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Modal global linear stability analysis of thermal convection is performed with the linearized lattice Boltzmann method (LLBM). The onset of Rayleigh--Bénard convection in rectangular cavities with conducting and adiabatic sidewalls and the instability of two-dimensional (2-D) and three-dimensional (3-D) natural convection in cavities are studied. The method of linearizing the local equilibrium probability distribution function that was first proposed by Pérez et al. (Theor. Comp. Fluid Dyn., vol. 31, 2017, pp. 643-664) is extended to solve the coupled linear Navier--Stokes equations together with the linear energy equation in this work. A multiscale analysis is also performed to recover the macroscopic linear Navier--Stokes equations from the discrete lattice Boltzmann equations for both the single and multiple relaxation time models. The present LLBM is implemented in the framework of the Palabos library. It is validated by calculating the linear critical value of 2-D natural convection that the LLBM with the multiple relaxation time model has an error less than 1% compared with the spectral method. The instability mechanism of the flow is explained by kinetic energy transfer analysis. It is shown that the buoyancy mechanism and inertial mechanism tend to stabilize the Hopf bifurcation of the 2-D natural convection at Pr<0.08 and Pr>1, respectively. For 3-D natural convection, subcritical bifurcation of the Hopf type is found for low-Prandtl-number fluids (Pr<0.1). [ABSTRACT FROM AUTHOR]

In this paper, we will show that solutions of the three-dimensional non-resistive and non-diffusive MHD-Boussinesq system are globally regular if the initial data is axisymmetric and the swirl components of the velocity and the magnetic vorticity are zero. Our main result extends previous ones on the three-dimensional non-resistive MHD system and non-diffusive Boussinesq system, and the method used here can also be applied to the magnetic Rayleigh-Bénard convection system. [ABSTRACT FROM AUTHOR]

The conventional denoising method in Rayleigh imaging in a general sense requires an additional hardware investment and the use of the underlying physics. This work demonstrates an alternative image denoising reconstruction model based on unsupervised learning that aims to remove Mie scattering and shot noise interference from two-dimensional (2D) Rayleigh images. The model has two generators and two discriminators whose parameters can be trained with either feature-paired or feature-unpaired data independently. The proposed network was extensively evaluated with a qualitative examination and quantitative metrics, such as PSNR, ER, and SSIM. The results demonstrate that the feature-paired training network exhibits a better performance compared with several other networks reported in the literature. Moreover, when the flame features are not paired, the feature-unpaired training network still yields a good agreement with ground truth data. Specific indicators of the quantitative evaluation show a promising denoising ability with a peak signal-to-noise ratio of ~37 dB, an overall reconstruction error of ~1%, and a structure similarity index of ~0.985. Additionally, the pre-trained unsupervised model based on unpaired training can be generalized to denoise Rayleigh images with extra noise or a different Reynolds number without updating the model parameters. [ABSTRACT FROM AUTHOR]

Recent developments in diagnostic and computing technologies offer to leverage numerous forms of nonintrusive modelling approaches from data where machine learning can be used to build computationally cheap and accurate surrogate models. To this end, we present a nonlinear proper orthogonal decomposition (POD) framework, denoted as NLPOD, to forge a nonintrusive reduced-order model for the Boussinesq equations. In our NLPOD approach, we first employ the POD procedure to obtain a set of global modes to build a linear-fit latent space and utilise an autoencoder network to compress the projection of this latent space through a nonlinear unsupervised mapping of POD coefficients. Then, long short-term memory (LSTM) neural network architecture is utilised to discover temporal patterns in this low-rank manifold. While performing a detailed sensitivity analysis for hyperparameters of the LSTM model, the trade-off between accuracy and efficiency is systematically analysed for solving a canonical Rayleigh–Bénard convection system. [ABSTRACT FROM AUTHOR]

The Rayleigh-Bénard convection for a couple-stress fluid with a thermorheological effect in the presence of an applied magnetic field is studied using both linear and non-linear stability analysis. This problem discusses the three important mechanisms that control the onset of convection; namely, suspended particles, an applied magnetic field, and variable viscosity. It is found that the thermorheological parameter, the couple-stress parameter, and the Chandrasekhar number influence the onset of convection. The effect of an increase in the thermorheological parameter leads to destabilization in the system, while the Chandrasekhar number and the couple-stress parameter have the opposite effect. The generalized Lorenz's model of the problem is essentially the classical Lorenz model but with coefficients involving the impact of three mechanisms as discussed earlier. The classical Lorenz model is a fifth-order autonomous system and found to be analytically intractable. Therefore, the Lorenz system is solved numerically using the Runge-Kutta method in order to quantify heat transfer. An effect of increasing the thermorheological parameter is found to enhance heat transfer, while the couple-stress parameter and the Chandrasekhar number diminishes the same. [ABSTRACT FROM AUTHOR]

We report direct numerical simulations (DNS) of the Nusselt number Nu, the vertical profiles of mean temperature Θ(z) and temperature variance Ω(z) across the thermal boundary layer (BL) in closed turbulent Rayleigh–Bénard convection (RBC) with slippery conducting surfaces (z is the vertical distance from the bottom surface). The DNS study was conducted in three RBC samples: a three-dimensional cuboid with length L = H and width W = H/4 (H is the sample height), and two-dimensional rectangles with aspect ratios Γ ≡ L/H = 1 and 10. The slip length b for top and bottom plates varied from 0 to ∞. The Rayleigh numbers Ra were in the range 106 ≤ Ra ≤ 1010 and the Prandtl number Pr was fixed at 4.3. As b increases, the normalised Nu/Nu0 (Nu0 is the global heat transport for b = 0) from the three samples for different Ra and Γ can be well described by the same function Nu/Nu0 = N0 tanh(b/λ0) + 1, with N0 = 0.8 ± 0.03. Here λ0 ≡ L/(2Nu0) is the thermal boundary layer thickness for b = 0. Considering the BL fluctuations for Pr > 1, one can derive solutions of temperature profiles Θ(z) and Ω(z) near the thermal BL for b≥0. When b = 0, the solutions are equivalent to those reported by Shishkina et al. (Phys. Rev. Lett., vol. 114, 2015, 114302) and Wang et al. (Phys. Rev. Fluids, vol. 1, 2016, 082301(R)), respectively, for no-slip plates. For b > 0, the derived solutions are in excellent agreement with our DNS data for slippery plates. [ABSTRACT FROM AUTHOR]

