Theory Of Convection Research Articles

Prediction of the Temperature Field in a Tunnel during Construction Based on Airflow–Surrounding Rock Heat Transfer

It is important to determine the ventilation required in the construction of deep and long tunnels and the variation law of tunnel temperature fields to reduce the numbers of high-temperature disasters and serious accidents. Based on a tunnel project with a high ground temperature, with the help of convection heat transfer theory and the theoretical analysis and calculation method, this paper clarifies the contribution of various heat sources to the air demand during tunnel construction, and reveals the important environmental parameters that determine the ventilation value by changing the construction conditions. The results show that increasing the fresh air temperature greatly increases the required air volume, and the closer the supply air temperature is to 28 °C, the more the air volume needs to be increased. The air temperature away from the palm face is not significantly affected by changes in the supply air temperature. Adjusting the wall temperature greatly accelerates the rate of temperature growth. The supply air temperature rose from 15 to 25 °C, while the tunnel temperature at 800 m only increased by 1.5 °C. Over a 50 m range, the wall temperature rose from 35 to 60 degrees Celsius at a rate of 0.0842 to 0.219 degrees Celsius per meter. The total air volume rises and the surface heat transfer coefficient decreases as the tunnel’s cross-section increases. For every 10 m increase in the tunnel diameter, the temperature at 800 m from the tunnel face drops by about 0.5 °C. Changing the distance between the air duct and the tunnel face has little influence on the temperature distribution law. The general trend is that the farther the air duct outlet is from the tunnel face, the higher the temperature is, and the maximum difference is within the range of 50 m~250 m from the tunnel face. The maximum difference between the air temperatures at 12 m and 27 m is 0.79 °C. The geological structure and geothermal background have the greatest influence on the temperature prediction of high geothermal tunnels. The prediction results are of great significance for guiding tunnel construction, formulating cooling measures, and ensuring construction safety.

Is the mantle transition zone uniform beneath Precambrian shields?

In the present study, we examine the mantle transition zone (MTZ) structure below the prominent Precambrian shields on the Earth to understand its thermal and compositional properties and depth distribution of MTZ discontinuities. For this study, we used data from Canadian, Brazilian, Baltic, African and Australian Shields. We migrate the receiver functions to the depth domain using 3D tomographic models to examine the topography of MTZ discontinuities that define the upper and lower boundaries of the MTZ. The depth migration results were obtained using two different 3D tomographic velocity models, LLNL_G3D_JPS and GyPSuM. The analysis shows that both models yield similar results. The findings indicate a thinner than usual MTZ beneath all the Precambrian shields with an average thickness of ∼238 ± 8 km. Notably, the present study reveals the upper boundary of the MTZ (410 km discontinuity) displays distinctive topography; in contrast, the lower boundary of the MTZ (660 km discontinuity) is situated at shallower depths. Therefore, the main factor causing the variation in MTZ thickness is the shallowing of the 660 km discontinuity, indicating that the post-spinel transition occurred at higher temperatures with a negative Clapeyron slope, supporting the theory of whole-mantle convection. This suggests that mantle plumes have some appreciable impact on the MTZ beneath Precambrian shields, which are limited to the base of the MTZ. Alternatively, the global mantle warming explanation could be invoked, as it best explains the similar characteristics of the 660 km discontinuity beneath the Precambrian shields. However, this phenomenon needs to be tested through numerical modelling.

Numerical study on the evaporation rate of an electronic cigarette atomizer

This work establishes an evaporation model for the electronic cigarette atomizer based on convective mass transfer theory, which is implemented through Fluent user-defined functions (UDFS). By adding the convection–diffusion equation and considering the energy loss caused by evaporation and the temperature variation over the atomizer body, the evaporation rate of the e-liquid from the atomizer is more accurately calculated, compared to the previous evaporation model based on the assumption of constant temperature over the atomizer body. The effects of external airflow velocity, atomizer porosity, heating power, atomizer shape, heating method, and groove width on the average surface temperature and evaporation rate of the atomizer are examined. The results show that compared with other factors, the external air flow velocity has relatively insignificant influence on the evaporation rate of the atomizer. Within a certain range, as the porosity of the atomizer decreases or the heating power increases, the evaporation rate of the atomizer increases. The cylindrical atomizer has better evaporation performance than the cuboid and grooved atomizer, if all atomizer surfaces are heated, however, when the heating area of the grooved atomizer is optimized, i.e., only the surfaces with large evaporation rates are heated, the evaporation rate of a grooved atomizer can be higher than that of a cylindrical atomizer. The evaporation rate increases with increasing groove width, in the parameter range studied.

