In this paper, we develop a multivariate regression model and a neural network model to predict the Reynolds number (Re) and Nusselt number in turbulent thermal convection. We compare their predictions with those of earlier models of convection: Grossmann-Lohse~[Phys. Rev. Lett. \textbf{86}, 3316 (2001)], revised Grossmann-Lohse~[Phys. Fluids \textbf{33}, 015113 (2021)], and Pandey-Verma [Phys. Rev. E \textbf{94}, 053106 (2016)] models. We observe that although the predictions of all the models are quite close to each other, the machine learning models developed in this work provide the best match with the experimental and numerical results.
A fully non-dimensional correlation for the Nusselt number associated to cooling processes in vertical storage tanks under laminar natural convection is presented. The derived correlation depends on the average temperature and can be used for the improvement of temperature profiles found from global methods. A Finite Volume method is employed using a transient bi-dimensional model in cylindrical coordinates and is experimentally validated. Forty cases of cooling with four aspect ratios, five overall heat transfer coefficients and two different volumes are considered. Thermal losses for the env…
In this paper, we extend Grossmann and Lohse's (GL) model [Phys. Rev. Lett. {\bf 86}, 3316 (2001)] for the predictions of Reynolds number (Re) and Nusselt number (Nu) in turbulent Rayleigh-Bénard convection (RBC). Towards this objective, we use functional forms for the prefactors of the dissipation rates in the bulk and the boundary layers. The functional forms arise due to inhibition of nonlinear interactions in the presence of walls and buoyancy compared to free turbulence, along with a deviation of viscous boundary layer profile from Prandtl-Blasius theory. We perform 60 numerical runs on a…
Results from direct numerical simulations for three dimensional Rayleigh-Benard convection in a cylindrical cell of aspect ratio 1/2 and Pr=0.7 are presented. They span five decades of Ra from $2\times 10^6$ to $2 \times10^{11}$. Good numerical resolution with grid spacing $\sim$ Kolmogorov scale turns out to be crucial to accurately calculate the Nusselt number, which is in good agreement with the experimental data by Niemela et al., Nature, 404, 837 (2000). In underresolved simulations the hot (cold) plumes travel further from the bottom (top) plate than in the fully resolved case, because t…
New insight into the contribution of the microscale vortex evolution towards convection heat transfer in porous media is presented in this paper. The objective is to determine how the microscale vortices influence convection heat transfer in turbulent flow inside porous media. The microscale temperature distribution is analyzed using flow visualization in 2D using streamlines and in 3D using Q structures. The pertinent observations are supplemented with the comparison of surface skin friction and heat transfer using: (1) surface skin friction lines and (2) joint PDF of pressure and skin fricti…
At the beginning of the second half of the twentieth century, Proudman and Pearson (J. Fluid. Mech.,2(3), 1956, pp.237-262) suggested that the functional form of the drag coefficient ($C_D$) of a single sphere subjected to uniform fluid flow consists of a series of logarithmic and power terms of the Reynolds number ($Re$).\ In this paper, we will explore the validity of the above statement for Reynolds numbers up to $10^{6}$ by using a symbolic regression machine learning method.\ The algorithm is trained by available experimental data and data from well-known correlations from the literature …
We consider the problem of horizontal convection in which non-uniform buoyancy, $b_{\rm s}(x,y)$, is imposed on the top surface of a container and all other surfaces are insulating. Horizontal convection produces a net horizontal flux of buoyancy, $\mathbf{J}$, defined by vertically and temporally averaging the interior horizontal flux of buoyancy. We show that $\overline{\mathbf{J}\cdot\mathbf{\nabla}b_{\rm s}}=-κ\langle|\boldsymbol{\nabla}b|^2\rangle$; overbar denotes a space-time average over the top surface, angle brackets denote a volume-time average and $κ$ is the molecular diffusivity o…
Rigorous upper limits on the vertical heat transport in two dimensional Rayleigh-Benard convection between stress-free isothermal boundaries are derived from the Boussinesq approximation of the Navier-Stokes equations. The Nusselt number Nu is bounded in terms of the Rayleigh number Ra according to $Nu \leq 0.2295 Ra^{5/12}$ uniformly in the Prandtl number Pr. This Nusselt number scaling challenges some theoretical arguments regarding the asymptotic high Rayleigh number heat transport by turbulent convection.
