Free Convection Regime Research Articles

Flux‐gradient relations and their dependence on turbulence anisotropy

AbstractMonin–Obukhov similarity theory (MOST) is used in virtually all Earth System Models to parametrize the near‐surface turbulent exchanges and mean variable profiles. Despite its widespread use, there is high uncertainty in the literature about the appropriate parametrizations to use. In addition, MOST has limitations in very stable and unstable regimes, over heterogeneous terrain and complex orography, and has been found to represent the surface fluxes incorrectly. A new approach including turbulence anisotropy as a non‐dimensional scaling parameter has recently been developed and has been shown to overcome these limitations and generalize the flux‐variance relations to complex terrain. In this article, we analyze the flux‐gradient relations for five well‐known datasets, ranging from flat and homogeneous to slightly complex terrain. The scaling relations show substantial scatter and highlight the uncertainty in the choice of parametrization even over canonical conditions. We show that, by including information on turbulence anisotropy as an additional scaling parameter, the original scatter becomes well bounded and new formulations can be developed that drastically improve the accuracy of the flux‐gradient relations for wind shear () in unstable conditions and for temperature gradient () in both unstable and stable regimes. This analysis shows that both and are strongly dependent on turbulence anisotropy and allows us finally to settle the extensively discussed free convection regime for , which clearly exhibits a power law when anisotropy is accounted for. Furthermore, we show that the eddy diffusivities for momentum and heat and the turbulent Prandtl number are strongly dependent on anisotropy and that the latter goes to zero in the free convection limit. These results highlight the necessity to include anisotropy in the study of near‐surface atmospheric turbulence and lead the way for theoretically more robust simulations of the boundary layer over complex terrain.

The appearance of oscillatory flows within a horizontal packed bed partly heated from below

We report on a numerical investigation of the unsteady mixed convective flow in a channel through a horizontal porous layer under localised isothermal heating from below to probe the oscillatory flow and thermal characteristics. The study was carried out for water flow within a plane channel containing stainless steel spherical particles. For this study, the channel height/particle diameter ratio was H/d=100 and the porosity was ɛ=0.35. The effects of the imposed pressure-driven flow characterised by the Péclet number (0.1≤Pe≤1000), and heating represented by the Rayleigh number (105≤Ra≤2×107), are investigated. The results reveal that for low Péclet numbers, steady free convective flows are dominant, while for high Péclet numbers, steady forced convective flows dominate. Importantly, no oscillatory flows are found to develop in the free and forced convection regimes. However, for moderate Péclet numbers, oscillatory mixed convective flows occur with different periodic, quasi-periodic, and chaotic flow behaviours. In addition, for low Rayleigh numbers, Ra≤106, the Nusselt number is not influenced by the Péclet number for Pe≤1. Nevertheless, for high Rayleigh numbers, Ra≥2×106, it is observed that there always exists a critical Péclet number for which the Nusselt number is a minimum. The effects of the Péclet and Rayleigh numbers on the local and average temperature disparity between the fluid and solid phases are then investigated.

Turbulent cylindrical heat flow visualization in free convection regime

Turbulent cylindrical heat flow visualization in free convection regime

Numerical simulation for nanofluid forced/free convection in a partially heated parallelogram enclosure: Effects of wall undulation and inclined Lorentz forces

AbstractThe present study possesses the mathematical computational analysis for mixed convection nanofluid (CuO–water) flow in a lid‐driven parallelogram enclosure with corrugated walls. A partially heated source is located at the bottom corrugated wall. The remaining portions of upper and lower corrugated boundaries are adiabatic. The verticals walls are kept cold. The flow dynamic established with wall undulation and inclined Lorentz forces generate complex mathematical formulation via partial differential equations. Finite element method is implemented to get numerical interpretation of these equations. The simulation is performed against various emerging parameters and the outcomes in terms of isotherms, streamlines and line graphs. The results are recorded against various Richardson numbers , Hartman number , nanoparticles volume fraction , and amplitude of the corrugated horizontal walls . It is observed that against smaller Richardson number streamlines indicate forced convection flow while at higher Richardson number flow divert toward free convection regime. Additionally, heat transportation is maximum when magnetic field is applied in perpendicular direction as well as at maximum amplitude of wall undulations.

