Boundary Layer Growth Research Articles

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.

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 to 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.

The use of 100 m scale NWP models to understand differences between different measures of mixing height in a morning growing clear convective boundary layer over London

AbstractAn important practical problem is to understand the depth to which pollutants will be mixed in the boundary layer over cities. This is particularly important shortly after sunrise on clear days when the mixed layer is often shallow and there may be large emissions from rush‐hour traffic. The 100 m scale NWP models currently under development have the potential to represent the boundary‐layer structure over cities on neighbourhood scales for air quality and other applications. Here we describe work with Met Office Unified Model (MetUM) configurations with grid lengths of 100, 50 and 25 m to represent the morning growth of a clear convective boundary layer over London compared to observations. All three models explicitly represent the convective overturning although it is not as well resolved at 100 m and this is a particular problem early in the day. It is found that in both the observations and in the models that the depth to which aerosol is mixed up into the model from the surface is lower than the turbulence mixed‐layer depth as measured from the vertical velocity variance. We present an analysis in the 25 m model that shows that the reason for the discrepancy is that the aerosol is transported upwards from the surface by convective plumes whereas further up there is wave motion which does not transport aerosol. The signature for these two layers can be seen both in the 25 m model and in the observations. We discuss the representation of these effects in the coarser‐resolution 100 and 55 m models and also possible mechanisms for the generation of the waves.

Topographic perturbation of turbulent boundary layers by low‐angle, early‐stage aeolian dunes

AbstractDecimeter‐scale early‐stage aeolian bedforms represent topographic features that differ notably from their mature dune counterparts, with nascent forms exhibiting more gently sloping lee sides and a reverse asymmetry in their flow‐parallel bed profile compared to mature dunes. Flow associated with the development of these “protodunes,” wherein the crest gradually shifts downstream towards its mature state, was investigated by studying the perturbation of the turbulent boundary layer over a succession of representative bedforms. Rigid, three‐dimensional models were studied in a refractive‐index‐matched experimental flume that enabled near‐surface quantification of mean velocities and Reynolds stresses using particle‐image velocimetry in wall‐normal and wall‐parallel measurement planes. Data indicate strong, topographically induced flow perturbations over the protodunes, to a similar relative degree to that found over mature dunes, despite their low‐angled slopes. The shape of the crest is found to be an important factor in the development of flow perturbations, and only in the case with the flattest crest was maximal speed‐up of flow, and reduction in turbulent stresses, found to occur upstream of the crest. Investigation of the log‐linearity of the boundary layer profile over the stoss sides showed that, although the profile is strongly perturbed, a log‐linear region exists, but is shifted vertically. A streamwise trend in friction velocity is thus present, showing a behavior similar to the trends in mean velocity. Analysis of the growth of the internal boundary layer on the dune stoss sides, beginning at the toe region, reveals a similar development for all dune shapes, despite clear differences in mean velocity and turbulent stress perturbations in their toe regions. The data presented herein provide the first documentation of flow over morphologies broadly characteristic of subtle, low‐angle, aeolian protodunes, and indicate key areas where further study is required to yield a more complete quantitative understanding of flow–form–transport couplings that govern their morphodynamics.

CO2 variability in the Mexico City region from in situ measurements at an urban and a background site

Urban areas are important contributors to the increase of global CO2 levels due to human activities, but continuous records of CO2 concentration in cities are scarce, especially in the developing world. In this study we present five years of simultaneous, in-situ measurements at a university campus in the south of Mexico City (UNAM) and at a high-altitude station, the Altzomoni atmospheric observatory (ALTZ), 60 km apart from the first site. The characteristics of the daily cycles, seasonality, and long-term trends were extracted from both time series. The features of the daily and seasonal cycles at UNAM are dominated by the dynamics of the boundary layer growth, while the seasonality at Altzomoni is determined by both the local meteorology and the photosynthetic activity of the vegetation. Annual CO2 growth rates of 2.4 and 2.6 ppm yr–1 were estimated for UNAM and Altzomoni, respectively, in close agreement with reported global growth rates and with previous estimates of total column CO2 trends. The simultaneous monitoring at the urban and the mountain sites revealed a regular exchange of air masses between the city and its vicinities. The annual cycle at UNAM shows a secondary CO2 maximum at the end of the dry season, the source of which is yet to be determined, but likely due to incoming air parcels enriched with emissions from agricultural burnings. Likewise, the daily CO2 cycle at ALTZ during the dry season shows evidence of a daily afternoon arrival of polluted air masses from the neighboring urban areas. This study lays the foundation of an upcoming expansion in the CO2 measurement sites and capabilities in the metropolitan area of Mexico City.