We investigate the influence of the thermal properties of the boundaries in turbulent Rayleigh-Benard convection on analytical bounds on convective heat transport. Using the Doering-Constantin background flow method, we systematically formulate a bounding principle on the Nusselt-Rayleigh number relationship for general mixed thermal boundary conditions of constant Biot number ηwhich continuously interpolates between the previously studied fixed temperature ($η= 0$) and fixed flux ($η= \infty$) cases, and derive explicit asymptotic and rigorous bounds. Introducing a control parameter R as a me…
A fluid between two spheres, concentric or not, at different temperatures will flow in the presence of a constant gravitational force. Although there is no possible hydrostatic state, energy transport is dominated by diffusion if temperature difference between the spheres is small enough. In this conductive regime the average Nusselt number remains approximately constant for all Rayleigh numbers below some critical value. Above the critical Rayleigh number, plumes appear and thermal convection takes place. We study this phenomenon, in particular the case where the inner sphere is displaced fro…
In this work, the Nusselt number is examined for periodically developed heat transfer in micro- and mini-channels with arrays of offset strip fins, subject to a constant heat flux. The Nusselt number is defined on the basis of a heat transfer coefficient which represents the spatially constant macro-scale temperature difference between the fluid and solid during conjugate heat transfer. Its values are determined numerically on a single unit cell of the array for Reynolds numbers between 1 and 600. Two combinations of the Prandtl number and the thermal conductivity ratio are selected, correspon…
The vaporization rate of aluminum droplets in shocked flows plays a crucial role in determining the energy release rate during the combustion of the aluminized energetic materials. In this paper, the physics of the vaporization of aluminum droplets in shocked flows is numerically investigated. Surrogate models for the temporally averaged Sherwood number and Nusselt number, cast as functions of shock Mach number and Reynolds number, are developed from the simulation-based data. The results show that the Sherwood number and the Nusselt number of the droplet increase monotonically with the Reynol…
Reduced-order models (ROMs) are systems of ordinary differential equations (ODEs) designed to approximate the dynamics of partial differential equations (PDEs). In this work, a distinguished hierarchy of ROMs is constructed for Rayleigh's 1916 model of natural thermal convection. These models are distinguished in the sense that they preserve energy and vorticity balances derived from the governing equations, and each is capable of modeling zonal flow. Various models from the hierarchy are analyzed to determine the maximal heat transport in a given model, measured by the dimensionless Nusselt n…
We consider laminar, fully-developed, Poiseuille flows of liquid in the Cassie state through diabatic, parallel-plate microchannels symmetrically textured with isoflux ridges. Through the use of matched asymptotic expansions we analytically develop expressions for (apparent hydrodynamic) slip lengths and variously-defined Nusselt numbers. Our small parameter ($ε$) is the pitch of the ridges divided by the height of the microchannel. When the ridges are oriented parallel to the flow, we quantify the error in the Nusselt number expressions in the literature and provide a new closed-form result. …
Laminar natural convection from two horizontally aligned isothermal cylinders in unconfined Power-law fluids has been investigated numerically. The effect of horizontal spacing (0<=(S/D)<=10) on both momentum and heat transfer characteristics has been delineated under the following pertinent parameters: Grashof number (10<=Gr<=1e3), Prandtl number (0.71<=n<=100), and Power-law index (0.4<=n<=1.6). The heat transfer characteristics are elucidated in terms of isotherms, local Nusselt number (Nu) distributions and average Nusselt number values, whereas the flow characteristics are interpreted in …
Bounds for the poloidal and toroidal kinetic energies and the heat transport are computed numerically for rotating convection at infinite Prandtl number with both no slip and stress free boundaries. The constraints invoked in this computation are linear or quadratic in the problem variables and lead to the formulation of a semidefinite program. The bounds behave as a function of Rayleigh number at fixed Taylor number qualitatively in the same way as the quantities being bounded. The bounds are zero for Rayleigh numbers smaller than the critical Rayleigh number for the onset of convection, they…
Previous numerical studies on homogeneous Rayleigh-Bénard convection, which is Rayleigh-Bénard convection (RBC) without walls, and therefore without boundary layers, have revealed a scaling regime that is consistent with theoretical predictions of bulk-dominated thermal convection. In this so-called asymptotic regime, previous studies have predicted that the Nusselt number ($Nu$) and the Reynolds number ($Re$) vary with the Rayleigh number ($Ra$) according to $Nu\sim Ra^{1/2}$ and $Re\sim Ra^{1/2}$ at small Prandtl number ($Pr$). In this study, we consider a flow that is similar to RBC but wit…
We study the melting dynamics of large ice balls in a turbulent von Karman flow at very high Reynolds number. Using an optical shadowgraphy setup, we record the time evolution of particle sizes. We study the heat transfer as a function of the particle scale Reynolds number for three cases: fixed ice balls melting in a region of strong turbulence with zero mean flow, fixed ice balls melting under the action of a strong mean flow with lower fluctuations, and ice balls freely advected in the whole flow. For the fixed particles cases, heat transfer is observed to be much stronger than in laminar f…
Measurements of heat transport, as expressed by the Nusselt number $Nu$, are reported for turbulent Rayleigh-Bénard convection of water containing up to 120 ppm by weight of poly-[ethylene oxide] with a molecular weight of $4\times10^6$ g/mole. Over the Rayleigh number range $ 5\times 10^9 \alt Ra \alt 7 \times 10^{10}$ $Nu$ is smaller than it is for pure water by up to 10%.