Development of correlations for steam condensation over a vertical tube in the presence of noncondensable gas using machine learning approach

Steam condensation is an important phenomenon encountered in nuclear reactor under severe accidents. Even though many correlations for predicting steam condensation heat transfer coefficient (HTC) in the presence of noncondensable gas (NCG) have been proposed over the past decade, a more reliable and accurate model is still required. Thus, in this study, multigene genetic programming (MGGP), a biologically inspired machine learning method, is applied to develop new correlations for condensation HTC of steam-NCG mixture over a vertical tube in turbulent free convection regime. To this end, a consolidated database with 1440 data points from 18 sources is compiled. Then, using the database, both a new empirical correlation and a MGGP model are developed for better comparison. The performance of the MGGP-based correlation selected using Pareto tournaments strategy is compared with the new developed empirical correlation and another 20 relevant correlations. The results reveal the superiority of the MGGP-based correlation. In addition, it is found that the tube length is excluded in the best-trained correlation, even though it is used as the input of MGGP, which agrees well with the results of previous theoretical and experimental studies. The present study demonstrates that MGGP is promising in developing explicit, accurate, and compact models for the complex heat transfer and multiphase flow phenomena such as steam condensation in the presence of NCG.

Impacts of uniform and sinusoidal heating in a nanofluid saturated porous chamber influenced by the thermal radiation and the magnetic field

A numerical investigation on the impacts of heater length increased from left corner along with the bottom wall in a Cu-water nanofluid-filled porous cavity in the existence of MHD and thermal radiation is performed out. The bottom wall is heated with two different types of heater (both uniform and nonuniform) separately. Three various lengths of heater are considered. Constant cold upper horizontal wall moves in the positive direction. The other sidewalls and excluding the heating portion of the bottom wall are considered to be adiabatic. The system of dimensionless form of governing equations is solved by finite volume method (FVM) with appropriate boundary and initial conditions and SIMPLE algorithm has been employed for the pressure term. For both types of heating, the highest heat transfer is attained with the length of heater for all taken Richardson number. The effect of magnetic field is very low on heat transfer with the thermal source length and nonuniform heating in free convection regime. On increasing the heater length in nonuniform heating, overall heat transfer rate is decreased first and then raised. The percentage of increasing of average Nusselt number with an increase of thermal radiation parameter in nonuniform heating is higher than uniform heating. The effect of magnetic field is significant for all taken solid volume fraction in uniform heating than the nonuniform heating with heater length

On the Influence of Thermal Stratification on Emitted Dust Flux

AbstractThe influence of the atmospheric boundary layer (ABL) stability on dust emitted from saltation is usually neglected. This has been challenged by two recent studies which suggested a dependency of the dust emission flux particle size distribution (PSD) to the thermal stratification. Both studies observed a dust flux enrichment in fine particles with instability but for two different explanations: (a) a larger eddy diffusivity of submicron particles with instability, and (b) an enhanced turbulence and friction velocity u* stochasticity with instability, increasing saltation bombardment and fine‐dust emission. Here, we discuss and investigate these two propositions using the WIND‐O‐V (WIND erOsion in presence of sparse Vegetation's) 2017 data set. We first show that the first explanation and the observed stability effect on the dust flux are questionable. We, then, investigate the second explanation in the context of the enhanced influence of ABL‐scale motions on the near‐surface turbulence and u* stochasticity with increasing instability. This second explanation appears only possible at the transition between windy and free convection regimes where u* is close to its erosion threshold value. However, this intermediate regime appears more convective than the erosion event from whom the second explanation was proposed. Overall, our results show no thermal stability effect on the dust emission flux PSD. Instead, u* and the air relative humidity seem to be the main meteorological variables influencing the dust emission flux PSD. We, in particular, suggest that the air relative humidity may have affected the surface soil moisture, and thus the interparticle cohesion, through water vapor adsorption.