Analytical Modeling of Laminar Developing Flow Between Hydrophobic Surfaces With Different Slip-Velocities

Abstract Theoretical analysis of the entrance hydrodynamics of microchannels is an important design aspect in connection with the development of microfluidic devices. In this paper, pressure-driven fluid flow in the entrance region of two infinite hydrophobic parallel plates with dissimilar slip-velocities is analytically modeled. The linearized momentum equation is solved by applying the Navier-slip model at the boundaries to achieve the most generalized two-dimensional form. The velocity profile is obtained by combining the developed and developing velocities, which is estimated by invoking the separation of variable method. It is observed that the velocity profile is asymmetric, and the shear-free region can be shifted from the geometrical central line by altering the wall hydrophobicity. Moreover, the zero shear zone is transferred more toward the surface having high hydrophobicity. The expression for wall shear stress is obtained analytically using Newton's law of viscosity. Moreover, the boundary layer growth from the upper and lower walls is found to be entirely different, and they merge at the entrance length and are noticed to be offsetted from the geometric centerline. The effect of slip-length on the entrance length is analyzed, and an empirical correlation is deduced.

Numerically consistent budgets of potential temperature, momentum, and moisture in Cartesian coordinates: application to the WRF model

Abstract. Numerically accurate budgeting of the forcing terms in the governing equations of a numerical weather prediction model is hard to achieve. Because individual budget terms are generally 2 to 3 orders of magnitude larger than the resulting tendency, exact closure of the budget can only be achieved if the contributing terms are calculated consistently with the model numerics. We present WRFlux, an open-source software that allows precise budget evaluation for the WRF model and, in comparison to existing similar tools, incorporates new capabilities. WRFlux transforms the budget equations from the terrain-following grid of the model to the Cartesian coordinate system, permitting a simplified interpretation of budgets obtained from simulations over non-uniform orography. WRFlux also decomposes the resolved advection into mean advective and resolved turbulence components, which is useful in the analysis of large-eddy simulation output. The theoretical framework of the numerically consistent coordinate transformation is also applicable to other models. We demonstrate the performance and a possible application of WRFlux with an idealized simulation of convective boundary layer growth over a mountain range. We illustrate the effect of inconsistent approximations by comparing the results of WRFlux with budget calculations using a lower-order advection operator and two alternative formulations of the coordinate transformation. With WRFlux, the sum of all forcing terms for potential temperature, water vapor mixing ratio, and momentum agrees with the respective model tendencies to high precision. In contrast, the approximations lead to large residuals: the root mean square error between the sum of the diagnosed forcing terms and the actual tendency is 1 to 3 orders of magnitude larger than with WRFlux.

Aerosol particle characteristics measured in the United Arab Emirates and their response to mixing in the boundary layer