Non-Oberbeck-Boussinesq (NOB) effects on the flow organization in two-dimensional Rayleigh-Benard turbulence are numerically analyzed. The working fluid is water. We focus on the temperature profiles, the center temperature, the Nusselt number, and on the analysis of the velocity field. Several velocity amplitudes (or Reynolds numbers) and several kinetic profiles are introduced and studied; these together describe the various features of the rather complex flow organization. The results are presented both as functions of the Rayleigh number Ra (with Ra up to 10^8) for fixed temperature differ…
In thermal convection, roughness is often used as a means to enhance heat transport, expressed in Nusselt number. Yet there is no consensus on whether the Nusselt vs. Rayleigh number scaling exponent ($\mathrm{Nu} \sim \mathrm{Ra}^β$) increases or remains unchanged. Here we numerically investigate turbulent Rayleigh-Bénard convection over rough plates in two dimensions, up to $\mathrm{Ra}=10^{12}$. Varying the height and wavelength of the roughness elements with over 200 combinations, we reveal the existence of two universal regimes. In the first regime, the local effective scaling exponent ca…
We report on direct numerical simulations of two-dimensional, horizontally periodic Rayleigh-Bénard convection, focusing on its ability to drive large-scale horizontal flow that is vertically sheared. For the Prandtl numbers ($Pr$) between 1 and 10 simulated here, this large-scale shear can be induced by raising the Rayleigh number ($Ra$) sufficiently, and we explore the resulting convection for $Ra$ up to $10^{10}$. When present in our simulations, the sheared mean flow accounts for a large fraction of the total kinetic energy, and this fraction tends towards unity as $Ra\to\infty$. The shear…
Results from direct numerical simulations of vertical natural convection at Rayleigh numbers $1.0\times 10^5$-$1.0\times 10^9$ and Prandtl number $0.709$ support a generalised applicability of the Grossmann-Lohse (GL) theory, which was originally developed for horizontal natural (Rayleigh-B{é}nard) convection. In accordance with the GL theory, it is shown that the boundary-layer thicknesses of the velocity and temperature fields in vertical natural convection obey laminar-like Prandtl-Blasius-Pohlhausen scaling. Specifically, the normalised mean boundary-layer thicknesses scale with the $-1/2$…
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 $\rm{Ra}$, this estimate interpolates between the Whitehead-Doering bound by $\rm{Ra}^{\frac{5}{12}}$ for free-slip conditions [13] and the classical Doering-Constantin $\rm{Ra}^{\frac{1}{2}}$ bound [4].