Constructal enhancement of cooling performance of local heating elements with different heat generation rates under free and mixed convection regimes

This study aims to obtain the optimum heat generation rate of local heating elements with different heat generation rates in a vertical duct. Covering free and mixed convection regimes, experimental and numerical studies are conducted. Various values of the modified Grashof and Reynolds numbers are taken into account. The influence of the heat generation rates of local heating elements on temperature of the hot spot, local temperatures, system's global conductance and Nusselt number are presented. It is shown that the heating elements with co-heat generation rates cause a rise in the temperature of the hot spot and reduce the global conductance, and the gradual decrease in the heat generation rates of heating elements improves the system's cooling performance.

Augmentation in heat transfer for a hybrid nanofluid flow over a roughened surface

Heat transfer characteristics of mixed convective flow of a hybrid nanofluid along a wavy surface are investigated. Dimensionless equations of the problem are solved utilizing finite difference method. Numerical results revealed that for increasing the amplitude-wavelength ratio, magnetic field strength and volume fractions of Cu and Al2O3 nanoparticles, the thermal boundary-layer increases. Skin friction coefficient and local Nusselt number considerably increase owing to the increase of the volume fractions of nanoparticles and magnetic field parameter. Heat transfer for a flat surface is remarkably higher than that for a wavy surface except around the crests of it. Whatever the forced, mixed or free convection regimes, skin friction coefficient and local Nusselt number are almost linearly correlated with the volume fraction of nanoparticles. Moreover, the Cu nanoparticles provide higher heat transfer than the Al2O3 nanoparticles. It is recognized that the local Nusselt number calculated on 5% volume fraction of Cu nanoparticles is higher by 0.5%, 1.0% and 7.7% respectively for forced, mixed and free convection processes, however, when the volume fraction of nanoparticles is 8% the corresponding increments are 0.9%, 1.6% and 13.3%.

Filmwise Condensation From Humid Air on a Vertical Superhydrophilic Surface: Explicit Roles of the Humidity Ratio Difference and the Degree of Subcooling

Abstract The process involving heat and mass transfer during filmwise condensation (FWC) in the presence of noncondensable gases (NCG) has great significance in a large variety of engineering applications. Traditionally, the condensation heat transfer is expressed in the literature as a function of the degree of subcooling—reckoned as the difference between the ambient dry bulb temperature and the condenser wall temperature. However, in the presence of NCG, there exists a finite gradient of vapor mass fraction near the condenser plate, which directly influences the vapor mass flux to the condenser surface, thus limiting the condensation rate. The effects of both these influencing thermodynamic parameters, i.e., the degree of subcooling and the difference of humidity ratio (between the freestream environment and on the condenser plate), have been characterized in this work both experimentally and through a mechanistic model. The vapor mass flux during condensation on a subcooled vertical superhydrophilic surface under free convection regime is experimentally measured in a controlled environment (temperature and humidity) chamber. The mechanistic model, based on the similarity of energy and species transports, is formulated for the thermogravitational boundary layer over the condenser plate and tuned against the experimental results. Further, the model is used to obtain comprehensive data of the condensate mass flux and condensation heat transfer coefficient (CHTC) as functions of the salient thermal operating conditions over a wide parametric range. Results indicate that humidity ratio difference has a more pronounced influence on the condensation mass transfer rather than the degree of subcooling. Regime maps of condensate flux and CHTC show how these can be explicitly identified in terms of the degree of subcooling and humidity ratio difference, regardless of the prevailing thermal and humidity conditions at the freestream and the condenser plate. The mechanistic model thus lends to the development of empirical correlations of condensate mass flux and CHTC as explicit functions of these two parameters for easy use in practical FWC configurations.

