with remote sensors controlled by a smart sampling protocol was developed to collect high-resolution (18 m, 15 s) observations throughout the atmospheric layer below 1.5 km. A series of four deployments was performed around the One Vanderbilt skyscraper (H1 = 427 m) located in Manhattan, NY to document wind flow and temperature in canyons with relatively high width-to-depth ratios (H2/W ~ 1.2–7.5; H2 being the height of the adjacent building) and steepness (H1/H2= 2.1–11.2) and that under a range of inflow wind and solar heating conditions.A series of flow features were common to all case studies with head-on winds. A stagnation point was observed 2/3 of the way up the impeded portion of the One Vanderbilt, pointing to the importance of the upwind building height in controlling vertical air flow. In the canyons parallel to the flow, three sets of mirroring counterrotating vortices were detected pointing to the fact that H2 is not as important a parameter in controlling flow in canyons parallel to the inflow wind.Plumes of rapidly rising air were detected near building heat vents under both 10 m s−1 and 3 m s−1 inflow wind conditions, at night and in the morning respectively. This suggests that anthropogenic heat may be an important energy source especially in the absence of solar heating. In the presence of solar heating, a systematic tendency for upward flow was observed above H1. We associate this pattern to the presence of rising thermals, a common mechanism for planetary boundary layer growth. Below H2, complete flow reversal (relative to mechanically driven circulations) was detected ~20 % of the time, showing evidence of dominant thermal effects even under 7 m s−1 inflow wind conditions.

Estimating the Heights of Martian Vortices from Mars 2020 MEDA Data

Small convective vortices occur ubiquitously on Mars, frequently as dust devils, and they produce detectable signals in meteorological data—in pressure, temperature, and wind speed and direction. In addition to being important contributors to the Martian dust budget, convective vortices may serve as probes of the boundary layer, providing clues to convective instability, boundary layer diurnal evolution, and surface–atmosphere interactions. Using vortices as boundary layer probes requires a detailed understanding of the link between their properties and occurrence rates and the conditions that produce them. Fortunately, the growing cache of data from the Mars Environmental Dynamics Analyzer instrument suite on board the Mars 2020 Perseverance rover promises to elucidate these relationships. In this study, we present a catalog of vortex detections from mission sols 90 through 179 to bolster our previous catalog based on sols 15 through 89. Consistent with predictions, we find more vortex encounters during this second half of the mission than from the first half. In addition to analyzing the pressure signals from these vortex encounters, we also use a Gaussian process analysis to recover contemporaneous temperature signals. By combining these signals with a long-established thermodynamics model, we estimate heights of the vortices and find some agreement with previous work and evidence for the diurnal growth and decay of the Martian boundary layer. We also discuss prospects for additional boundary layer studies using Martian vortex encounters.

Mixed convection MHD boundary layer flow, heat, and mass transfer past an exponential stretching sheet in porous medium with temperature-dependent fluid properties

The mixed convection MHD boundary layer flow, heat and mass transfer of a Newtonian fluid mixture across an exponentially stretched permeable sheet in porous medium with Soret and Dufour effects subject to temperature-dependent fluid properties have been investigated numerically. The distribution of temperature and concentration at the surface is supposed to grow exponentially. Temperature is considered to affect fluid viscosity and thermal conductivity. The guiding partial differential equations with appropriate boundary conditions are converted into coupled, nonlinear ordinary differential equations with variable coefficients via a similarity transformation. Matlab's built in solver bvp4c is used to find numerical solutions. Using a graphical approach, the effects of several emerging physical parameters on velocity, temperature and concentration distributions on a flow field of a chemically nonreacting fluid mixture are examined and discussed. Results are compared to earlier literature available and found to be in good agreement. Furthermore, this research demonstrates that flow, heat and mass transmission are greatly influenced by mixed convection parameters, magnetic field, Prandtl number, viscosity, conductivity, permeability, and Schmidt number. Skin friction grows for mixed convection parameter, magnetic, viscosity. Highest growths of wall temperature and wall concentration gradients are observed for Prandtl number and Schmidt number, respectively. HIGHLIGHTS Heat and mass transfer rates increase with higher values of mixed convection parameters and Darcy parameter. To reduce heat transfer rate magnetic field may be used. Fluid with lower thermal conductivity and with higher Prandtl number may be employed to boost the cooling rate in conducting flows. Higher Schmidt enhances mass transfer rates. Suction stabilizes boundary layer growth. Soret effect can be used to separate light and medium molecular weight components from a fluid mixture and hence can be used for control of air pollution.