We perform large-scale numerical simulations to study Rayleigh–Darcy convection in three-dimensional fluid-saturated porous media up to Rayleigh–Darcy number Ra = 8 × 104. At these large values of Ra, the flow is dominated by large columnar structures – called megaplumes – which span the entire height of the domain. Near the boundaries, the flow is hierarchically organized, with fine-scale structures interacting and nesting to form larger-scale structures called supercells. We observe that the correlation between the flow structure in the core of the domain and at the boundaries decreases only slightly for increasing Ra, and remains rather high even at the largest Ra considered here. This confirms that supercells are the boundary footprint of megaplumes dominating the core of the domain. In agreement with available literature predictions, we show that the thickness of the thermal boundary layer scales very well with the Nusselt number as δ ∼ 1/Nu. Measurements of the mean wavenumber – inverse of the mean length scale – in the core of the flow support the scaling k¯ ∼ Ra0.49, in very good agreement with theoretical and numerical predictions. Interestingly, the behaviour of the mean wavenumber near the boundaries scales as k¯ ∼ Ra0.81, which is distinguishably different from the presumed linear behaviour. We hypothesize that a linear behaviour can only be observed in the ultimate regime, which we argue to set in only at Ra in excess of 5 × 105, whereas a sublinear behaviour is recovered at more modest Ra. The present results are expected to help the development of long desired reliable models to predict the large- and fine-scale structure of Rayleigh–Darcy convection in the high-Ra regime typically encountered in geophysical processes, such as for instance in geological carbon dioxide sequestration. [ABSTRACT FROM AUTHOR]

This paper examines the capability of hybrid lattice Boltzmann method to simulate developed turbulent buoyancy-driven flows in closed rectangular cavities. The two-relaxation time mesoscopic lattice Boltzmann method is used as a fluid dynamics solver, whereas the thermal behavior is described in terms of the macroscopic energy equation. Numerical simulation is performed for air-filled square and tall cavities in a range of the Rayleigh number 10 9 ≤ R a ≤ 10 11 . An in-house numerical code is developed in this study and successfully validated against up-to-date numerical and experimental data of other researches. It is found that the proposed hybrid approach accurately predicts the location of thermal plumes at the isothermal walls despite an insignificant error in the heat transfer rate with the R a ≥ 3 · 10 10 . [ABSTRACT FROM AUTHOR]

This paper examines the capability of hybrid lattice Boltzmann method to simulate developed turbulent buoyancy-driven flows in closed rectangular cavities. The two-relaxation time mesoscopic lattice Boltzmann method is used as a fluid dynamics solver, whereas the thermal behavior is described in terms of the macroscopic energy equation. Numerical simulation is performed for air-filled square and tall cavities in a range of the Rayleigh number 10 9 ≤ R a ≤ 10 11 . An in-house numerical code is developed in this study and successfully validated against up-to-date numerical and experimental data of other researches. It is found that the proposed hybrid approach accurately predicts the location of thermal plumes at the isothermal walls despite an insignificant error in the heat transfer rate with the R a ≥ 3 · 10 10 . [ABSTRACT FROM AUTHOR]

The heat transfer behaviour of convection-driven dynamos in a rotating plane layer between two parallel plates, heated from the bottom and cooled from the top, is investigated. At a fixed rotation rate (Ekman number, E = 10-6) and fluid properties (thermal and magnetic Prandtl numbers, Pr = Prm = 1), both dynamo convection (DC) and non-magnetic rotating convection (RC) simulations are performed to demarcate the effect of magnetic field on heat transport at different thermal forcings (Rayleigh number, Ra = 3.83 × 109-3.83 × 1010). In this range, our turbulence resolving simulations demonstrate the existence of an optimum thermal forcing, at which heat transfer between the plates in DC exhibits maximum enhancement, as compared with the heat transport in the RC simulations. Unlike any global force balance reported in the literature, the present simulations reveal an increase in the Lorentz force in the thermal boundary layer, due to stretching of magnetic field lines by the vortices near the walls with a no-slip boundary condition. This increase in Lorentz force mitigates turbulence suppression due to the Coriolis force, resulting in enhanced turbulence and heat transfer. [ABSTRACT FROM AUTHOR]

The existence of Bolgiano-Obukhov (BO) scaling in Rayleigh-Bénard convection (RBC) has long been speculated. However, due to the inhomogeneity and anisotropy of the flow, and the lack of clear scale separation, no conclusive evidence has been found. To avoid these non-ideal factors, we construct an idealized isotropic convection system by introducing an additional horizontal buoyancy field to RBC in a doubly periodic domain. We focus on the two-dimensional case so that its upscale kinetic energy flux can enable a long inertial range for detecting the BO scaling. Through direct numerical simulations of this system, we justify the existence of BO scaling using second- and third-order structure functions, which are in good agreement with our theoretically obtained scaling relations from the Kármán-Howarth-Monin equations. These theoretical and numerical results provide direct support for the conjecture that the existence of the BO scaling in RBC is associated with the inverse kinetic energy cascade. For higher-order structure functions, we found strong intermittent effects in the buoyancy field, but not in the velocity. By comparing the present system with the canonical anisotropic RBC in a periodic domain, the effects of anisotropy on the scaling properties are elucidated. [ABSTRACT FROM AUTHOR]

We perform direct numerical simulations to study the effect of the gravity centre offset in spherical Rayleigh-Bénard convection. When the gravity centre is shifted towards the south, we find that the shift of the gravity centre has a pronounced influence on the flow structures. At low Rayleigh number Ra, a steady-state large-scale meridional circulation induced by the baroclinic imbalance, created by the misalignment of the gravity potentials and isotherms, is formed. At high Ra, an energetic jet is created on the northern side of the inner sphere that is directed towards the outer sphere. The large-scale circulation induces a strong co-latitudinal dependence in the local heat flux. Nevertheless, the global heat flux is not affected by the changes in the large-scale flow organization induced by the gravity centre offset. [ABSTRACT FROM AUTHOR]

In 1966 Francis Crick declared that: "The ultimate aim of the modern movement in biology is to explain all biology in terms of physics and chemistry." This motivated us to contemplate approaches that unify biology at a fundamental level. Exploration led us to consider the features of energy, entropy, and motion. Overall, it can be considered that motion of matter is the feature of life function. No motion. No function. In initial work we evaluated the hypothesis that the scope for biologic function is mediated mechanistically by a differential for energy transfer. Maximal treadmill running capacity served as a proxy for energy transfer. The span for capacity was estimated "biologically" by application of two-way artificial selection in rats for running capacity. Consistent with our "Energy Transfer Hypothesis" (ETH), low physical health and dysfunction segregated with low running capacity and high physical health and function segregated with high running capacity. The high energy yield of aerobic metabolism is also consonant with the ETH; that is, amongst the elements of the universe, oxygen is second only to fluorine in electronegativity. Although we deem these energy findings possibly correct, they are based on correlation and do not illuminate function via fundamental principles. For consideration of life, Entropy (2nd Law of thermodynamics) can be viewed as an open system that exchanges energy with the universe operating via nonequilibrium thermodynamics. The Principle of Maximal Entropy Production (MEP) states that: If a source of free energy is present, complex systems can intercept the free energy flow, and self-organize to enhance entropy production. The development of Benard convection cells in a water heat gradient demonstrate simplistic operation of MEP. A direct step forward would be to explain the mechanism of the obligatory motion of molecules for life function. Motion may be mediated by operation of "action at a distance" for molecules as considered by the Einstein-Podolsky-Rosen Paradox and confirmed by JS Bell. Magnetism, electricity, and gravity are also examples of action at a distance. We propose that some variant of "action at a distance" as directed by the property of Maximal Entropy Production (MEP) underwrites biologic motion. [ABSTRACT FROM AUTHOR]