The possible transition to the so-called ultimate regime, wherein both the bulk and the boundary layers are turbulent, has been an outstanding issue in thermal convection, since the seminal work by Kraichnan [Phys. Fluids 5, 1374 (1962)]. Yet, when this transition takes place and how the local flow induces it is not fully understood. Here, by performing two-dimensional simulations of Rayleigh-Bénard turbulence covering six decades in Rayleigh number Ra up to $10^{14}$ for Prandtl number Pr $=1$, for the first time in numerical simulations we find the transition to the ultimate regime, namely a…
Thermal convection driven by internal heat sources and sinks was recently shown experimentally to exhibit the mixing-length, or "ultimate", scaling-regime: the Nusselt number $Nu$ (dimensionless heat flux) increases as the square-root of the Rayleigh-number $Ra$ (dimensionless internal temperature difference). While for standard Rayleigh-Bénard convection this scaling regime was proven to be a rigorous upper bound on the Nusselt number, we show that this is not so for convection driven by internal sources and sinks. To wit, we introduce an asymptotic expansion to derive steady nonlinear soluti…
We study turbulent Rayleigh-Bénard convection over four decades of Rayleigh numbers 4E8 < Ra < 2E12, while harmonically modulating the temperatures of the plates of our cylindrical cell. We probe the flow by temperature sensors placed in the cell interior and embedded in the highly conducting copper plates and detect thermal waves propagating at modulation frequency in the bulk of the convective flow. We confirm the recent numerical prediction [PRL 125, 154502 (2020)] of the significant enhancement of Nusselt number and report its dependence on the frequency and amplitude of the temperature mo…
To understand how internal flow structures manifest themselves in the global heat transfer, we study the correlation between different flow modes and the instantaneous Nusselt number ($Nu$) in a two-dimensional square Rayleigh-Bénard convection cell. High-resolution and long-time direct numerical simulations are carried out for Rayleigh numbers between $10^{7}$ and $10^{9}$ and a Prandtl number of 5.3. The investigated Nusselt numbers include the volume-averaged $Nu_{\text{vol}}$, the wall-averaged $Nu_{\text{wall}}$, the kinetic energy dissipation based $Nu_{\text{kinetic}}$, and the thermal …
We measured Reynolds numbers R_e of turbulent Rayleigh-Benard convection over the Rayleigh-number range 2 times 10^8 < R < 10^11 and Prandtl-number range 3.3 < sigma < 29 for cylindrical samples of aspect ratio Gamma = 1. For R < R_c = 3 times 10^9 we found R_e ~ R^beta_eff with beta_eff = 0.46 < 1/2. Here both the sigma- and R-dependences are quantitatively consistent with the Grossmann-Lohse (GL) prediction. For R > R_c we found R_e = 0.106 sigma^-3/4 R^1/2, which differs from the GL prediction. The relatively sharp transition at R_c to the large-R regime suggests a qualitative and sudden ch…
Under the limit of infinite Prandtl number, we derive analytical expressions for the large-scale quantities, e.g., Péclet number Pe, Nusselt number Nu, and rms value of the temperature fluctuations $θ_\mathrm{rms}$. We complement the analytical work with direct numerical simulations, and show that $\mathrm{Nu} \sim \mathrm{Ra}^γ$ with $γ\approx (0.30-0.32)$, $\mathrm{Pe} \sim \mathrm{Ra}^η$ with $η\approx (0.57-0.61)$, and $θ_\mathrm{rms} \sim \mathrm{const}$. The Nusselt number is observed to be an intricate function of $\mathrm{Pe}$, $θ_\mathrm{rms}$, and a correlation function between the v…
Natural convection from a stack of isothermal solid horizontal cylinders has been investigated numerically in a three dimensional computational domain. Simulations were conducted in both laminar and turbulent flow regimes of Rayleigh number (Ra) spanning in the range (10^4 to 10^8) and (10^10 to 10^13), respectively. In the present study, the length to diameter ratio of the cylinders has been varied in the range 0.5 to 20. Three different stack arrangements were considered for the numerical simulations by arranging three, six and ten number of cylinders in a triangular manner. The present comp…
Turbulent Rayleigh-Bénard convection in slender cylindrical cells exhibits rich dynamics of the large-scale circulation (LSC), with several rolls stacked on top of each other. We propose that the elliptical instability is the mechanism which causes the twisting and breaking of the LSC into multiple rolls and that the volume-averaged heat and momentum transport, represented by the Nusselt number and Reynolds number, is generally weaker for larger number $n$ of the LSC rolls. This is supported by direct numerical simulations for $Ra=5\times10^5$, $Pr=0.1$, $H=5D$ and $1\leq~n\leq4$.
We invoke the concepts of magnetic boundary layer and magnetic Rayleigh number and use the magnetic energy dissipation rates in the bulk and the boundary layers to derive some scaling laws expressing how Nusselt number depends on magnetic Rayleigh number, Prandtl number and magnetic Prandtl number for the simple case of turbulent magnetohydrodynamic Rayleigh-Benard convection in the presence of uniform vertical magnetic field.
In this paper we present scaling of large-scale quantities like Peclét and Nusselt numbers, and the dissipation rates of kinetic energy and entropy. Our arguments are based on the scaling of bulk quantities and earlier experimental and simulation results. We also present the inertial-range properties of spectra and fluxes of kinetic energy and entropy.