A transient formulation of entropy and heat transfer coefficients of Newton's cooling law with the unifying entropy potential difference in compressible flows

The original Newton's law of cooling is considered an ideal convection model of a point source ignoring conduction, but its unknown convection conductance and inconsistent thermal potential difference make it difficult to further elucidate the transient heat transfer mechanism of convection because of the no-slip condition at the interface between a body and a fluid. For this purpose, both the convective entropy transfer theory and the hypothesis of the isothermal velocity sublayer are developed to recast Newton's law of cooling into a standard Ohm's law form via the unified entropy driving force and the unambiguous entropy transfer coefficient. An explicit expression for the transient heat transfer coefficient is presented theoretically and experimentally in compressible flows by virtue of the product of the free-stream velocity, the volumetric thermal capacity of the fluid, and the near-wall velocity constant. The unified thermal potential difference is established between the body temperature and the total temperature (reduced to the ambient temperature for incompressible fluids). The physical mechanism of convection mode in the original Newton's cooling law is reasonably explained by the entropy transfer theory and entropy transfer efficiency, and the formulae for the entropy flux vector driven by the standard entropy potential difference and the rate of entropy generation are obtained. The analytical heat transfer coefficients as well as the standard thermal driving forces are validated by comparison with the forced convection experiment with a maximum error of 4.6 % in incompressible flows and the previous Newton's benchmark cooling experiments with the maximum error of 6.7 % in compressible flows. The effects of radiation on the total heat transfer coefficient are also analyzed quantitatively.

Large-scale semi-organized rolls in a sheared convective turbulence: Mean-field simulations

Based on a mean-field theory of a non-rotating turbulent convection [T. Elperin et al., Phys. Rev. E 66, 066305, (2002)], we perform mean-field simulations (MFS) of sheared convection that takes into account an effect of modification of the turbulent heat flux by the non-uniform large-scale motions. This effect is caused by the production of additional essentially anisotropic velocity fluctuations generated by tangling of the mean-velocity gradients by small-scale turbulent motions due to the influence of the inertial forces during the lifetime of turbulent eddies. These anisotropic velocity fluctuations contribute to the turbulent heat flux. As the result of this effect, there is an excitation of large-scale convective-shear instability, which causes the formation of large-scale semi-organized structures in the form of rolls. The lifetimes and spatial scales of these structures are much larger compared to the turbulent scales. By means of MFS performed for stress-free and no-slip vertical boundary conditions, we determine the spatial and temporal characteristics of these structures. Our study demonstrates that the modification of the turbulent heat flux by non-uniform flows leads to a strong reduction of the critical effective Rayleigh number (based on the eddy viscosity and turbulent temperature diffusivity) required for the formation of the large-scale rolls. During the nonlinear stage of the convective-shear instability, there is a transition from a two-layer vertical structure with two rolls in the vertical direction before the system reaches steady-state to a one-layer vertical structure with one roll after the system reaches steady state. This effect is observed for all effective Rayleigh numbers. We find that inside the convective rolls, the spatial distribution of the mean potential temperature includes regions with a positive vertical gradient of the potential temperature caused by the mean heat flux of the convective rolls. This study might be useful for understanding the origin of large-scale rolls observed in atmospheric convective boundary layers, as well as in numerical simulations and laboratory experiments.