The effect of variable gravity on rotating convection in a sparsely packed porous layer is studied numerically. For gravity force variation, the linear, parabolic, cubic, and exponential functions are considered. Boundary conditions for the governing equations are considered to be either free or rigid. The normal mode method is employed, and the resulting eigenvalue problem is solved numerically for free–free and rigid–rigid boundaries using bvp4c in MATLAB R2020b. The influence of Darcy number (Da $Da$), gravity variation parameter (δ1 ${\delta }_{1}$), and Taylor number (Ta $Ta$) on the stability of the system is investigated graphically. It is confirmed that the gravity variation parameter and Taylor number delay the onset of convection and Darcy number enhances the onset of convection. The size of convection cells decreases on raising the variable gravity parameter and rotation parameter, while the Darcy number amplifies the size of convection cells. It is also observed that the system is stable for exponential gravity function and less stable for the cubic gravity function. [ABSTRACT FROM AUTHOR]

We adopt the stretched spiral vortex sub-grid model for large-eddy simulation (LES) of turbulent convection at extreme Rayleigh numbers. We simulate Rayleigh–Bénard convection (RBC) for Rayleigh numbers ranging from 106 to 1015 and for Prandtl numbers 0.768 and 1. We choose a box of dimensions 1:1:10 to reduce computational cost. Our LES yields Nusselt and Reynolds numbers that are in good agreement with the direct-numerical simulation (DNS) results of Iyer et al. ["Classical 1/3 scaling of convection holds up to Ra = 10 15 ," Proc. Natl. Acad. Sci. U. S. A. 117, 7594–7598 (2020)] albeit with a smaller grid size and at significantly reduced computational expense. For example, in our simulations at R a = 10 13 , we use grids that are 1/120 times the grid resolution as that of the DNS [Iyer et al., "Classical 1/3 scaling of convection holds up to Ra = 10 15 ," Proc. Natl. Acad. Sci. U. S. A. 117, 7594–7598 (2020)]. The Reynolds numbers in our simulations span 3 orders of magnitude from 1000 to 1 700 000. Consistent with the literature, we obtain scaling relations for Nusselt and Reynolds numbers as N u ∼ R a 0.321 and R e ∼ R a 0.495 . We also perform LES of RBC with periodic side walls, for which we obtain the corresponding scaling exponents as 0.343 and 0.477, respectively. Our LES is a promising tool to push simulations of thermal convection to extreme Rayleigh numbers and, hence, enable us to test the transition to the ultimate convection regime. [ABSTRACT FROM AUTHOR]

A possible explanation for the apparent phase stability of the 11.07-year Schwabe cycle of the solar dynamo was the subject of a series of recent papers [1-3]. The synchronization of the helicity of an instability with the azimuthal wavenumber m = 1 by a tidal m = 2 perturbation played a key role here. To analyze this type of interaction in a paradigmatic setup, we study a thermally driven Rayleigh-Bénard convection of a liquid metal under the influence of a tide-like electromagnetic forcing. As shown previously, the time-modulation of this forcing emerges as a peak frequency in the m = 2 mode of the radial flow velocity component. In this paper, we present new numerical results on the interplay between the large-scale circulation of a Rayleigh-Bénard convection flow and the time modulated electromagnetic forcing. [ABSTRACT FROM AUTHOR]

The present paper deals with the theoretical study of a weakly non-linear Rayleigh–Bénard convection in temperature-dependent viscosity Newtonian liquids with temperature/gravity modulation. The effect of temperature-dependent variable viscosity and temperature/gravity modulation renders the problem analytically intractable. The imposed thermal boundary condition and gravity field consist of a steady part and a time-periodic oscillatory part as described by Venezian. The instability of convective rolls due to temperature/gravity modulation is expanded in terms of the power series of the amplitude of convection, which is quite small. The Ginzburg–Landau equation derived in this problem is a non-autonomous differential equation and is solved using the numerical technique. The authors have demonstrated that one can suppress or enhance heat transfer by tuning the parameters involved. The effect of different parameters on the heat transfer and streamlines is also studied. [ABSTRACT FROM AUTHOR]

In this paper, we focus on the first stage of transition to Rayleigh–Bénard convection in soft-jammed systems (yield stress fluids) confined in a parallelepiped box heated from the bottom. Up to yielding, the material is in a solid-state with a constant elastic modulus. By means of a linear thermoelastic model, an analytical solution for stresses and strains induced by the gravity and the temperature gradient is derived. The analytical solution allows us to emphasize the appropriate dimensionless parameters. The onset of plastic deformation is then investigated using the classical yield criteria (Tresca, von Mises and Drucker–Prager). This analysis is subsequently applied to experimental data of the literature dealing with Rayleigh–Bénard convection in Carbopol micro gels. [ABSTRACT FROM AUTHOR]

Natural convection is intensively explored, especially in a valley-shaped trapezoidal enclosure, because of its broad presence in both technical settings and nature. This study deals with a trapezoidal cavity, which is initially filled with linearly stratified air. Although the sidewalls remain adiabatic, the bottom wall is heated, and the top wall is cooled. For the stratified fluid (air), the temperature of the fluid adjacent to the top and the bottom walls is the same as that of the walls. Natural convection in the trapezoidal cavity is simulated in two dimensions using numerical simulations, by varying Rayleigh numbers (Ra) from 100 to 108 with constant Prandtl number, Pr = 0.71, and aspect ratio, A = 0.5. The numerical results demonstrate that the development of natural convection from the beginning is dependent on the Rayleigh numbers. According to numerical results, the development of transient flow within the enclosure owing to the predefined conditions for the boundary may be categorized into three distinct stages: early, transitional, and steady or unsteady. The flow characteristics at each of the three phases and the impact of the Rayleigh number on the flow's growth are quantified. Unsteady natural convection flows in the enclosure are described and validated by numerical results. In addition, heat transfer through the bottom and the top surfaces is described in this study. [ABSTRACT FROM AUTHOR]