Abstract. Aerosol particles play an important role in the microphysics of clouds and hence in their likelihood to precipitate. In the changing climate already-dry areas such as the United Arab Emirates (UAE) are predicted to become even drier. Comprehensive observations of the daily and seasonal variation in aerosol particle properties in such locations are required, reducing the uncertainty in such predictions. We analyse observations from a 1-year measurement campaign at a background location in the United Arab Emirates to investigate the properties of aerosol particles in this region, study the impact of boundary layer mixing on background aerosol particle properties measured at the surface, and study the temporal evolution of the aerosol particle cloud formation potential in the region. We used in situ aerosol particle measurements to characterise the aerosol particle composition, size, number, and cloud condensation nuclei (CCN) properties; in situ SO2 measurements as an anthropogenic signature; and a long-range scanning Doppler lidar to provide vertical profiles of the horizontal wind and turbulent properties to monitor the evolution of the boundary layer. Anthropogenic sulfate dominated the aerosol particle mass composition in this location. There was a clear diurnal cycle in the surface wind direction, which had a strong impact on aerosol particle total number concentration, SO2 concentration, and black carbon mass concentration. Local sources were the predominant source of black carbon as concentrations clearly depended on the presence of turbulent mixing, with much higher values during calm nights. The measured concentrations of SO2, instead, were highly dependent on the surface wind direction as well as on the depth of the boundary layer when entrainment from the advected elevated layers occurred. The wind direction at the surface or of the elevated layer suggests that the oil refineries and the cities of Dubai and Abu Dhabi and other coastal conurbations were the remote sources of SO2. We observed new-aerosol-particle formation events almost every day (on 4 d out of 5 on average). Calm nights had the highest CCN number concentrations and lowest κ values and activation fractions. We did not observe any clear dependence of CCN number concentration and κ parameter on the height of the daytime boundary layer, whereas the activation fraction did show a slight increase with increasing boundary layer height due to the change in the shape of the aerosol particle size distribution where the relative portion of larger aerosol particles increased with increasing boundary layer height. We believe that this indicates that size is more important than chemistry for aerosol particle CCN activation at this site. The combination of instrumentation used in this campaign enabled us to identify periods when anthropogenic pollution from remote sources that had been transported in elevated layers was present and had been mixed down to the surface in the growing boundary layer.

Numerical Investigation of Geometric Parameters Effects on Heat Transfer Enhancement in a Manifold Microchannel Heat Sink

Microchannel heat sink has been employed and as a part of electronic equipment extensively investigated. In this investigation, heat transfer and fluid flow features of laminar flow of water in a manifold microchannel heat sink (MMHS) was numerically simulated. Selected heat flux was 100 W/m^2 and water was as working fluid. The effect of length of inlet/outlet ratio (λ=Linlet/Loutlet), the height of microchannel (Hch), and width of the microchannel (Wch) at Reynolds number (Re) range from 20 to 100 as independent parameters on the fluid flow and heat transfer features were examined. Obtained results demonstrate that in MMHS, the impinging jet on the bottom channel surface, inhibits the growth of hydrodynamic and thermal boundary layers, resulting in an enhanced heat transfer rate. Also, by increasing Re and keeping the geometric parameters constant, the heat transfer rate increases. Based on the present investigation, for low Re, it is better to choose a λ=Linlet/Loutlet >1 and for high Re, choose a λ<1. For low Re, maximum of performance evaluation criterion (PECmax) is obtained at Hch=300µm, and for high Re, PECmax is obtained at Hch=240µm. for Re=20 to 100, the maximum of PECmax is 1.765 and obtained at Re=100 and Hch=240µm.

Vortex evolution in a rotating tank with an off-axis drain

Fluid entering the periphery of a steadily rotating cylindrical tank exits through an off-axis drain hole, located in the tank's base at the half-radius. Experiments show that, though a concentrated vortex forms over the drain, it soon advects around the tank in what is at first a circular path. Though inviscid vortex dynamics predicts continued motion, our experiments show that the vortex moves inwards from the predicted circular path, finally coming to rest at approximately $50^{\circ }$ from the drain. In this final state, the vorticity is concentrated in a thin shear layer bounding an irrotational core, which passes over the drain. The broadening of the vortex structure and eventual steady-state formation are believed to be due to the growing boundary layer on the outer wall.

Atmospheric humidity deficits tell us how soil moisture deficits down-regulate ecosystem evaporation