The progress in our understanding of several aspects of turbulent Rayleigh-Benard convection is reviewed. The focus is on the question of how the Nusselt number and the Reynolds number depend on the Rayleigh number Ra and the Prandtl number Pr, and on how the thicknesses of the thermal and the kinetic boundary layers scale with Ra and Pr. Non-Oberbeck-Boussinesq effects and the dynamics of the large-scale convection-roll are addressed as well. The review ends with a list of challenges for future research on the turbulent Rayleigh-Benard system.
Rayleigh-Benard convection and Taylor-Couette flow are two canonical flows that have many properties in common. We here compare the two flows in detail for parameter values where the Nusselt numbers, i.e. the thermal transport and the angular momentum transport normalized by the corresponding laminar values, coincide. We study turbulent Rayleigh-Benard convection in air at Rayleigh number Ra=1e7 and Taylor-Couette flow at shear Reynolds number Re_S=2e4 for two different mean rotation rates but the same Nusselt numbers. For individual pairwise related fields and convective currents, we compare …
We study Rayleigh Bénard convection based on the Boussinesq approximation. We are interested in upper bounds on the Nusselt number $\mathrm{Nu}$, the upwards heat transport, in terms of the Rayleigh number $\mathrm{Ra}$, that characterizes the relative strength of the driving mechanism and the Prandtl number $\mathrm{Pr}$, that characterizes the strength of the inertial effects. We show that, up to logarithmic corrections, the upper bound $\mathrm{Nu}\lesssim \mathrm{Ra}^{\frac{1}{3}}$ of Constantin and Doering in 1999 persists as long as $\mathrm{Pr}\gtrsim \mathrm{Ra}^{\frac{1}{3}}$ and then…
Dynamics of a liquid drop falling through a quiescent medium of another liquid is investigated in external uniform electric field. The electrohydrodynamics of a drop is governed by inherent deformability of the drop (defined by capillary number), the electric field strength (defined by Masson number) and the surface charge convection (quantified by electric Reynolds number). Surface charge convection generates nonlinearilty in a electrohydrodynamics problem by coupling the electric field and flow field. In Stokes limit, most existing theoretical models either considered weak charge convection …
The convective heat transfer and flow behavior of graphene-water nanofluids are studied experimentally by focusing on transitional flow. Graphene-water nanofluids with different particle mass fractions (0.025, 0.1 and 0.2%) are produced following two-step method and using PVP as a surfactant. Thermo-physical characterization is performed by measuring viscosity and thermal conductivity of the nanofluids. Convection characteristics are experimentally studied from laminar to turbulent flow regimes. It is seen that pressure drop increases dramatically in the transition region, and laminar to turbu…
Using direct numerical simulations of Rayleigh-Bénard convection (RBC) under free-slip boundary condition, we show that the normalized correlation function between the vertical velocity field and the temperature field, as well as the normalized viscous dissipation rate, scales as $Ra^{-0.22}$ for moderately large Rayleigh number $Ra$. This scaling accounts for the Nusselt number ($Nu$) exponent to be around 0.3 observed in experiments. Numerical simulations also reveal that the above normalized correlation functions are constants for the convection simulation under periodic boundary conditions…
Penetrative turbulent Rayleigh-Bénard convection which depends on the density maximum of water near $4^\circ\rm{C}$ is studied using two-dimensional (2D) and three-dimensional (3D) direct numerical simulations (DNS). The working fluid is water near $4^\circ\rm{C}$ with Prandtl number $Pr=11.57$. The considered Rayleigh numbers $Ra$ range from $10^7$ to $10^{10}$. The density inversion parameter $θ_m$ varies from 0 to 0.9. It is found that the ratio of the top and bottom thermal boundary-layer thickness ($F_λ=λ_t^θ/λ_b^θ$) increases with increasing $θ_m$, and the relationship between $F_λ$ and …
In this paper we estimate the relative strengths of various terms of the Rayleigh-Bénard equations. Based on these estimates and scaling analysis, we derive a general formula for the large-scale velocity, $U$, or the Péclet number that is applicable for arbitrary Rayleigh number $\mathrm{Ra}$ and Prandtl number $\mathrm{Pr}$. Our formula fits reasonably well with the earlier simulation and experimental results. Our analysis also shows that the wall-bounded convection has enhanced viscous force compared to free turbulence. We also demonstrate how correlations deviate the Nusselt number scaling …
We conduct direct numerical simulations for turbulent Rayleigh-Bénard (RB) convection, driven simultaneously by two scalar components (say, temperature and salt concentration) with different molecular diffusivities, and measure the respective fluxes and the Reynolds number. To account for the results, we generalize the Grossmann-Lohse theory for traditional RB convections~(Grossmann and Lohse, J. Fluid Mech., 407, 27-56; Phys. Rev. Lett., 86, 3316-3319; Stevens et al., J. Fluid Mech., 730, 295-308) to this two-scalar turbulent convection. Our numerical results suggest that the generalized theo…
A solvable turbulent model is used to predict both the structure of the boundary layer and the scaling laws in thermal convection. The transport of heat depends on the interplay between the thermal, viscous and integral scales of turbulence, and thus, on both the Prandtl number and the Reynolds numbers. Depending on their values, a wide variety of possible regimes is found, including the classical 2/7 and 1/3 law, and a new $4/13=0.308$ law for the Nusselt power law variation with the Rayleigh number.