In this paper, we study the Prandtl number effect on Rayleigh–Bénard convection systems modulated by an oscillatory bottom plate. Direct numerical simulations are carried out in a Prandtl number range of 0. 2 ≤ P r ≤ 4. 6 and a fixed Rayleigh number of R a = 1 0 8 . The initial drop and subsequent rise evolutionary behaviour of the heat transfer efficiency, characterised by the Nusselt number at the bottom plate N u b , with respect to the characteristic oscillatory velocity V o s c is observed in the whole parameter space under consideration. If the oscillatory bottom plate does not induce boundary layer instabilities but thickens the boundary layer only, then one observes a heat transfer reduction, corresponding to a high P r and a low V o s c. If periodic boundary layer instabilities are triggered, then both heat transfer reduction and enhancement are possible. The reduction is generally seen when P r ≤ 1. 0. Under such circumstance, the velocity boundary layer is embedded in the thermal boundary layer, if the instability induced by a certain V o s c is not strong enough to compensate the heat resistance of the thermal boundary layer, one still observes a reduction in spite of the boundary layer instabilities. The enhancement is generally seen for a low P r and/or a high V o s c , in which case violent boundary layer instabilities will be triggered, leading to a sufficient emission of hot plumes. Furthermore, the critical velocity V ̄ c , characterising the boundary layer instability, is found to be increasing with P r as V c ̄ ∼ P r 0. 5 ; and the Reynolds number at the equilibrium state evolves in a similar way as N u b . In the end, modal analyses are performed based on standard and extended proper orthogonal decompositions. Energetic contribution of the modes and modal distributions confirm well the modulation of the oscillatory bottom plate and the induced boundary layer instabilities on the heat transfer and flow structures of the convection system. • Due to the effect of Prandtl number, heat transfer can be enhanced or reduced in spite of the presence of the boundary layer instabilities. • The critical velocity characterising the boundary layer instability rises with P r , scaling as V ̄ c ∼ P r 0. 5 . • Modal analyses confirmed the influences of the boundary layer instability on heat transfer and flow structures of the system. [ABSTRACT FROM AUTHOR]

We report the results of direct numerical simulations (DNS) of centrifugal convection (CC) in an annular container, heated at the outer sidewall and cooled at the inner wall, all subjected to a constant rotation around the vertical axis. This setup mimics the annular centrifugal Rayleigh–Bénard convection (ACRBC) facility used in the CC experiments in Chao Sun's Lab at Tsinghua University. For a fixed size of the container and a given fluid, the strengths of centrifugal and thermal driving in such a system are characterized, respectively, by the dimensionless Froude number Fr and Rayleigh number Ra. Our DNS of CC cover the following range of control parameters: 0 ≤ Fr ≤ 100 and 2 × 1 0 5 ≤ Ra ≤ 8. 88 × 1 0 8 . For a fixed Ra , with increasing Fr from 0 (no-rotation) to 100 (strong centrifugal buoyancy), we observe an evolution of the global flow structure and heat transport scaling properties from those typical for vertical convection, where the imposed temperature gradient is orthogonal to the driving force (gravitational buoyancy), to those typical for Rayleigh–Bénard convection, where the temperature gradient is parallel to the force (centrifugal buoyancy). With increasing centrifugal buoyancy, the flow undergoes a transition from a three-dimensional global flow structure to a quasi-two-dimensional one, which is characterized by a suppressed mixing in the vertical direction (Taylor–Proudman theorem). Our DNS show that for larger values of Ra , larger Fr values are required for the transition. [Display omitted] • Direct numerical simulations of centrifugal convection (CC) in an annular container are conducted for a range of Rayleigh numbers Ra from 2 × 1 0 5 to 8. 88 × 1 0 8 and Froude numbers Fr from 0 to 100, to investigate flow structure and heat transport in CC. • For a fixed Ra (thermal driving) and increasing Fr (centrifugal driving), the global flow structure and heat transport scaling properties undergo a transition from those typical for vertical convection, where the imposed temperature gradient is orthogonal to the driving force (gravitational buoyancy), to those typical for Rayleigh–Bénard convection, where the temperature gradient is parallel to the force (centrifugal buoyancy). • For larger Ra values, larger values of Fr are required for the transition between gravitational buoyancy-dominated and centrifugal buoyancy-dominated regimes. [ABSTRACT FROM AUTHOR]

In this paper, a thermodynamically consistent numerical solution of the interfacial Riemann problem for the first-order hyperbolic continuum model of Godunov, Peshkov and Romenski (GPR model) is presented. In the presence of phase transition, interfacial physics are governed by molecular interaction on a microscopic scale, beyond the scope of the macroscopic continuum model in the bulk phases. The developed approximate two-phase Riemann solvers tackle this multi-scale problem, by incorporating a local thermodynamic model to predict the interfacial entropy production. Using phenomenological relations of non-equilibrium thermodynamics, interfacial mass and heat fluxes are derived from the entropy production and provide closure at the phase boundary. We employ the proposed Riemann solvers in an efficient sharp interface level-set Ghost-Fluid framework to provide coupling conditions at phase interfaces under phase transition. As a single-phase benchmark, a Rayleigh-Bénard convection is studied to compare the hyperbolic thermal relaxation formulation of the GPR model against the hyperbolic-parabolic Euler-Fourier system. The novel interfacial Riemann solvers are validated against molecular dynamics simulations of evaporating shock tubes with the Lennard-Jones shifted and truncated potential. On a macroscopic scale, evaporating shock tubes are computed for the material n-Dodecane and compared against Euler-Fourier results. Finally, the efficiency and robustness of the scheme is demonstrated with shock-droplet interaction simulations that involve both phase transfer and surface tension, while featuring severe interface deformations. • Novel two-phase Riemann solver with phase transition for the Godunov-Peshkov-Romenski equations. • Multi-scale modeling of phase transition via parameter-free evaporation model. • Sharp interface Ghost-fluid method for complex droplet dynamics. • Validation against Euler-Fourier and molecular dynamics simulations. • Study of shock-droplet interactions under phase transition. [ABSTRACT FROM AUTHOR]

A thermophilic suspension of nanoparticles heated from below exhibits a complex stability diagram determined by the competition between the stabilizing flux of nanoparticles induced by thermophoresis and the destabilizing flux determined by thermal convection. We investigate Rayleigh-Bénard convection in a suspension of highly thermophilic nanoparticles with large negative separation ratio ψ = −3.5 heated from below. We show that transient localized states appear in the range of Rayleigh numbers 2200