A Conservation-Based Transitional Boundary Layer Model

Abstract A simple, flow-physics-based model of flat-plate, transitional boundary layer skin friction and heat transfer is presented. The model is based on the assumption of negligible time-, spanwise-, and streamwise-average wall-normal velocity at the top of the boundary layer. This results in a threefold increase in boundary layer thickness over the transition region. This simple velocity assumption and its boundary-layer growth implications seem to be reasonably consistent with more sophisticated (direct numerical simulation (DNS)) modeling simulations. Only two modeling parameters need to be assumed, the Reynolds numbers at the onset and at the completion of transition, for which there is guidance based on freestream turbulence intensity for smooth plates. Several experimental datasets for air are modeled. New criteria are proposed to help define the onset and completion of transition: zero net vertical (wall-normal) velocity or mass flux (integrated in time and space, spanwise and streamwise) at the top of the boundary layer, and tripling of boundary layer thickness. Also presented is a minor improvement to a previously published unheated starting length factor for flat-plate laminar boundary layers with uniform wall heat flux.

Effects of flow fluctuations and buoyancy on heat transfer from a sphere in non-Newtonian nano fluids: Potential for intensification

This work numerically explores the combined effects of buoyancy-induced flow and pulsating velocity for nanofluids (power-law type fluids) over a sphere to ascertain the potential of this approach for process intensification. The pertinent field equations are solved numerically for a range of dimensionless variables as, Richardson number (0 ≤ Ri ≤ 5), amplitude of fluctuations (0 ≤ A ≤ 0.8), frequency of pulsation (π/4 ≤ ω* ≤ π), Reynolds number (5 ≤ Re ≤ 100), power-law index (0.3 ≤ n ≤ 1.5) and Prandtl number (1 ≤ Pr ≤ 100). The aiding-buoyancy flow suppresses the transient effects of the flow pulsations. The recirculation length (wake) is considerably shortened as the buoyancy-driven flow strengthens. Even a weak buoyancy-induced flow (for instance, Ri = 1) is sufficient to mar the influence of pulsatile velocity. The Richardson and Prandtl numbers do not influence the phase difference in the growth of the momentum boundary layer. Overall, the improvement in the Nusselt number is significantly lowered by the aiding-buoyancy mixed convection than that in the forced convection regime. While this may seem like a detrimental effect on the overall heat transfer, this offers a potential tool for modulating the rate of heat transfer for the processing of temperature-sensitive materials wherein the main consideration is to limit the maximum temperature in the system. The present results can be used to devise an operating envelope of conditions depending upon the envisaged application. Finally, the mean Nusselt number is correlated by using the modified velocity and viscosity scales accounting for the contribution of the mean flow and the buoyancy-induced flow.

Assessment of Reynolds-stress models for aeronautical applications

Three Reynolds-Stress Models (RSMs) have been benchmarked on industrial configurations with aeronautical applications. The models are first compared on a zero-pressure-gradient boundary layer, which highlights the differences in the near-wall approaches of the models. Results are then analyzed for the Skåre & Krogstad adverse-pressure-gradient boundary layer and the Common Research Model (CRM) aircraft for two Reynolds numbers. Both cases display improvements in using RSMs over the eddy-viscosity Spalart-Allmaras model. Two of the considered second-moment closures better predict the boundary layer growth and its shape factor in the Skåre & Krogstad test case, and all noticeably improve the drag-due-to-lift in the CRM case.

