Although transient convection is ubiquitous in natural and manmade phenomena, few research works attempted to make a compact model for it, altogether, others attempted a compact model that contradicts problem physics. The correct modelling pattern is deduced here analytically for a simple geometry, but it can readily be used for many common applications such as the transient heating of an evacuated solar tube due to temporary cloud shading or for a more precise model of transient building wall heating in a zero-energy building approach. As opposed to detailed model, which is based on the governing PDE with a fixed and rigid boundary and initial conditions, usually solved numerically, aiming at obtaining temperatures everywhere and at any time for a prescribed boundary and initial conditions, the compact model on the contrary is based on a few simple equations, and aims at giving directly the relation between heat flux and the temperature difference producing it, for any boundary and initial conditions. For transient convection prevails as of today an unphysical approach consisting of modeling it by using a time variant thermal resistance. In this work, starting from the energy PDE, applied to a simple but typical transient forced convection problem, we will get analytically the correct modelling pattern. This has two main advantages: It replaces the classical unphysical approach, with a pair of time constants, one for each important temperature (the fluid bulk and that near the wall), which has an evident physical meaning and can be readily extended to more complex geometries. In contrast with the time varying resistance model, one and the same model as deduced here can be reused for any arbitrary time varying function of the input heat flux. Model validation was made by comparing with a fully blown CFD simulation.
The paper is devoted to the study of the formation of stratification in an incompressible fluid due to convective laminar flows in horizontal layers heated from the side. Medium and intensive modes of stationary laminar thermal, concentrational and thermo-concentrational (in particular thermohaline) convection are considered, in which nonlinear flow features are manifested, which can radically change the flow structure and the characteristics of heat and mass transfer. The solutions of the problems of laminar problems of convection show the features of the formation of layered structures, vert…
A comprehensive study of the problem of laminar film condensation with both a gravitational type body force and a moving vapour concurrent and parallel to the surface has been presented here. It demonstrates where both the body force and vapour velocity are significant through a comprehensive numerical solution obtained by a modified Keller box method. Important parameters governing condensation and heat transfer of pure vapour are determined. A perturbation analysis is applied in the leading edge and downstream regimes. The thin film approximations for the both regimes are obtained and compar…
This study aims to build a theoretical model to describe the ignition process of spherical spray flame laden with fuel droplets under overall fuel-lean condition. Two characteristic fronts are introduced to reveal where the evaporation starts and ends in the ignition process. The results demonstrate that the flame has been strengthened with extra fuel droplet adding while the minimum ignition energy (MIE) is decreased. The evolution of the two evaporation fronts in the flame kernel and propagating branches has also be revealed coupled with the evaporation zone length.
Liquid-infused surfaces (LIS) can reduce friction drag in both laminar and turbulent flows. However, the heat transfer properties of such multi-phase surfaces have still not been investigated to a large extent. We use numerical simulations to study conjugate heat transfer of liquid-filled grooves. It is shown that heat transfer can increase for both laminar and turbulent liquid flows due to recirculation in the surface texture. For the increase to be substantial, the thermal conductivity of the solid must be similar to the thermal conductivity of the fluids, and the recirculation in the groove…
This article represents a set of results numerically studied in the framework of laminar double diffusive natural convection. We have investigated the thermophysical comportment of Water-based incompressible nanofluids circulating, due to buoyancy forces, inside a two-dimensional enclosed rectangular cavity for two comparable cases of considering or not a centered isothermal block. Results of this investigation are mainly built on parametric study of the most analytical variables that govern the flow. The buoyancy ratio ranged from -5 to 100, while Rayleigh number ranged from 103 to 106, and L…