The lacking of analytic solutions of diverse partial differential equations (PDEs) gives birth to a series of computational techniques for numerical solutions. Although numerous latest advances are accomplished in developing neural operators, a kind of neural-network-based PDE solver, these solvers become less accurate and explainable while learning long-term behaviors of non-linear PDE families. In this paper, we propose the Koopman neural operator (KNO), a new neural operator, to overcome these challenges. With the same objective of learning an infinite-dimensional mapping between Banach spaces that serves as the solution operator of the target PDE family, our approach differs from existing models by formulating a non-linear dynamic system of equation solution. By approximating the Koopman operator, an infinite-dimensional operator governing all possible observations of the dynamic system, to act on the flow mapping of the dynamic system, we can equivalently learn the solution of a non-linear PDE family by solving simple linear prediction problems. We validate the KNO in mesh-independent, long-term, and zero-shot predictions on five representative PDEs (e.g., the Navier-Stokes equation and the Rayleigh-Bénard convection) and three real dynamic systems (e.g., global water vapor patterns and western boundary currents). In these experiments, the KNO exhibits notable advantages compared with previous state-of-the-art models, suggesting the potential of the KNO in supporting diverse science and engineering applications (e.g., PDE solving, turbulence modeling, and precipitation forecasting). • We propose a new neural operator model for partial differential equation (PDE) solving and realize an effective linear prediction of non-linear dynamics via Koopman operator. • Our approach achieves robust and accurate modeling of the long-term non-linear dynamics of PDE families or real systems. • Our model may serve as a basic unit for constructing new frameworks of PDE solving and dynamic system modeling. [ABSTRACT FROM AUTHOR]

We investigate the stability of statistically stationary conductive states for Rayleigh–Bénard convection that arise due to a bulk stochastic internal heating. Our results indicate that stochastic forcing at small magnitude has little to no effect, while strong stochastic forcing has a destabilizing effect. The methodology put forth in this article, which combines rigorous analysis with careful computation, provides an approach to hydrodynamic stability which is applicable to a variety of systems subject to a large scale stochastic forcing. • Nonlinear stability is defined for stochastic hydrodynamic systems with a stationary distribution. • Partially rigorous justification is provided. • Monte Carlo simulations imply that stochastic forcing has a destabilizing effect. • The marginally stable setting has rare events that are strongly destabilizing. [ABSTRACT FROM AUTHOR]

CO 2 -based binary mixtures are promising in energy engineering to improve efficiencies of thermodynamic cycles where supercritical CO 2 prevails. Indeed, under supercritical pressure and transcritical temperature conditions, special thermophysical properties of binary mixtures make the heat transfer process accompanied by enhanced cross-diffusion effects, i.e., the Soret effect and the Dufour effect. Their influences on heat transfer have not been well understood yet. This paper numerically investigates turbulent Rayleigh–Bénard convection in CO 2 - C 2 H 6 binary mixture. Calculations are performed based on a spectral element method solver considering various temperature differences and pressures. Results indicate that the flow field presents a double-vortex structure. The thickness of the boundary layer is negatively correlated with the flow intensity. Under a positive separation ratio, the concentration gradient induced by cross-diffusion effects enhances buoyancy, which in turn reinforces the natural convection and heat transfer. The enhancement becomes stronger as the critical pressure is approached. Turbulent fluctuations are also strengthened by cross-diffusion effects, except for temperature fluctuations. The unusual reduction in temperature fluctuations is attributed to the increased size of the thermal plume caused by the Dufour effect. • Transcritical temperature conditions and cross-diffusion effects are studied in Rayleigh–Bénard convection. • Time-averaged quantities and fluctuations for various fields are analyzed. • Present cases indicate heat transfer can be enhanced by cross-diffusion effects by more than 20%. • Unique behavior of temperature fluctuation is identified and explained. [ABSTRACT FROM AUTHOR]

• Mixed convection heat transfer of molten salt inside horizontal tubes is studied. • Buoyancy parameter, Bo , which can characterize the buoyancy effect is selected. • The critical Bo cr,1 where buoyancy starts to affect heat transfer is proposed. • The critical Bo cr,2 where the tube average Nu starts to decrease is proposed. • Heat transfer variations are presented for different regions of the horizontal tubes. Molten salt is a widely used heat transfer medium in the field of energy systems. In the engineering design, mixed convection heat transfer often occurs in the high heat flux tube convection heat transfer process, which can significantly change the convective heat transfer capability. However, optimizing the heat exchange conditions can improve the heat transfer capacity of molten salt. In this study, turbulent mixed convection heat transfer characteristics of Hitec molten salt inside horizontal cooling tubes are investigated numerically using the Reynolds stress turbulence model. The results show that the secondary flow caused by buoyancy can lead to significant nonuniform in heat transfer and wall temperature on the wall surface of the horizontal tube cross section. In addition, the buoyancy parameter Bo is selected to characterize the buoyancy effect on Hitec mixed convection heat transfer inside a horizontally cooled circular tube, and within the Bo range from 2.82 × 10−8 to 1.61 × 10−5, as the Bo increases, the relative average Nusselt number for the upper half tube wall gradually increases, the relative average Nusselt number for the lower half tube wall decreases, and the relative average Nusselt number for the entire tube wall shows the combined results of the upper half wall and the lower half wall relative average Nusselt numbers, which slightly increases and then decreases. Furthermore, based on the numerical data, the critical buoyancy parameters Bo cr,1 = 10−7 and Bo cr,2 = 6.96 × 10−6 at which the buoyancy force starts to affect heat transfer and the average Nusselt number for the entire tube wall starts to decrease are proposed, and variations of the mixed convection heat transfer against the buoyancy parameter Bo are presented respectively for different regions of the horizontal cooling tubes. Based on this research, a reasonable and widely applicable buoyancy parameter selection criterion can be constructed to guide the future engineering designs. [ABSTRACT FROM AUTHOR]

We consider the Navier–Stokes–Fourier system governing the motion of a general compressible, heat conducting, Newtonian fluid driven by random initial/boundary data. Convergence of the stochastic collocation and Monte Carlo numerical methods is shown under the hypothesis that approximate solutions are bounded in probability. Abstract results are illustrated by numerical experiments for the Rayleigh–Bénard convection problem. [ABSTRACT FROM AUTHOR]

• Rayleigh–Bénard Convection in a cubic cavity is considered. • The sensitivity of this system to the thermal boundary conditions is examined. • The emerging spatio-temporal behaviors are studied numerically and experimentally. • Attention is paid to the hierarchy of bifurcations and the related multiplicity of solutions. Thermal buoyancy flows and related heat transfer problems play a crucial role in a variety of fields and industrial applications. The present study is structured around the main objective of systematically investigating the response of fluid convection of the Rayleigh–Bénard type to heat loss taking place through the lateral walls of the considered fluid container. We elucidate, both experimentally and numerically, new aspects which deeply affect the dynamics when the classical assumptions of adiabatic or conducting walls cease to be valid. The emerging spatio-temporal behaviors are examined with respect to several parameters or conditions, including the dimensionality of the system (made accessible by dedicated numerical simulations based on the time-dependent and non-linear governing equations), the average temperature of the liquid, the applied temperature difference, the dependence of fluid properties on temperature and the intensity of heat transfer to the ambient. The results reveal the interesting triadic relationship among the heat exchanged through non-thermally controlled walls, the hierarchy of bifurcations displayed by the flow and the related multiplicity of solutions. [ABSTRACT FROM AUTHOR]