Entropy transfer efficiency-effectiveness method for heat exchangers, part 1: Local entropy generation number and operation performance limits

Here, to resolve the open problem of the second-law efficiency evaluation for heat exchangers, an efficiency-effectiveness method is developed from pure convection theory, where the entropy transfer efficiency defined as the outlet temperature ratio of cold and hot fluids exchanging entropy and local entropy generation number can measure the global and local irreversibilities of heat transfer. The efficiency and effectiveness are related by the inlet temperature ratio τ and capacity rate ratio φ, and their maxima subject to the local entropy generation number are determined for different flow arrangements. When τ = φ2, the effectiveness maxima are 0.5/(1 + φ) and 1/(1 + φ) while the highest efficiencies are φ and unity for parallelflow and counterflow arrangements, respectively. The optimum operating points of counterflow exchangers, at which the equal outlet temperature τT1∞ (T1∞ represents the hot inlet temperature) of two fluids with a critical capacity rate ratio τ induces uniform irreversibility, the effectiveness limit of 1/(1+τ), and the efficiency limit of unity, are obtained. A linear temperature difference method is also developed based on the redefined convective and overall heat transfer coefficients, invariably yielding an effectiveness equal to the number of heat transfer units. This method has potentials to be extended to wet heat exchangers with phase-change flows.

Fundamental heat and entropy transfer mechanisms of convection underlying the first and second laws for an unsteady multiport system and their applications in parallel flow heat exchangers

Although thermal convection is ubiquitous in nature and technology, it has long been argued whether convection can be considered as an independent mode of heat transfer. Here, we show that pure convection mode is generally recognized from the classical first and second laws via mass flow by rooting the unsteady mass conservation relation through an equivalent multiport system. The fundamental distinction is made between convection driven by the thermal and entropy potential differences and mass flow accompanied by zero potential difference. The constitutive relations of the convective heat and entropy fluxes and their thermodynamic relationship are developed in terms of their potential differences with the exponential distribution of temperature difference in a compressible flow. In the absence of work transfer, the first and second laws are simply expressed by the standard Maxwell’s electromagnetic type equations via the total heat and entropy flux vectors. The pure convection theory is applied to a parallel-flow heat exchanger and the linear temperature difference distribution is obtained for both streams via the first-law definitions of the convective and overall heat transfer coefficients in an internal flow. The entropy generation rate inside a heat exchanger is recalculated and indicated to be driven by the difference between the reciprocal of outlet temperatures of two streams, from which the entropy generation number between outlets is developed to eliminate the entropy generation paradox. The present linear temperature difference profiles agree well with the experimental data, and the outlet entropy generation number is also justified by comparing with the previous nondimensionalizing entropy generation numbers.

Bridging theory and observations in stellar pulsations: the impact of convection and metallicity on the instability strips of classical and type-II cepheids

ABSTRACT The effect of metallicity on the theoretical and empirical period–luminosity relations of Cepheid variables is not well understood and remains a highly debated issue. Here, we examine empirical colour–magnitude diagrams (CMDs) of Classical and Type-II Cepheids in the Magellanic Clouds and compare those with the theoretically predicted instability strip (IS) edges. We explore the effects of incorporating turbulent flux, turbulent pressure, and radiative cooling into the convection theory on the predicted IS at various metallicities using Modules for Experiments in Stellar Astrophysics – Radial Stellar Pulsations. We find that the edges become redder with the increasing complexity of convection physics incorporated in the fiducial convection sets, and are similarly shifted to the red with increasing metallicity. The inclusion of turbulent flux and pressure improves the agreement of the red edge of the IS, while their exclusion leads to better agreement with observations of the blue edge. About 90 per cent of observed stars are found to fall within the predicted bluest and reddest edges across the considered variations of turbulent convection parameters. Furthermore, we identify and discuss discrepancies between theoretical and observed CMDs in the low-effective temperature and high-luminosity regions for stars with periods greater than ∼20 d. These findings highlight the potential for calibrating the turbulent convection parameters in stellar pulsation models or the prediction of a new class of rare, long-period, ‘red Cepheids’, thereby improving our understanding of Cepheids and their role in cosmological studies.