Development of a general correlation for free convection vapor condensation over a horizontal tube in the presence of a noncondensable gas

In applications involving external condensation in the presence of noncondensable gases (NCG), there is a growing interest in horizontal tubes because they minimize condensate resistance, and hence reduce the adverse effects of NCGs. In the literature, experimental heat transfer rates are summarized in empirical correlations that fit the underlying data, but do not cover the spectrum of possible steam-NCG mixtures and thermal conditions. In this work, we aim at developing a general correlation that is applicable to a wide range of physical and geometrical conditions.We first present a CFD model for laminar free convection regimes, taking into account the resistance of the gas phase and the liquid condensate. The model is validated against recent condensation data on steam-N2 and steam-CO2 mixtures. The predictions agree well with the data, being mostly within the experimental uncertainty.Subsequently, close to 200 parametric CFD simulations are conducted for steam-air mixtures across a wide range of steam mass fraction (0.05–0.99), wall temperature subcooling (5-50 K), pressure (1–5 bar) and tube diameter (0.01–0.04 m). The resulting data are cast in a compact correlation that is compatible with the heat and mass transfer analogy. The proposed correlation is in good agreement with empirical correlations in the literature.

Experimental investigation of transient pool boiling characteristics of [formula omitted] ferrofluid in comparison with deionized water

Pool boiling heat transfer and critical heat flux (CHF) in ferrofluid were experimentally studied under transient power conditions. The heat flux increment was begun from the free convection regime to the film boiling regime. Transient boiling heat transfer coefficient (TBHTC), transient CHF, scanning electronic microscopy (SEM) images of surface wire, and high-speed camera images were obtained. The following results were obtained for ferrofluid: as the time period increased, (1) the heat transfer coefficient of the nucleate boiling increased because of bubble production and its movement, then decreased in the transition from the nucleate to the film boiling because of an unstable layer of vapor around the wire heater and finally increased again in the film boiling because of the high temperature of the wire surface and radiation heat transfer; (2) the CHF and its wire superheat temperatures at CHF point decreased by up to a period of 100 s; (3) the incipient boiling point decreased. In the second part of the film boiling, the heat transfer coefficient was decreased because of the high heat flux and the more vapor film thickness around the wire. A comparison between two working fluids show that by increasing the time period, the nucleate boiling range of ferrofluid boiling was increased more than the deionized (DI) water boiling. Furthermore, the wire superheat temperature of the ferrofluid in all its regimes was decreased and the CHF of ferrofluid boiling were increased more than the DI water boiling. The ferrofluid CHF at the time period of 1 s decreased by 11.3% relative to DI water, and at the time period 5000 s increased by 160%.

Heating of liquid foods in cans: Effects of can geometry, orientation, and food rheology

AbstractIn this work, the effect of geometry and orientation of food cans on the heating characteristics of processed liquid foods and the resulting lethality target values as a function of the processing times have been investigated. For this purpose, the governing differential equations have been solved numerically for elliptical and cylindrical cans of varying aspect ratios in different orientations in order to delineate their effect on the heating rate (especially of the slowest heating zone [SHZ]) and lethality values over wide ranges of rheological features including shear thinning (n < 1), Newtonian (n = 1), and shear thickening (n > 1) behaviors. The flow and heat transfer characteristics were analyzed with the help of velocity vectors, isotherm contours, average Nusselt number, SHZ temperature and heat penetration parameters, and lethality target values. Also, comparisons were made in terms of the sterilization time and heat penetration parameters to identify the preferable geometries and orientations of food cans for effective heating of non‐Newtonian foodstuffs. Finally, favorable conditions in terms of the shape and orientation of the can and the rheological properties have been delineated which lead to superior heating characteristics.Practical ApplicationsProcessed foodstuffs are produced in various forms ranging from that in solid, liquid, or as heterogeneous mixtures. Often such liquid and heterogeneous suspensions products are viscous non‐Newtonian in character and their thermal processing (including pasteurization, sterilization, etc.) tends to be much more challenging than that of their Newtonian counterparts like air and water. This work explores heating of non‐Newtonian liquid foodstuffs in cans of various shapes, geometries and in different orientations in the free convection regime. The results show that depending upon the rheological properties of the products, some orientations and/or geometries offer potential advantages in terms of shorter processing times and lethality values. This information can be of great potential in customizing the design of containers for different food products as well as of different rheological properties.