Large-eddy simulations (LES) of centrifugal convection in a closed rotating cavity with different thermal boundary conditions are presented for Rayleigh numbers (Ra) 10 7 ∼ 10 9. Previous results for radial convection with a positive radial temperature gradient and for axial convection with low Ra are confirmed. For axial convection, turbulence develops in the core flow at R a = 10 9 , but is considerably weaker than the turbulence for the radial and mixed convection. In mixed convection, the mean core temperature shows little radial variation as in radial convection, but has a significant axial temperature gradient as in axial convection. Compared to the radial and axial convection cases, both shroud and disc heat transfer are increased in mixed convection. Changes in disc heat transfer from the axial convection case are particularly strong. In all the conditions, laminar kinematic Ekman layers occur on the discs, but the disc thermal boundary layers for axial and mixed convection are considerably thicker. • Open-source CFD code is applied to the pure centrifugal buoyant driven flow with critical comparisons to previous data. • Large-eddy simulations are extended to axial convection and mixed convection with Rayleigh numbers up to 109. • Axial and mixed convection show axial temperature gradients and mean flow circulation in the cavity. • Mixed convection increases flow turbulence and heat transfer on the shroud and discs. [ABSTRACT FROM AUTHOR]

• The variation of evaporation rate with the liquid layer depth is determined. • The evolution of the flow pattern with various parameters is simulated. • The interaction between flow and temperature fields is elucidated. • The equation between temperature jump and heat flux on vapor side is fitted out. • The important role of convective heat transfer in energy transport is confirmed. The fundamental connection among interface phenomena, flow characteristics and energy transport during the evaporation process is crucial. In this work, a combination of experimental measurements and numerical calculations is used to study the water evaporation and the induced thermal convection in a cylindrical pool at low pressures. The temperature axial and radial distributions of the liquid and vapor phases near the interface are experimentally measured at different working conditions, and corresponding simulations are performed to obtain the flow fields. Based on the results, it is found that the flow pattern in the liquid layer and the length of the thermal conduction path are important factors affecting the evaporation rate. The dominant convection within the liquid layer varies with the heating wall temperature. The existence of a temperature jump at the interface is confirmed, and its correlation equation with the heat flux in the vapor phase is fitted. Importantly, almost all the energy required for evaporation is provided by the liquid phase, and the energy balance cannot be satisfied by thermal conduction alone. The convective heat transfer in the liquid phase is even dominant in strong evaporation. [ABSTRACT FROM AUTHOR]

Natural convection is a commonly occurring heat-transfer problem in many industrial flows and its prediction with conventional large eddy simulations (LES) at higher Rayleigh numbers using progressively coarser grids leads to increasingly inaccurate estimates of important performance indicators, such as Nusselt number (Nu). Thus, to improve the heat transfer predictions, we utilize Gene Expression Programming (GEP) to develop sub-grid scale (SGS) stress and SGS heat-flux models simultaneously for LES. The models' development is performed using reference direct numerical simulation data of a typical natural convection case, i.e. the Rayleigh–Bénard convection (RBC). The training frameworks are built by using alignment as the evaluation metrics of the basis functions when comparing to the Gaussian-filtered SGS stress and SGS heat-flux. The trained models in isotropic form, by utilizing the L 2 norm of the grid cell Δ L 2 as the length scale, demonstrate good performance in the bulk region, but less improved performance in the near wall region. It is shown, that for LES of wall-bounded flow, the GEP models in anisotropic form, i.e. using different grid length scale for the different spatial directions, are required to obtain generalized models suitable for different regions. Consequently, the a-priori results demonstrate a significant improvement in the prediction of both instantaneous and mean quantities for a wide range of filter widths. • The application of a machine-learning method is introduced to the Rayleigh–Bénard convection case. • The GEP models in anisotropic form are required for wall-bounded large-eddy simulations modelling. • The developed data-driven SGS stress and SGS heat-flux models are shown to perform well for a wide range of filter widths. [ABSTRACT FROM AUTHOR]

In this paper we report on direct numerical simulations of turbulent convection in a cuboidal pool that contains liquid water in the lower part and air in the upper one. The bottom wall is uniformly heated and natural convection is established in both phases, accompanied by water evaporation across the free surface of the water. The descent of the free surface due to evaporation is computed via a newly developed tracking algorithm based on the ghost-fluid method. We present results for three different cases which correspond to different pool heights. In all of them, the natural convection in the water lies in the soft-turbulence regime. Whereas in the gas, it lies in the laminar, transitional and soft-turbulence regimes, respectively. Our analysis focuses on the characteristics of the convective patterns in the two phases and the statistics of the various flow quantities of interest. According to our simulations, the flow in the water is organized in a single-roll Large-Scale Circulation (LSC). In the gas, it is organized in single or dual-roll LSCs, depending on the aspect ratio of the pool. Interestingly, the impingement points of the LSCs of the two phases at the free surface remain very close to one another, which is attributed to the continuity of the shear stresses across the free surface. Further, after the initial transient period, both the free-surface temperature and the evaporative mass flux are stabilized and remain almost constant, but they exhibit small-scale fluctuations in time due to turbulence. Also, the transport of water vapor in air has similar properties as the heat transport, and the ratio between the Sherwood and Nusselt numbers is very close to the Lewis number for air. [Display omitted] • Direct numerical simulations of turbulent convection in water pools with evaporation. • Dynamic computation of the evaporation rate and descent of the free surface. • The impingement points of the large-scale circulations at the free surface coincide. • The evaporation rate is stabilized but exhibits small fluctuations due to turbulence. • The ratio of the Sherwood and Nusselt numbers in air is close to the Lewis number. [ABSTRACT FROM AUTHOR]

We investigate the large-scale circulation (LSC) in a turbulent Rayleigh-Bénard convection flow in a cubic closed convection cell by means of direct numerical simulations at a Rayleigh number Ra = 106. The numerical studies are conducted for single flow trajectories up to 105 convective free-fall times to obtain a sufficient sampling of the four discrete LSC states, which can be summarized to one macrostate, and the two crossover configurations which are taken by the flow in between for short periods. We find that large-scale dynamics depends strongly on the Prandtl number Pr of the fluid which has values of 0.1, 0.7, and 10. Alternatively, we run an ensemble of 3600 short-term direct numerical simulations to study the transition probabilities between the discrete LSC states. This second approach is also used to probe the Markov property of the dynamics. Our ensemble analysis gave strong indication of Markovianity of the transition process from one LSC state to another, even though the data are still accompanied by considerable noise. It is based on the eigenvalue spectrum of the transition probability matrix, further on the distribution of persistence times and the joint distribution of two successive microstate persistence times. This article is part of the theme issue 'Mathematical problems in physical fluid dynamics (part 1)'. [ABSTRACT FROM AUTHOR]