Penetrative magneto-convection of a rotating Boussinesq flow in f-planes

In this study, we conducted linear instability analysis of penetrative magneto-convection in rapidly rotating Boussinesq flows within tilted f-planes, under the influence of a uniform background magnetic field. We integrated wave theory and convection theory to elucidate the penetration dynamics in rotating magneto-convection. Our findings suggest that efficient penetration in rapidly rotating flows with weakly stratified stable layers at low latitudes can be attributed to the resonance of wave transmission near the interface between unstable and stable layers. In the context of strongly stratified flows, we derived the scaling relationships of penetrative distances Δ with the stability parameter δ. Our calculation shows that, for both rotation-dominated and magnetism-dominated flows, Δ obeys a scaling of Δ∼O(δ−1/2). In rotation-dominated flows, we noted a general decrease in penetrative distance with an increased rotational effect, and a minor decrease in a penetrative distance with an increased latitude. When a background magnetic field is introduced, we observed a significant shift in the penetrative distance as the Elsasser number Λ approaches one. The penetrative distance tends to decrease when Λ≪1 and increase when Λ≫1 with the rotational effect, indicating a transition from rotation-dominated to magnetism-dominated flow. We have further investigated the impact of the background magnetic field when it is not aligned with the rotational axis. This presents a notable contrast to the case where the magnetic field is parallel to the rotational axis.

New vision of convection induced freckle formation theory in nickel-based superalloys by electron microscopy

Freckles, one of the common defects in blades used in heavy-duty gas turbines, hugely deteriorate the mechanical properties and liability of blades under service conditions. The thermal-solutal convection theory is a widely adopted formation mechanism, but few solid experimental pieces of evidence have been reported. Here, the grain microstructure in freckle chains taken from four different Nickel-based superalloys with either single-crystal or directionally solidified alloy is analyzed for the first time. The relationship between the internal stress and the misorientation throughout the freckle chains is studied by means of state-of-the-art electron microscopy. The results supply new experimental evidence of the thermal-solutal convection theory, which is further supported by the fact that borides at the boundary are randomly orientated to alloys. Therefore, this research enriches the methodology of freckle study, providing new insight into the formation mechanism of casting defects.

Sharp Instability Estimates for Bidisperse Convection with Local Thermal Non-equilibrium

We analyse a theory for thermal convection in a Darcy porous material where the skeletal structure is one with macropores, but also cracks or fissures, giving rise to a series of micropores. This is thus thermal convection in a bidisperse, or double porosity, porous body. The theory allows for non-equilibrium thermal conditions in that the temperature of the solid skeleton is allowed to be different from that of the fluid in the macro- or micropores. The model does, however, allow for independent velocities and pressures of the fluid in the macro- and micropores. The threshold for linear instability is shown to be the same as that for global nonlinear stability. This is a key result because it shows that one may employ linearized theory to ensure that the key physics of the thermal convection problem has been captured. It is important to realize that this has not been shown for other theories of bidisperse media where the temperatures in the macro- and micropores may be different. An analytical expression is obtained for the critical Rayleigh number and numerical results are presented employing realistic parameters for the physical values which arise.Article HighlightsA two-temperature regime for a bidisperse Darcy porous medium is proposed to study the thermal convection problem.The optimal result of coincidence between the linear instability and nonlinear stability critical thresholds is proven.Numerical analysis enhances that the scaled heat transfer coefficient between the fluid and solid and the porosity-weighted conductivity ratio stabilize the problem significantly.

The scale-free theory of stellar convection

Context. A new, self-consistent, scale-free theory of stellar convection was recently developed (SFCT) in which velocities, dimensions, and energy fluxes carried by the convective elements are defined in a rest frame co-moving with the convective element itself. As the dynamics of the problem is formulated in a different framework with respect to the mixing length theory (MLT), the SFCT equations are sufficient to determine all the properties of stellar convection in accordance with the physics of the environment alone, with no need for the mixing length parameter (MLP). Subsequently, the SFCT was improved by introducing suitable boundary conditions at the surface of the external convective zones of the stars, and the first stellar models and evolutionary tracks on the Hertzsprung–Russell diagram were calculated. Aims. The SFCT received alternatively positive and negative attention that spurred us to reconsider the whole problem. In this work, we aim to re-examine the physical foundations and results of the SFCT, elucidate some misconceptions on its physical foundations, reply to reported criticisms, and present some recent improvements to the SFCT. Methods. The analysis was done using the same formalism of the previous studies, but novel arguments and demonstrations are added to better justify the controversial points, in particular the relaxation of instantaneous hydrostatic equilibrium between a convective element and the surrounding medium. Results. The main results include (i) a novel detailed discussion of the boundary conditions to ensure that the temperature gradients in the outermost regions of a star are adequate for analyses of stability or instability in asteroseismology; (ii) a quantitative comparison with the MLT; and, finally, (iii) the recovery of the MLT as a particular case of the SFCT, but also in this case with no need for the MLP. Conclusions. In conclusion, the SFCT is a step forward with respect to the classical MLT.