Pool Boiling of Dilute Emulsions on Flat Surfaces

We report measurements of steady state boiling heat transfer in a dilute emulsion of FC72™ in water on upward and downward facing surfaces. Augmented heat transfer coefficients are expressed as a free convection regime followed by a significant increase when the surface temperature exceeds the saturation temperature of the disperse component. Augmented heat transfer coefficients reach three times that in free convection for all volume fractions at surface temperatures near the saturation temperature of the continuous component, followed by a rapid decrease as film boiling commences. For the downward facing surface, the augmentation effect is seen when the surface temperature approaches the saturation temperature of the continuous component. At that point, the presence of the disperse component produces a doubling of the heat transfer coefficient.

Correcting for tube curvature effects on condensation in the presence of a noncondensable gas in laminar regimes

Filmwise vapor condensation in the presence of noncondensable gases (NCG) continues to attract interest due to its widespread range of applications. In studies of NCG effects on condensation over external surfaces, experimentalists and analysts alike usually employ correction factors to transfer tube condensation rates to flat plate equivalents or vice-versa. For laminar flows over vertical cylinders, these factors are estimated from pure convection correlations as a function of the Grashof number and tube curvature only. We show that this procedure is not rigorous and leads to significant errors, especially at low NCG fractions and small tube radii. Indeed, the usual way of correcting for curvature is strictly valid only in the limit where the NCG fraction is so large that convection heat transfer dominates condensation. On the other hand, as the NCG fraction becomes vanishingly small, the vapor condensation rates should tend to values predicted by the Nusselt film theory, and no enhancement due to tube curvature is to be expected.This paper focuses on vapor condensation as the gas mixture moves along a vertical tube in the laminar free convection regime. The gas and liquid film boundary layer equations are coupled at the gas/film interface and a marching solution procedure using local non-similarity is adopted. The methodology is first verified for near pure free convection flows as well as previous analyses of condensation over a flat surface. The model is subsequently validated against data on steam condensation on a square plate in the presence of air. Finally, a correlation is deduced from the parametric numerical results to allow a proper correction for curvature effects when vapor condenses in the presence of a NCG. The proposed correction spans the whole range of NCG fractions, and displays the expected behavior at the extremes of this range.

Combined MHD convection and thermal radiation of nanofluid in a lid-driven porous enclosure with irregular thermal source on vertical sidewalls

Mixed convective heat transfer of Cu–water nanofluid in a porous cavity with non-uniform temperature profiles on vertical sidewalls in the presence of thermal radiation and magnetic field is examined numerically. The vertical sidewalls are heated sinusoidally. Thermally insulated walls are considered at the remaining sides of the cavity. The magnetic field is applied parallel to the horizontal walls uniformly. The SIMPLE algorithm based on finite volume approach is applied to solve the governing equations. The numerical outcomes are discussed in the wide range of the parameters, Richardson number, phase deviation, amplitude ratio, Darcy number, Hartmann number, the thermal radiation, and the solid volume fraction. It is found that the average Nusselt number is decreased in value with the raise in the either Hartmann number or Richardson number in the presence of thermal radiation. The average heat transfer rate is enhanced with an augment in the solid volume fraction, and this enhancement is more effective in the presence of thermal radiation than that of in the absence of thermal radiation. The highest heat transfer rate is obtained for $$\varphi =0$$ in the forced convection regime, whereas it is maximum at $$\varphi =3\pi /4$$ in the mixed and free convection regimes.

Experimental study of the time period of continued heating rate on the pool boiling characteristics of saturated water