Recent direct numerical simulations (DNS) and computations of exact steady solutions suggest that the heat transport in Rayleigh–Bénard convection (RBC) exhibits the classical 1/3 scaling as the Rayleigh number Ra→∞ with Prandtl number unity, consistent with Malkus–Howard's marginally stable boundary layer theory. Here, we construct conditional upper and lower bounds for heat transport in two-dimensional RBC subject to a physically motivated marginal linear-stability constraint. The upper estimate is derived using the Constantin–Doering–Hopf (CDH) variational framework for RBC with stress-free boundary conditions, while the lower estimate is developed for both stress-free and no-slip boundary conditions. The resulting optimization problems are solved numerically using a time-stepping algorithm. Our results indicate that the upper heat-flux estimate follows the same 5/12 scaling as the rigorous CDH upper bound for the two-dimensional stress-free case, indicating that the linear-stability constraint fails to modify the boundary-layer thickness of the mean temperature profile. By contrast, the lower estimate successfully captures the 1/3 scaling for both the stress-free and no-slip cases. These estimates are tested using marginally-stable equilibrium solutions obtained under the quasi-linear approximation, steady roll solutions and DNS data. This article is part of the theme issue 'Mathematical problems in physical fluid dynamics (part 1)'. [ABSTRACT FROM AUTHOR]

The background method is a widely used technique to bound mean properties of turbulent flows rigorously. This work reviews recent advances in the theoretical formulation and numerical implementation of the method. First, we describe how the background method can be formulated systematically within a broader 'auxiliary function' framework for bounding mean quantities, and explain how symmetries of the flow and constraints such as maximum principles can be exploited. All ideas are presented in a general setting and are illustrated on Rayleigh–Bénard convection between stress-free isothermal plates. Second, we review a semidefinite programming approach and a timestepping approach to optimizing bounds computationally, revealing that they are related to each other through convex duality and low-rank matrix factorization. Open questions and promising directions for further numerical analysis of the background method are also outlined. This article is part of the theme issue 'Mathematical problems in physical fluid dynamics (part 1)'. [ABSTRACT FROM AUTHOR]

We study two-dimensional Rayleigh–Bénard convection with Navier-slip, fixed temperature boundary conditions and establish bounds on the Nusselt number. As the slip-length varies with Rayleigh number Ra , this estimate interpolates between the Whitehead–Doering bound by Ra512 for free-slip conditions (Whitehead & Doering. 2011 Ultimate state of two-dimensional Rayleigh–Bénard convection between free-slip fixed-temperature boundaries. Phys. Rev. Lett.106, 244501) and the classical Doering–Constantin Ra12 bound (Doering & Constantin. 1996 Variational bounds on energy dissipation in incompressible flows. III. Convection. Phys. Rev. E53, 5957–5981). This article is part of the theme issue 'Mathematical problems in physical fluid dynamics (part 1)'. [ABSTRACT FROM AUTHOR]

We present an experimental and numerical study of turbulent thermal convection in the presence of an effective horizontal buoyancy that generates extra shear at the boundary. Geometrical confinements are also applied by varying the streamwise and spanwise aspect ratios of the convection cell to condense the plumes. With these, we systematically explore the effects of plume and shear on heat transfer. It is found that a streamwise confinement results in increased plume coverage but decreased shear compared with spanwise confinement. The fact that streamwise confinement leads to a higher vertical heat transfer efficiency than the spanwise confined case suggests that the increase of plume coverage is the dominant effect responsible for the enhanced heat transfer. Our results highlight the potential applications of coherent structure manipulation in efficient passive heat transfer control and thermal engineering.We also analyse the energetics of the present system and derive the expression of mixing efficiency accordingly. The mixing efficiency is found to increase with both the buoyancy ratio and streamwise dimension. [ABSTRACT FROM AUTHOR]

The onset of thermosolutal convection in a uniformly rotating horizontal nanofluid layer is investigated. By employing an order-1 Galerkin residual method, an approximation of the instability threshold has been determined. A sufficient condition for the onset of steady convection has been found. [ABSTRACT FROM AUTHOR]

The occurrence and shape of turbulent structures in mixed convection flows through a differently heated vertical channel are investigated in terms of thermally induced attenuation and amplification of turbulent velocity, pressure, and temperature fluctuations using direct numerical simulations. It is shown that the wall‐normal momentum transport is decreased and increased near the heated and cooled wall, respectively, and that this leads to a reduced and elevated production of turbulent velocity fluctuations in the streamwise velocity component in the aiding and opposing flow, respectively. The corresponding flow structures are smoother, faster and warmer in the aiding flow and aligned along the main flow, while the colder structures in the opposing flow are more frayed and less directed. The warmer flow structures in the aiding flow are overall more stable than the colder structures in the opposing flow. Besides, the study reveals that the position of the maximum temperature fluctuations moves toward the heated wall, so that the sweeps produced at the two walls are affected differently by the former. As a consequence, the distance and time period over which the fluctuations develop in the aiding flow are shorter than in the opposing flow. It is further shown that vortex structures oriented in the streamwise direction usually arise with an offset to the right or left above a sweep or an ejection, whereby the decreasing values of the correlation coefficients with increasing Grashof number indicate a weakening of the vortex structures. Since none of the evaluated vortex criteria, that is, the distributions of the vorticity, λ2‐ value or Rortex‐value correlate well with the evaluated minima of the pressure fluctuations, they do not allow a clear identification of the vortex structures. Finally, analyzing the budget of the turbulent kinetic energy it is confirmed that the velocity fluctuations are only indirectly influenced by the buoyancy force. Thus, the attenuation and amplification of the turbulent velocity fluctuations is reflected in the reduction and exaggeration of the Reynolds shear stresses in the aiding and opposing flow, respectively. [ABSTRACT FROM AUTHOR]

We study the stability of steady convection rolls in two-dimensional Rayleigh-Bénard convection with free-slip boundaries and horizontal periodicity over 12 orders of magnitude in the Prandtl number (10-6 = Pr = 106) and 6 orders of magnitude in the Rayleigh number (8π4 < Ra = 108). The analysis is facilitated by partitioning our modal expansion into so-called even and odd modes. With aspect ratio Γ = 2, we observe that zonal modes (with horizontal wavenumber equal to zero) can emerge only once the steady convection roll state consisting of even modes only becomes unstable to odd perturbations. We determine the stability boundary in the (Pr, Ra) plane and observe remarkably intricate features corresponding to qualitative changes in the solution, as well as three regions where the steady convection rolls lose and subsequently regain stability as the Rayleigh number is increased. We study the asymptotic limit Pr → 0 and find that the steady convection rolls become unstable almost instantaneously, eventually leading to nonlinear relaxation osculations and bursts, which we can explain with a weakly nonlinear analysis. In the complementary large-Pr limit, we observe that the zonal modes at the instability switch off abruptly at a large, but finite, Prandtl number. [ABSTRACT FROM AUTHOR]