Heat and mass transfers of the evaporation of rotating hydrocarbons liquid droplet of ternary components, in forced convection are studied numerically. Comparison between our numerical results and those obtained in the literature shows qualitative and quantitative satisfactory agreements, in rotatory forced convection. Optimal values of the wind and rotational velocities of the liquid droplet have been determined. New correlations expressing the evaporation rate in terms of Dgheim & Reynolds numbers are proposed. Other new correlations expressing the evaporation rate in terms of Dgheim, Reynol…
A theoretical study is presented in this paper to investigate the conjugate heat transfer across a vertical finite wall separating two forced and free convection flows at different temperatures. The heat conduction in the wall is in the transversal direction and countercurrent boundary layers are formed on the both sides of the wall. The governing equations of this problem and their corresponding boundary conditions are all cast into a dimensionless form by using a non-similarity transformation. These resultant equations with multiple singular points are solved numerically using a very efficie…
Hydrogen-enrichment of conventional natural gas mixtures is an actively-explored strategy for reducing pollutant emissions from combustion. This study investigates the effect of hydrogen enrichment on the unsteady flame response to perturbations, with a view to understanding the implications for thermoacoustic stability. The Level Set Approach for kinematically tracking the flame front was applied to a laminar conical premixed methane / hydrogen / air flame subjected to 2D incompressible velocity perturbations. For hydrogen enrichment levels ranging from 0% to 80% by volume, the resulting unst…
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…
In the above paper [Chaos, Solitons & Fractals, 13 (2002) 1843-1850] the author treats the boundary layer flow along a vertical isothermal plate of an electrically conducting fluid. The plate lies in a vertical free stream of constant velocity $u_\infty$, constant temperature $T_\infty$ and constant mass concentration $C_\infty$. The plate moves vertically with a velocity which is a linear function of distance $x$ ($u_w=cx$). A transverse magnetic field with constant strength $B_0$ is imposed on the flow. The boundary layer equations are integrated numerically. However, there is a fundamental …
Laminar natural convection at unity Schmidt number over a horizontal surface with a weak normal velocity at the wall is studied using an integral analysis. To characterise the strength of the blowing, we define a non-dimensional parameter called the blowing parameter. After benchmarking with the no blowing case, the effect of the blowing parameter on boundary layer thickness, velocity and concentration profiles is obtained. Weak blowing is seen to increase the wall shear stress. For blowing parameters greater than unity, the diffusional flux at the wall becomes negligible and the flux is almos…
In this study, we performed highly resolved large-eddy simulations (LES) to investigate the influence of variable properties on the forced turbulent convection in a channel. The constant heat flux boundary condition permits wall temperature fluctuations and thus induces variations of fluid properties. Since the effect of viscosity on the flow exhibits $Re_τ^{-1}$ scaling, we only considered $Re_τ= 180$ in the present study. Compared to the flow with constant properties, results indicate that the variable properties have trivial effects on the mean velocity and temperature profiles, Reynolds sh…
We investigate the dependency of the magnitude of heat transfer in a convection cell as a function of its inclination by means of experiments and simulations. The study is performed with a working fluid of large Prandtl number, $Pr \simeq 480$, and at Rayleigh numbers $Ra \simeq 10^{8}$ and $Ra \simeq 5 \times 10^{8}$ in a quasi-two-dimensional rectangular cell with unit aspect ratio. By changing the inclination angle ($β$) of the convection cell, the character of the flow can be changed from moderately turbulent, for $β= 0^o$, to laminar and steady at $β= 90^o$. The global heat transfer is fo…
A fluid dynamics video is linked to this article, which have been submitted to the Gallery of Fluid Motion as part of the 65th American Physical Society meeting of the Division of Fluid Dynamics, held in San Diego, California, USA, over 17-20 November 2012. The video serves to visualize flows generated in a rectangular enclosure that are subjected to both mechanical and thermal forcing through a common horizontal boundary. This system exhibits features consistent with either horizontal convection or lid-driven cavity flows depending on the ratio between thermal and mechanical stirring, and thr…
This paper presents a study on wave cancellation in forced jets. Building on recent work on real-time control of forced turbulent jets [1,2], we here assess the effect of jet upstream conditions and nonlinearity on wave-cancellation performance. The experiments are performed in jets with laminar and turbulent boundary layers inside the nozzle. An open-loop campaign is first conducted, in which the goal is to analyse the jet response to stochastic forcing with variable bandwidth. The upstream conditions of the jet are found to have a strong influence on the jet response. For narrow forcing band…