Thermal study on the performance of Joule heating and Sour-Dufour influence on nonlinear mixed convection radiative flow of Carreau nanofluid

BackgroundWith the progress of solar energy application and nano-technology, nanofluid heat assortment has fascinated noteworthy consideration. The solar plasmatic nano-fluids with substantial limited surface Plasmon resonance influence have shown greater performances in thermo-physical aspects, ophthalmic stuff, and photo-thermal exchange efficacy. The theory of nanofluid has induced broad attention from scientists around the globe because of their unique thermo-physical possessions and various prospective benefits and uses in essential arenas for example, atmosphere, energy, microchip technology and bio-medicine. MotivationThis research study encourages the scientists and researchers about the heat transport features, fluid properties, and its influencing aspects, influencing mechanisms of nanofluids and influencing rules. The current article elaborates the latest study effects in the open workings on nanofluids, with the intention of scientists in the field of energy variation which have an extra broad and perfect sympathetic understanding of the energy modification possessions and usages of nanofluids. Purpose of the workThis paper sums up the modern and new features of 3D magneto radiative Carreau fluid considering the thermal phenomenon of Joule heating, heat sink/source, convective concept and solutal phenomenon of activation energy and chemical reaction. Additionally, with nonlinear mixed convection, Soret-Dufour influence and zero mass flux theory are studied. MethodologyThe considered problem of Carreau nanofluid with diverse aspects has been solved numerically via the bvp4c algorithm. ResultsThe larger values of thermo Biot and Dufour factors enhance the Carreau fluid temperature field. The Brownian factor has a reverse influence on temperature and concentration graphs. The Soret number impact on concentration field and Eckert number on temperature field have the same performance. Moreover, thermophoretic and Soret numbers exaggerate the transport rate of heat. It is also noted that average increase of Nusselt number with respect toNT is 3.69% while average decrease of Nusselt number with respect of Ec is 7.75%.

A Review of the Mixing Length Theory of Convection in 1D Stellar Modeling

We review the application of the one-dimensional Mixing Length Theory (MLT) model of convection in stellar interiors and low-mass stellar evolution. We summarize the history of MLT, present a derivation of MLT in the context of 1D stellar structure equations, and discuss the physical regimes in which MLT is relevant. We review attempts to improve and extend the formalism, including to higher dimensions. We discuss the interactions of MLT with other modeling physics, and demonstrate the impact of introducing variations in the convective mixing length, αMLT, on stellar tracks and isochrones. We summarize the process of performing a solar calibration of αMLT and state-of-the-art on calibrations to non-solar targets. We discuss the scientific implications of changing the mixing length, using recent analyses for demonstration. We review the most prominent successes of MLT, and the remaining challenges, and we conclude by speculating on the future of this treatment of convection.

Modeling evaporation with a meshfree collocation approach

In this paper, a new model for the below-boiling point evaporation process with a meshfree collocation method is developed. In order to capture the phase change process, two different approaches are proposed: multi-phase and single-phase. First, a multi-phase approach is considered, where a novel mass transfer model assumes that the diffusion driven by the vapor concentration gradient in the air phase near the interface is the primary driving force for the mass transfer between phases as both the liquid water and air/vapor phases are simulated. Then, a water-only single-phase approach is also proposed, in which only the liquid water phase is simulated. For this, appropriate free surface boundary conditions are developed based on the convective mass transfer theory to model evaporation and incorporate airflow effects without explicitly simulating the air phase. In order to validate the proposed models, a series of experiments with varying air temperature, relative humidity, and airflow rate is conducted. The numerical results show a good agreement with the evaporation rate measured in the experiments. The multi-phase simulations agree better with the experiments, while the single-phase simulations also produce good results with a much lower computational effort.