We present numerical simulations of three-dimensional thermal convective flows in a cubic cell at high Rayleigh number using thermal lattice Boltzmann (LB) method. The thermal LB model is based on double distribution function approach, which consists of a D3Q19 model for the Navier-Stokes equations to simulate fluid flows and a D3Q7 model for the convection-diffusion equation to simulate heat transfer. Relaxation parameters are adjusted to achieve the isotropy of the fourth-order error term in the thermal LB model. Two types of thermal convective flows are considered: one is laminar thermal co…
A detailed study of the Rayleigh-Bénard convection in two-dimensions with free-slip boundaries is presented. Pseudo-spectral method has been used to numerically solve the system for Rayleigh number up to $3.3 \times 10^7$. The system exhibits various convective states: stationary, oscillatory, chaotic and soft-turbulent. The `travelling rolls' instability is observed in the chaotic regime. Scaling of Nusselt number shows an exponent close to 0.33. Studies on energy spectrum and flux show an inverse cascade of kinetic energy and a forward cascade of entropy. This is consistent with the shell-to…
Measurements of the Nusselt number $Nu$ and of temperature variations $ΔT_b$ in the bulk fluid are reported for turbulent Rayleigh-Bénard convection of a cylindrical sample. They cover the Rayleigh-number range $10^{9} \alt Ra \alt 3\times 10^{14}$ using He (Prandtl number $Pr = 0.67$), N$_2$ ($Pr = 0.72$) and SF$_6$ ($Pr = 0.79$ to 0.84) at pressures up to 15 bars and near-ambient temperatures. The sample had a height $L=2.24$m and diameter $D = 1.12$m and was located in a new High-Pressure Convection Facility (HPCF) at the Max Planck Institute for Dynamics and Self-Organization in Göttingen,…
The hydrodynamic and thermal characteristics of a freely-vibrating circular cylinder in mixed convection flow are numerically investigated at low Reynolds numbers. The numerical investigations are conducted for a range of parameters, Ur = [2.0, 10], Pr = [0.7, 10] and Ri = [0.5, 2.0]. Whereas the Reynolds number, the mass ratio and the damping ratio are fixed. A secondary VIV lock-in region is found in the cases of high Richardson number Ri=2.0 for high reduced velocity values, in which the buoyancy-driven flow is non-trivial. A wide VIV lock-in region is formed with tremendous energy transfer…
We present a numerical study of Rayleigh-Bénard convection disturbed by a longitudinal wind. Our results show that under the action of the wind, the vertical heat flux through the cell initially decreases, due to the mechanism of plumes-sweeping, and then increases again when turbulent forced convection dominates over the buoyancy. As a result, the Nusselt number is a non-monotonic function of the shear Reynolds number. We provide a simple model that captures with good accuracy all the dynamical regimes observed. We expect that our findings can lead the way to a more fundamental understanding …
We study turbulent natural convection in enclosures with conjugate heat transfer. The simplest way to increase the heat transfer in this flow is through rough surfaces. In numerical simulations often the constant temperature is assigned at the walls in contact with the fluid, which is unrealistic in laboratory experiments. The DNS (Direct Numerical Simulation), to be of help to experimentalists, should consider the heat conduction in the solid walls together with the turbulent flow between the hot and the cold walls. Here the cold wall, $0.5h$ thick (where $h$ is the channel half-height) is sm…