We report on the presence of the boundary zonal flow in rotating Rayleigh-Bénard convection evidenced by two-dimensional particle image velocimetry. Experiments were conducted in a cylindrical cell of aspect ratio Γ = D/H = 1 between its diameter (D) and height (H). As the working fluid, we used various mixtures of water and glycerol, leading to Prandtl numbers in the range 6.6 ≲ Pr ≲ 76. The horizontal velocity components were measured at a horizontal cross-section at half height. The Rayleigh numbers were in the range 108 = Ra = 3 × 109. The effect of rotation is quantified by the Ekman number, which was in the range 1.5 × 10-5 = Ek = 1.2 × 10-3 in our experiment. With our results we show the first direct measurements of the boundary zonal flow (BZF) that develops near the sidewall and was discovered recently in numerical simulations as well as in sparse and localized temperature measurements. We analyse the thickness δd of the BZF as well as its maximal velocity as a function of Pr, Ra and Ek, and compare these results with previous results from direct numerical simulations. [ABSTRACT FROM AUTHOR]

Moderate rotation and moderate horizontal confinement similarly enhance the heat transport in Rayleigh-Bénard convection (RBC). Here, we systematically investigate how these two types of flow stabilization together affect the heat transport. We conduct direct numerical simulations of confined-rotating RBC in a cylindrical set-up at Prandtl number Pr = 4.38, and various Rayleigh numbers 2 × 108 < Ra < 7 × 109. Within the parameter space of rotation (given as inverse Rossby number 0 < Ro-1 < 40) and confinement (given as height-to-diameter aspect ratio 2 < Γ-1 < 32), we observe three heat transport maxima. At lower Ra, the combination of rotation and confinement can achieve larger heat transport than either rotation or confinement individually, whereas at higher Ra, confinement alone is most effective in enhancing the heat transport. Further, we identify two effects enhancing the heat transport: (i) the ratio of kinetic and thermal boundary layer thicknesses controlling the efficiency of Ekman pumping, and (ii) the formation of a stable domain-spanning flow for an efficient vertical transport of the heat through the bulk. Their interfering efficiencies generate the multiple heat transport maxima. [ABSTRACT FROM AUTHOR]

The interplay between convective, rotational and magnetic forces defines the dynamics within the electrically conducting regions of planets and stars. Yet their triadic effects are separated from one another in most studies, arguably due to the richness of each subset. In a single laboratory experiment, we apply a fixed heat flux, two different magnetic field strengths and one rotation rate, allowing us to chart a continuous path through Rayleigh-Bénard convection (RBC), two regimes of magnetoconvection, rotating convection and two regimes of rotating magnetoconvection, before finishing back at RBC. Dynamically rapid transitions are determined to exist between jump rope vortex states, thermoelectrically driven magnetoprecessional modes, mixed wall- and oscillatory-mode rotating convection and a novel magnetostrophic wall mode. Thus, our laboratory 'pub crawl' provides a coherent intercomparison of the broadly varying responses arising as a function of the magnetorotational forces imposed on a liquid-metal convection system. [ABSTRACT FROM AUTHOR]

A hybrid (LB–FD) mathematical model has been constructed to investigate thermogravitational convection in closed rectangular cavities limited on one side by a heat-conducting wall of finite thickness. Within the framework of the formulated approach, the hydrodynamics is simulated by the lattice Boltzmann equation method using a Bhatnagar–Gross–Krook approximation and a two-dimensional nine-velocity scheme, and energy and heat conduction equations are solved by the method of finite differences. Numerical simulation has been conducted in varying the Rayleigh number, thickness, and relative heat conductivity of a wall. It has been established that the developed hybrid model provides an adequate reproduction of local and average characteristics of coupled heat transfer. The computation speed of the LB–FD model is 10 times higher compared to the approach based on solving Navier–Stokes equations in transformed "vorticity–flow function" variables. [ABSTRACT FROM AUTHOR]

The heat transfer effectiveness of nanofluids is adversely affected by the delay in convection onset. The lesser effectiveness, when compared to that of base fluid, is observed in a range of nanofluid layer thickness. The heat transfer coefficient of water–Al2O3 nanofluid can be enhanced by sustaining the equilibrium between Rayleigh number, temperature, particle volume fraction, and enclosure aspect ratio. In this paper, the specific correlation of fluid layer thickness and the onset of convection, which can significantly dominate the heat transfer characteristics of nanofluids are investigated using the concept of critical Rayleigh number. The water layer thickness for convection onset is first experimentally assessed for different real‐life heat flux densities. It is then performed for Al2O3–water nanofluid for varying volume fractions. With the increase in volume fraction even though thermal conductivity increases, the overall heat transfer enhancement of the nanofluid is reduced. Temperature involved (heat flux density), the volume fraction of the nanofluid used, nanofluid layer thickness (space availability for the cooling system), and mass of the nanoparticle influence heat transfer enhancement. A higher volume fraction may not always result in enhancement of heat transfer as far as nanofluids are concerned. [ABSTRACT FROM AUTHOR]

We analyze the power spectra and structure functions (SFs) of the temperature and radial velocity fields, calculated in the radial and azimuthal directions, in annular centrifugal Rayleigh–Bénard convection (ACRBC) for Rayleigh number Ra ∈ [ 10 8 , 10 11 ] , Prandtl number Pr = 10.7, and inverse Rossby number Ro − 1 = 16 using the spatial data obtained by quasi-two-dimensional direct numerical simulation. Bolgiano and Obukhov-like (BO59-like) scalings for the energy spectrum in both the azimuthal and radial directions and thermal spectrum in the azimuthal direction are observed. The range of BO59-like scaling becomes wider as Ra increases. At Ra = 10 11 , it is found that BO59-like scaling E u (k r) ∼ k r − 11 / 5 spans nearly two decades for the energy spectrum calculated in the radial direction. Power-law fittings in the range larger than the Bolgiano scales, the scaling exponents of transverse and longitudinal velocity SFs vs the order coincide with the theoretical prediction of BO59 scaling ζ p u = 3 p / 5 basically. The second-order temperature SFs exhibit a gradual transition from the Obukhov–Corrsin behavior at scales smaller than the Bolgiano scales to the BO59 behavior at scales larger than the Bolgiano scales. The slopes from the third to sixth-order temperature SFs are similar, which is similar to classical Rayleigh–Bénard convection and Rayleigh–Taylor turbulence. The probability density functions (p.d.f.) of temperature fluctuations δ T / σ T reveal the cold plumes are strong and the p.d.f. in different regions at high Ra are similar. The stronger turbulent-mixing and larger centrifugal buoyancy in ACRBC may result in the BO59-like scaling. [ABSTRACT FROM AUTHOR]