Functional magnetic Maxwell viscoelastic nanofluids for tribological coatings- a model for stretching flow using the generalized theory of heat-mass fluxes, Darcy-Forchheimer formulation and dual convection

A theoretical and computational study of an improved Fourier and Fickian model for locally non-similar magnetohydrodynamic Maxwell (non-Newtonian) nanofluid convective flow under thermo-solutal buoyancy forces in a non-Darcian (Darcy-Forchheimer) porous medium is presented. Heat sink/source is included. Buongiorno’s two-component nanofluid model is used to simulate nanoscale characteristics featuring thermophoresis and Brownian diffusions. The problem under consideration is formulated utilizing fundamental relations of fluid dynamics. The primitive partial differential expressions (PDEs) are transfigured to ordinary ones with apposite transformations. The emerging locally non-similar boundary value problem is solved via series expansions utilizing a homotopy algorithm. Characteristics of sundry parameters on velocity, temperature, nanoparticle concentration and skin-friction coefficients are interpreted graphically. Convergence results acquired via homotopy algorithm are presented. Comparison results are included for the authentication of the homotopy solutions. The velocity distribution is increased with greater mixed convection and non-Newtonian material parameters whereas velocity distribution is reduced with increment in Hartmann (magnetic) number, porosity and buoyancy ratio parameters. The temperature distribution is reduced when Prandtl number and thermal-relaxation (non-Fourier) parameter are augmented whereas temperature distribution is increased for larger Brownian diffusion and thermophoresis. Additionally, it is observed that increment in the heat absorption variable diminishes temperature whereas an enhancement in the heat generation variable augments temperature. Nanoparticle concentration is enhanced subjected to higher values of thermophoresis factor whereas it reduces with larger Schmidt number, Brownian movement and solutal-relaxation (non-Fickian) parameters. Furthermore, it is noticed that elevation in Hartmann number, porosity and inertial (non-Darcy) coefficient parameters increase the skin friction coefficient whereas elevation in Deborah number and buoyancy ratio is found to suppress skin friction. The simulations are relevant to hydromagnetic nano-materials processing operations for coatings deployed in multi-functional tribological systems and surface protection.

Convection theory on thermally radiative peristaltic flow of Prandtl tilted magneto nanofluid in an asymmetric channel with effects of partial slip and viscous dissipation

A theoretical investigation has been conducted to analyze the peristaltic motion of an asymmetric channel carrying magneto-Prandtl nanofluid under the influence of double-diffusive convection, which includes both thermal and concentration gradients. Moreover, the effects of thermal radiation, viscous dissipation, and partial slip have also been taken into consideration. The mathematical expressions for mixed convection and viscous dissipation have been derived and the influential dynamic parameters have been depicted as geographical flow patterns with a focus on double-diffusive convection and partial slip. NDSolve in Mathematica, the computational technique, has been used to obtain the results. The outcomes for the classic Newtonian fluid have been taken as a special parameter of the study. The findings of this investigations can be beneficial in improving gastrointestinal movements and pumping in various engineering devices. Such analysis also provides a provision to flow of physiological fluids within vessels and arteries for transportation of food nutrients, blood circulation, carrying oxygen, waste excretion, heat, and other nutrients in the human body.