Knowing how actual evaporation is down-regulated from potential evaporation during periods with soil moisture deficits is one of the greatest challenges towards computing evaporation everywhere on a regular basis. We propose the hypothesis that vegetated landscapes transmit information on soil moisture deficits through its down-regulation of evaporation, which in turn affects the humidification and growth of the planetary boundary layer. To test this hypothesis, we examined how the evaporative fraction, defined as the ratio between actual and potential evaporation, corresponds with the soil moisture stress index, defined as the relative humidity with a power law dependence on vapor pressure deficit times a parameter, β.We tested the parameterized soil moisture stress index with direct eddy covariance measurements of actual evaporation and computations of potential evaporation based on meteorological conditions, averaged on monthly time steps. The analysis was conducted on a dataset obtained from 144 FLUXNET sites. These sites spanned much of the world's climates and biomes and contained over 5900 months of observations.Observations of the evaporative fraction fit the model of the soil moisture stress index best for semi-arid and arid ecosystems, and least for the humid and wet ecosystems. Consequently, a significant relationship between measurements of the evaporative fraction and soil moisture stress index held for about one-half of the population of sites. Under this condition, the median value of the parameter, β, was 1.41.To investigate the mechanism of this empirical soil moisture stress index, we diagnosed it with a coupled evaporation-planetary boundary layer model. The soil moisture stress index is strongly related to surface resistance, as defined by inverting Penman-Monteith equation. Consequently, this index provides an independent estimate of surface resistance based on easy to measure mean monthly weather conditions like relative humidity and temperature. Thereby, this soil moisture stress index has potential to be applied to weather, climate and biogeochemical models and the interpretation of satellite derived evaporation products, like the one provided by the ECOSTRESS mission.

Significance of Nonsimilar Numerical Simulations in Forced Convection from Stretching Cylinder Subjected to External Magnetized Flow of Sisko Fluid

The practice of flowing effort is participating in various industries especially in nutrition productions all around the world. These fluids practices are utilized extensively in nutrition handling productions by making use of sticky liquids to produce valuable food manufactured goods in bulk. Nevertheless, such productions ought to guarantee that involved equipment such as pipelines are maintained clean as well as are cleared out for the efficient movement of fluids. The nonsimilar characteristics of involuntary convection from circular cylinder stretching in the axial direction subjected to an external flow of Sisko fluid characterized by the freely growing boundary layers (BL) are presented in this research. A circular cylinder is submerged in a stationary fluid. The axial stretching of the cylinder causes external fluid flow. The magnetic force of strength ″ B 0 ″ is enforced in the transverse direction. Because of the fluid's high viscosity, frictional heating due to viscous dissipation is quite significant. The flow is three dimensional but with no circumferential variations. The governing equations for axisymmetric flow that include the mass balance, x -momentum, and heat equation are modeled through conservation laws. The dimensionless system is developed by employing appropriate nonsimilar transformations. The numerical analyses are presented by adapting local nonsimilarity via finite-difference (FDM)-based MATLAB algorithm bvp4c. The characteristics of dimensionless numbers are determined by graphs that are plotted on momentum and heat equations. The nonsimilar simulations have been compared with the existing local similar solutions. Fluid velocity is increased as the material and curvature parameters are increased, resulting in improved heat transfer. The deviation in skin friction and local Nusselt number against the various dimensionless numbers is also analyzed.

Effects of Dufour and thermal diffusion on unsteady MHD free convection and mass transfer flow through an infinite vertical permeable sheet

In this paper, the effects of Dufour and thermal diffusion and on unsteady MHD (magnetohydrodynamic) free convection and mass transfer flow through an infinite vertical permeable sheet have been investigated numerically. The non-dimensional governing equations are solved numerically by using the superposition method with the help of “Tec plot” software. The numerical solution regarding the non-dimensional velocity, temperature, and concentration variables against the non-dimensional coordinate variable has been carried out for various values of pertinent numbers and parameters like the suction parameter left( {v_{0} } right), Prandtl number left( {P_{r} } right), magnetic parameter left( M right), Dufour number left( {D_{f} } right), Soret number left( {S_{0} } right), Schmidt number left( {S_{c} } right), and for constant values of modified local Grashof number left( {G_{{text{m}}} } right) and local Grashof number left( {G_{r} } right).The velocity field decreases for increasing the suction parameter which is focusing on the common fact that the usual suction parameter stabilizing the effect on the boundary layer growth. The thermal boundary layer thickness becomes thinner for rising values of the Dufour and Soret numbers. The skin friction enhances for uplifting values of Soret number and Dufour number but reduces for moving suction parameter, Magnetic force number, Prandtl number, and Schmidt number. The heat transfer rate increases for increasing the suction parameter, Dufour number, Prandtl number, and Soret number. The mass transfer rate increases for enhancing the values of suction parameter, Magnetic force number, Soret number, and Prandtl number but decreases for Dufour number and Schmidt number.