Unsteady Separated Stagnation-Point Flow Past a Moving Plate with Suction Effect in Hybrid Nanofluid

Previous research has shown that incorporating stagnation-point flow in diverse manufacturing industries is beneficial due to its importance in thermal potency. Consequently, this research investigates the thermophysical properties of the unsteady separated stagnation-point flow past a moving plate by utilising a dual-type nanoparticle, namely a hybrid nanofluid. The impact of suction imposition on the entire hydrodynamic flow and heat transfer as well as the growth of boundary layers was also taken into account. A new mathematical hybrid nanofluid model is developed, and similarity solutions are obtained in the form of ordinary differential equations (ODEs). The bvp4c approach in MATLAB determines the reduced ODEs estimated solutions. The results show that increasing the stagnation strength parameters expands the skin friction coefficient and heat transfer rate. The addition of the suction parameter also resulted in an augmentation of thermal conductivity. Interestingly, reducing the unsteadiness parameter proportionately promotes heat-transfer performance. This significant involvement is noticeable in advancing industrial development, specifically in the manufacturing industries and operations systems.

Design and testing of an additively manufactured flameholder for scramjet flows

A small-scale cavity flameholder for high-speed, premixed ethylene combustion has been designed, additively manufactured, and tested at Mach 5 enthalpy. The work has enabled a comprehensive study on the effects of flow compressibility and heat release on turbulent flame structures and stabilization mechanisms. The cavity is sized to produce a practical computational domain for Direct Numerical Simulations. Likewise, the flameholder is supported away from the flow path walls to minimize boundary layer growth upstream and simplify the numerical calculations. Optical access is provided for laser diagnostics. Challenges related to transforming a direct-connect combustor flow path into a semi-free jet flow path for immersed models were encountered, primarily flow blockage and heat removal. The final design can sustain an ethylene flame for repeated cycles lasting more than an hour. The flameholder was fabricated from Inconel 718 with internal cooling passages incorporated throughout. This paper presents a methodology for design and fabrication of additively manufactured scramjet combustor components and documents the first published conversion of a direct-connect, high-speed combustion wind tunnel to a semi-free jet configuration. While additive manufacturing enables novel designs with complex geometries, residual stresses and geometric distortion are notable concerns that must be considered in the design stages.

Partially-covered fractal induced turbulence on fins thermal dissipation

The impacts of partially-covered fractal grids induced turbulence on the forced convective heat transfer across plate-fin heat sink at Reynolds number ReDh = 22.0 × 103 were numerically and experimentally investigated. Results showed that partially covered grids rendered a higher thermal dissipation performance, with partially-covered square fractal grid (PCSFG) registering an outstanding increase of 43% in Nusselt number relative to the no grid configuration. The analyzation via an in-house developed single particle tracking velocimetry (SPTV) system displayed the findings of unique “Turbulence Annulus” formation, which provided a small degree of predictivity in the periodic annulus oscillations. Further assessments on PCSFG revealed the preferred inter-fin flow dynamics of (i) high flow velocity, (ii) strong turbulence intensity, (iii) vigorous flow fluctuations, (iv) small turbulence length scale, and (v) heightened decelerated flow events. These features stemmed from the coupling effects of multilength-scale fractal bar thicknesses in generating a veracity of eddy sizes, and a vertical segmentation producing heightened mass flow rate while inducing favourable wake-flow structures to penetrate inter-fin regions. Teeming effects of such energetic eddies within plate-fin array unveiled a powerful vortex shedding effect, with PCSFG achieving fluctuation frequency f = 18.5 Hz close to an optimal magnitude. The coaction of such traits limits the growth of fin boundary layers, providing superior thermal transfer capabilities which benefits the community in developing for higher efficiency heat transfer systems.