The coupled cooling effect of ventilation and spray in the deep-buried high-temperature tunnel

The utilization of ventilation and spray cooling technology is becoming increasingly popular in high-temperature workplaces due to its convenience and environmental friendliness. To investigate the coupled cooling effect of ventilation and spray in a construction tunnel, we established a droplet evaporation model under convective heat transfer conditions by combining the convective heat transfer theory and the droplet heat and mass transfer model. Based on this model, the study focused on the energy change of droplet evaporation in a moving medium by using numerical simulation in the context of a railroad construction tunnel. The material of the droplets used in the study was water. According to the simulation and field measurement results, it was obtained that, firstly, increased air volume of the tunnel and reduced airflow temperature could make the convective heat exchange stronger between the airflow and the wall. Secondly, the particle size of droplets formed by spraying was mainly 30–40 μm in the tunnel. A part of the droplets was evaporated in the high-temperature environment, and another part was trapped by the rock wall and ground. Third, adopting the coupled cooling method of ventilation and spray, the temperature and humidity fields in the tunnel changed significantly, and a low-temperature and high-humidity zone appeared near the nozzle. At the same time, the evaporation rate of droplets increased, the heat index of the workplace decreased, and the cooling effect was effective. Therefore, the coupled cooling method of ventilation and spray can effectively improve the thermal environment in high-temperature construction tunnels and enhance the thermal comfort of personnel. This study serves as a reference for the parameters and cooling effect of ventilation and spray cooling systems in construction sites.

Compelling Heat Transfer Augmentation of Laminar Natural Convection from Vertical Plates to Binary Gas Mixtures Formed with Light Helium and Selected Heavier Gases

The present study addresses a remarkable behavior of certain binary gas mixtures in connection to laminar natural convection along a heated vertical plate at constant temperature. The binary gas mixtures are formed with light helium (He) as the primary gas and selected heavier secondary gases. The heavier secondary gases are nitrogen (N2), oxygen (O2), xenon (Xe), carbon dioxide (CO2), methane (CH4), tetrafluoromethane (CF4) and sulfur hexafluoride (SF6). The central objective in the study is to investigate the attributes of the set of seven He‒based binary gas mixtures for heat transfer enhancement with respect to the heat transfer with helium (He) and air. From heat convection theory, four thermo‒physical properties: viscosity η, density ρ, thermal conductivity λ, and isobaric heat capacity Cp affect the thermo‒buoyant convection of fluids. In this study it became necessary to construct a particular correlation equation consigned to the set of seven He‒based binary gas mixtures, which operate in the Prandtl number closed sub‒interval [0.1, 1]. The heat transfer rate with the set of seven He‒based binary gas mixtures from the vertical plate involves four thermo‒physical properties: density ρmix, viscosity ηmix, thermal conductivity λmix, and isobaric heat capacity Cp, mix that vary with the molar gas composition w. A case study is performed to elucidate the unique characteristics of the modified convective heat transport that the set of seven He‒based binary gas mixtures brings forward as compared to the convective heat transport of He and air. It was found that the He+SF6 binary gas mixture renders an absolute maximum heat transfer enhancement rate that is 39 times higher than the heat transfer rate provided by He and 78 times higher than air.

Evaporating Rayleigh–Bénard convection: prediction of interface temperature and global heat transfer modulation

We propose an analytical model to estimate the interface temperature $\varTheta _{\varGamma }$ and the Nusselt number $Nu$ for an evaporating two-layer Rayleigh–Bénard configuration in statistically stationary conditions. The model is based on three assumptions: (i) the Oberbeck–Boussinesq approximation can be applied to the liquid phase, while the gas thermophysical properties are generic functions of thermodynamic pressure, local temperature and vapour composition, (ii) the Grossmann–Lohse theory for thermal convection can be applied to the liquid and gas layers separately and (iii) the vapour content in the gas can be taken as the mean value at the gas–liquid interface. We validate this setting using direct numerical simulations in a parameter space composed of the Rayleigh number ( $10^6\leq Ra\leq 10^8$ ) and the temperature differential ( $0.05\leq \varepsilon \leq 0.20$ ), which modulates the variation of state variables in the gas layer. To better disentangle the variable property effects on $\varTheta _\varGamma$ and $Nu$ , simulations are performed in two conditions. First, we consider the case of uniform gas properties except for the gas density and gas–liquid diffusion coefficient. Second, we include the variation of specific heat capacity, dynamic viscosity and thermal conductivity using realistic equations of state. Irrespective of the employed setting, the proposed model agrees very well with the numerical simulations over the entire range of $Ra$ – $\varepsilon$ investigated.