Design, Construction and Evaluation of an Oscillating Vane Gust Generator for Atmospheric Flow Simulation

The study of unsteady aerodynamic phenomena in wind tunnels is supported by gust-generating devices capable of generating adjustable magnitude and periodicity velocity fluctuations in a flowfield. Gusts are typically generated actively by introducing moving vanes to direct the flow, or passively by tailoring the boundary layer growth and shape in the tunnel. The flow facility used here is a student-built closed-return low-speed wind tunnel, with a test section size of 750 mm × 750 mm and a maximum speed of 25 m/s. A two-vane gust generator utilizing NACA0018 airfoil sections of 150 mm chord length was designed and installed upstream of the test section. The flowfield was mapped with the installed vanes with and without gust actuation, utilizing a hot wire system. The tunnel with gust vanes exhibits a spatially uniform baseline turbulence intensity of 5%, with a steady state velocity deficit of 1 m/s in the vane–wake region. Upon introducing the gusting conditions at vane deflection angles of up to ±45°, velocity differences of up to 4 m/s were attained at 18 m/s freestream velocity at oscillation frequencies ranging between 1 Hz and 2 Hz.

Transient growth in a flat plate boundary layer under a stream with uniform shear

One of the simplest problems involving external vorticity in boundary layer flows is the flow over a semi-infinite plate under a stream of uniform shear. We study the transient growth phenomenon in this flow to investigate the role of freestream shear on energy amplification and analyze the differences with the Blasius flow. The initial optimal disturbance that triggers the maximum growth is found to be streamwise vortices, as in other shear flows. Compared to the Blasius boundary layer, higher optimum energy and larger spanwise wavelength of streamwise vortices have been observed. We provide scaling laws for the maximum optimal amplification, which is found to increase exponentially with the freestream shear gradient.

Large eddy simulation of boundary-layer turbulence over the heterogeneous surface in the source region of the Yellow River

Abstract. Lake breezes are proved by downdrafts and the divergence flows of zonal wind in the source region of the Yellow River (SRYR) in the daytime based on ERA-Interim reanalysis data. In order to depict the effect of the circulations induced by surface anomaly heating (patches) on the boundary-layer turbulence, the UK Met Office Large Eddy Model was used to produce a set of 1D strip-like surface heat flux distributions based on observations, which were obtained by a field campaign in the Ngoring Lake basin in the summer of 2012. The simulations show that for the cases without background wind, patch-induced circulations (SCs) promote the growth of convective boundary layer (CBL), enhance the turbulent kinetic energy (TKE), and then modify the spatial distribution of TKE. Based on phase-averaged analysis, which separates the attribution from the SCs and the background turbulence, the SCs contribute no more than 10 % to the vertical turbulent intensity, but their contributions to the heat flux can be up to 80 %. The thermal internal boundary layer (TIBL) reduces the wind speed and forms the stable stratification, which produces the obvious change of turbulent momentum flux and heat flux over the heterogeneous surfaces. The increased downdrafts, which mainly occur over the lake patches, carry more warm, dry air down from the free atmosphere. The background wind inhibits the SCs and the development of the CBL; it also weakens the patch-induced turbulent intensity, heat flux, and convective intensity.

A Parametric Study on the Fluid Dynamics and Performance Characteristic of Micronozzle Flows

Abstract This study investigates the fluid dynamics and performance characteristics in micronozzle flows with changes in various geometric parameters using Navier–Stokes simulation based on slip wall boundary conditions. The various geometric parameters considered for the study are (1) area ratio with fixed throat dimension and (2) the semidivergence angle variation with no change in area ratio. The simulation results show that the flow choking for micronozzle happens not at the geometric throat; rather pushed downstream to the divergent channel of the nozzle. This is due to the thick boundary layer growth, which reduces the effective flow area and shifts the minimum allowable flow area downstream to the throat. The distance to which the choking point shifts downstream to the throat reduces with Maxwell's slip wall conditions compared to the conventional no-slip wall condition. The downstream movement of the choking point from the throat reduces with an increase in area ratio and with increase in divergence angle with fixed area ratio. This is due to the fact that the increase in area ratio and divergence angle increases the nozzle height at any particular section in the divergent portion of the nozzle. As a result of this, the boundary layer profile also moves upward and the restriction of potential core by the thick boundary layer reduces, which in turn leads to an increase in the effective minimum flow area downstream to the throat.