Traveling waves of an FKPP-type model for self-organized growth

We consider a reaction–diffusion system of densities of two types of particles, introduced by Hannezo et al. (Cell 171(1):242–255.e27, 2017). It is a simple model for a growth process: active, branching particles form the growing boundary layer of an otherwise static tissue, represented by inactive particles. The active particles diffuse, branch and become irreversibly inactive upon collision with a particle of arbitrary type. In absence of active particles, this system is in a steady state, without any a priori restriction on the amount of remaining inactive particles. Thus, while related to the well-studied FKPP-equation, this system features a game-changing continuum of steady state solutions, where each corresponds to a possible outcome of the growth process. However, simulations indicate that this system self-organizes: traveling fronts with fixed shape arise under a wide range of initial data. In the present work, we describe all positive and bounded traveling wave solutions, and obtain necessary and sufficient conditions for their existence. We find a surprisingly simple symmetry in the pairs of steady states which are joined via heteroclinic wave orbits. Our approach is constructive: we first prove the existence of almost constant solutions and then extend our results via a continuity argument along the continuum of limiting points.

On the enhancement of boundary layer skin friction by turbulence: an angular momentum approach

Turbulence enhances the wall shear stress in boundary layers, significantly increasing the drag on streamlined bodies. Other flow features such as free stream pressure gradients and streamwise boundary layer growth also strongly influence the local skin friction. In this paper, an angular momentum integral (AMI) equation is introduced to quantify these effects by representing them as torques that alter the shape of the mean velocity profile. This approach uniquely isolates the skin friction of a Blasius boundary layer in a single term that depends only on the Reynolds number most relevant to the flow's engineering context, so that other torques are interpreted as augmentations relative to the laminar case having the same Reynolds number. The AMI equation for external flows shares this key property with the so-called FIK relation for internal flows (Fukagata et al., Phys. Fluids, vol. 14, 2002, pp. L73–L76). Without a geometrically imposed boundary layer thickness, the length scale in the Reynolds number for the AMI equation may be chosen freely. After a brief demonstration using Falkner–Skan boundary layers, the AMI equation is applied as a diagnostic tool on four transitional and turbulent boundary layer direct numerical simulation datasets. Regions of negative wall-normal velocity are shown to play a key role in limiting the peak skin friction during the late stages of transition, and the relative strengths of terms in the AMI equation become independent of the transition mechanism a very short distance into the fully turbulent regime. The AMI equation establishes an intuitive, extensible framework for interpreting the impact of turbulence and flow control strategies on boundary layer skin friction.

Rheological Modeling of Metallic Oxide Nanoparticles Containing Non-Newtonian Nanofluids and Potential Investigation of Heat and Mass Flow Characteristics.

Nanofluids have great potential due to their improved properties that make them useful for addressing various industrial and engineering problems. In order to use nanofluids on an industrial scale, it is first important to discuss their rheological behavior in relation to heat transfer aspects. In the current study, the flow characteristics of nanofluids are discussed using a mathematical model that is developed by fundamental laws and experimental data. The data are collected in the form of viscosity versus shear rate for different homogeneous ethylene glycol- (EG) based nanofluids, which are synthesized by dispersing 5–20% nanoparticle concentrations of SiO2, MgO, and TiO2 with diameters of (20–30 nm, 60–70 nm), (20 nm, 40 nm), and (30 nm, 50 nm), respectively. The data are fitted into a rheological power-law model and further used to govern equations of a physical problem. The problem is simplified into ordinary differential equations by using a boundary layer and similarity transformations and then solved through the numerical Runge–Kutta (RK) method. The obtained results in the form of velocity and temperature profiles at different nanoparticle concentrations and diameters are displayed graphically for discussion. Furthermore, displacement and momentum thicknesses are computed numerically to explain boundary-layer growth. The results show that the velocity profile is reduced and the temperature profile is raised by increasing the nanoparticle concentration. Conversely, the velocity profile is increased and the temperature profile is decreased by increasing the nanoparticle diameter. The results of the present investigation regarding heat and mass flow behavior will help engineers design equipment and improve the efficacy and economy of the overall process in the industry.