Pool boiling heat transfer and critical heat flux (CHF) in saturated water were experimentally studied under transient power conditions. A chrome-aluminum-iron alloy wire supported horizontally in a pool of water was used as the heating element. The heating rate in the test section was increased linearly depending on time by applying voltage control for 1 s to 5000 s. The heat flux was obtained by a second-order function of time. In this study, the increase in heat flux starts from the free convection regime to the film boiling regime. The transient boiling heat transfer coefficient (TBHTC), transient wire superheat temperature, transient heat flux and transient CHF were also obtained. The results showed that with increasing the time period, the TBHTC in the nucleate boiling increased, decreased in transition from the nucleate boiling to the film boiling, and again increased in the film boiling and the incipient boiling point decreased which may be due to a decreased number of nucleation sites and the explosive nature of the initial stage of nucleate boiling. The TBHTC decreased in the second part of the film boiling as both the heat flux and the vapor film thickness around the wire had increased. In addition, increasing the time period decreased the CHF and superheating temperatures in the CHF by up to a period of 100 s. After that, its trend approached the steady state boiling. The transient CHF reduction in the time period of 100 s is 40.5% relative to steady state condition which is the minimum transient CHF. The maximum increase in the transient CHF is in the time period of 1 s and equals to 46.7%. A high-speed camera was used to show bubble and vapor film behavior around the heating wire.

On Moisture Flux of the Indian Summer Monsoon: A New Perspective

AbstractMoisture flux is the driver of the Indian summer monsoon on all space‐time scales and its accurate representation in monsoon simulation models is crucial. For the first time, the moisture flux measurements are made over India during the PRWONAM (Prediction of Regional Weather using Observational meso‐Network and Atmospheric Modelling) program. These measurements best represented low wind free convection regime (U10 < 2 m/s). Here we show moisture flux scaled linearly with appropriate near‐surface humidity and temperature differentials. The drag scaled linearly with wind speed unlike the moisture and sensible heat fluxes. The sensible heat flux scaled as “4/3” power of a near‐surface temperature differential consistent with Rao et al. (1996a, https://doi.org/10.1029/96GL02368) and Rao (2004, https://doi.org/10.1023/B:BOUN.0000016495.85528.d7). A striking result is that the moisture flux is a linear function of the sensible heat flux at all wind speeds; while drag does not show any dependence on heat flux.

Development of a new empirical correlation for steam condensation rates in the presence of air outside vertical smooth tube

In the past several decades, experimentalists have proposed a large number of correlations to estimate steam condensation rates in the presence of noncondensable gases within free convection regime. However, these correlations are in different forms, and even express conflicting dependencies of the condensation coefficient on some parameters. This study is to aim at developing a new correlation which can faithfully reflect the complex dependencies of condensation coefficient on pressure, air mass fraction and wall subcooling. Considering that more measured data can certainly help to analyze the relationship between condensation coefficient and these parameters, total 374 sets of experimental data have been obtained. It is found that there is a negative power function relation between condensation coefficient and wall subcooling, and the exponent varies with wall subcooling and total pressure. The new correlation, covering two orders of magnitude in the condensation heat transfer coefficient, is valid for pressure ranging from 0.2 to 0.5 MPa, air mass fraction ranging from 0.1 to 0.8 and wall subcooling ranging from 10 to 70 °C. Finally, we have made comparison with experimental data obtained by other investigators which shows that the new correlation is applicative for not only steam-air condensation but also steam-nitrogen and steam-argon condensation, and it can be extended to larger scope of engineering applications.

Physical investigation on silver-water nanofluid natural convection for an F-shaped cavity under the magnetic field effects

The effects of a magnetic field on a free convection regime of silver-water nanofluid are investigated. The considered geometry is an F-shaped cavity under the influence of a constant magnetic field. The left vertical walls temperature is Th, while the middle and right walls are at a constant temperature Tc, and the other walls are insulated. A FORTRAN program is developed for the numerical simulation of the considered problem. The governing equations are solved using the FVM with the SIMPLE algorithm. The effect of important physical parameters such as the Rayleigh number, the Hartmann number, AR and $ \phi$ on the problem are discussed in detail. We have concluded that the increase in the Hartmann number causes a decrease in vertical velocity and heat transfer. By increasing the Rayleigh number, the influence of the Hartmann number will be increased. An increase in the dimensional ratio of the cavity causes a decrease in the Nusselt number except in AR = 0.4. The AR has the maximum impact on the local Nusselt number, at the bottom of the hot wall. The effect of the dimensional ratio of the cavity on the Nusselt number is reversed on top of the wall. The maximum value of the Nusselt number is observed at AR = 0.4.