Flow Nonuniformities Behind Accelerating and Decelerating Shock Waves in Shock Tubes

Shock tubes are used to investigate the chemical kinetics and radiative properties of gasses. Analyses of the flow conditions produced in shock tubes typically assume a single, constant shock speed even though the shock speed varies due to driver effects, boundary-layer growth, and diaphragm rupture effects. This paper will investigate the dependence of flow properties upon the entire shock speed history for a 100-mm-diam, 8-m-long shock tube using the FROSST axisymmetric shock tube Navier–Stokes code. A perfect gas is applied to remove the complexity of thermochemistry and allow a focus upon the flow details. Shock speed profiles ranging from accelerating to decelerating are simulated to qualitatively represent different experimental conditions, and the resulting test slugs compared. All shocks reach the test section at the same final shock Mach number of 6.53. Pressure variations caused by the accelerating shock are found to combine with entropy gradients introduced by the changing shock strength, yielding differences in maximum temperature of the test slug by as much as 56%, and differences in maximum pressure as high as 22% despite the shared tube-end Mach number. Local temperature and pressure around gas packets in the test slug are found to relax significantly through time in response to changing postshock conditions. Test slug variations due to boundary-layer effects are found to be present, but overwhelmed by the relaxation processes under many conditions.

The Diurnal Cycle of Entrainment and Detrainment in LES of the Southern Ocean Driven by Observed Surface Fluxes and Waves

AbstractEmpirical rules for both entrainment and detrainment are developed from LES of the Southern Ocean boundary layer when the turbulence, stratification, and shear cannot be assumed to be in equilibrium with diurnal variability in surface flux and wave (Stokes drift) forcing. A major consequence is the failure of downgradient eddy viscosity, which becomes more serious with Stokes drift and is overcome by relating the angle between the stress and shear vectors to the orientations of Lagrangian shear to the surface and of local Eulerian shear over 5 m. Thus, the momentum flux can be parameterized as a stress magnitude and this empirical direction. In addition, the response of a deep boundary layer to sufficiently strong diurnal heating includes boundary layer collapse and the subsequent growth of a morning boundary layer, whose depth is empirically related to the time history of the forcing, as are both morning detrainment and afternoon entrainment into weak diurnal stratification. Below the boundary layer, detrainment rules give the maximum buoyancy flux and its depth, as well a specific stress direction. Another rule relates both afternoon and nighttime entrainment depth and buoyancy flux to surface layer turbulent kinetic energy production integrals. These empirical relationships are combined with rules for boundary layer transport to formulate two parameterizations; one based on eddy diffusivity and viscosity profiles and another on flux profiles of buoyancy and of stress magnitude. Evaluations against LES fluxes show the flux profiles to be more representative of the diurnal cycle, especially with Stokes drift.

Nanofluid flow past a vertical plate with nanoparticle aggregation kinematics, thermal slip and significant buoyancy force effects using modified Buongiorno model

The flow of ethylene glycol-based titania nanoliquid passing through a vertical plate induced by significant buoyancy forces (nonlinear convection) is analyzed with quadratic thermal radiation and considering the aggregation kinematics of the nanoparticles. The nanoliquid is modeled accounting for thermo-migration, Brownian motion, and the effectual thermophysical properties. The realistic zero mass flux and thermal slip conditions are considered on the surface of the plate. In addition, the mechanisms of exponential space-related heat source (ESHS) and thermal-based heat source (THS) are incorporated. The finite-difference technique-based bvp5c routine is used to obtain the numerical solution of thenonlinear system of equations. The effects of the parameters are examined on the dimensionless profiles of velocity, temperature, heat transport rate, the volume fraction of nanoparticles, and streamlines. It was found that the aggregation of nanoparticles significantly advances the temperature field while the velocity field is reduced. The ESHS and THS modulations improve the thickness of the thermal boundary layer. The quadratic thermal convection aspect improves the velocity of nanoliquid. Furthermore, the effects of quadratic thermal radiation assist the growth of the thermal boundary layer. The present results are relevant to various thermal systems including flat plate solar collectors, heat exchangers, and nuclear reactors.