While there has been a large interest in studying the role of dissolution-driven free convection in the context of geological sequestration, the contribution of forced convection has been largely ignored. This manuscript considers CO$_2$ sequestration in saline aquifers with natural background flow and uses theoretical arguments to compute the critical background velocity needed to establish the forced convective regime. The theoretical arguments are supported by two dimensional high-resolution numerical simulations which demonstrate the importance of forced convection in enhancing dissolution…
The present work focuses on the study of mixed convection of a purely viscous shear-thinning fluid in a horizontal annular eccentric duct. The inner and outer cylinders are heated with constant and uniform heat flux densities. The objective of this work is to study the effect of the variation of eccentricity, rheological behavior of the fluid as well as the thermodependency of the rheological parameters on the reorganization of the flow and thermal stratification caused by the buoyancy forces. At the entrance of the heating zone, the dynamic regime is assumed to be established and the temperat…
A starting plume or jet has a well-defined, evolving head that is driven through the surrounding quiescent fluid by a localized flux of either buoyancy or momentum, or both. We studied the scaling and morphology of starting plumes produced by a constant flux of buoyant fluid from a small, submerged outlet. The plumes were laminar and spanned a wide range of plume Richardson numbers Ri. Ri is the dimensionless ratio of the buoyancy forces to inertial effects, and is thus our measurements crossed over the transition between buoyancy-driven plumes and momentum-driven jets. We found that the ascen…
Heat and momentum transfer of low-Prandtl-number fluid ($Pr=0.029$) in a closed rectangular cavity ($100\times60\times10$ mm$^3$) heated at one side and cooled at the opposite side are analyzed. The electromagnetic forces into the liquid metal are generated by the travelling magnetic field inductor and directed towards buoyancy forces. Large eddy simulations are performed with the Grashof number $Gr$ from $1.9\cdot 10^5$ to $7.6\cdot 10^7$ and the electromagnetic forcing parameter $F$ from $2.6\cdot 10^4$ to $2.6\cdot10^6$. An experimental validation of the simulation results of vertical conve…
Dependence of boundary layer thickness on layer height in laminar and transient regimes is studied for convection from localised heat source with an open surface. The measurements of Nusselt number and characteristic frequency of thermal plume formation are done for a wide range of Rayleigh number, different Prandtl numbers and different aspect ratios. The obtained results prove that for the developed (but not turbulent) convective flow the boundary layer thickness is almost independent of the layer height and it is mainly defined by applied temperature difference and physical properties of th…
Fully developed forced convective flow in a channel filled with porous material bounded by two impermeable walls subject to constant heat flux is considered. We consider Brinkman-Forchhimer equation to govern the flow inside the porous medium which accounts for the presence of inertial term. We assume that the porous medium is anisotropic in nature and permeability is varying along all the directions, correspondingly, permeability will be a matrix which appear as a positive semi-definite matrix in the momentum equation. The anisotropic nature of the porous medium is characterized by anisotropi…
We consider two common heat transfer processes and perform a through sensitivity study of the variables involved. We derive and discuss analytical formulas for the heat transfer coefficient in function of film velocity, air temperature and pipe diameter. The according plots relate to a qualitative analysis of the multi-variable function $h$, according to functional optimization. For each process, we provide with graphs and tables of the parameters of interest, such as the Reynolds number. This method of study and the specific values can constitute a useful reference for didactic purposes.
In this paper, we present results from an experimental study into turbulent Rayleigh-Benard convection forced externally by periodically modulated unidirectional rotation rates. We find that the azimuthal rotation velocity $\dotθ$(t) and thermal amplitude $δ$(t) of the large-scale circulation (LSC) are modulated by the forcing, exhibiting a variety of dynamics including increasing phase delays and a resonant peak in the amplitude of $\dotθ$(t). We also focus on the influence of modulated rotation rates on the frequency of occurrence $η$ of stochastic cessation/reorientation events, and on the …
We carry out direct numerical simulation (DNS) of flow in a turbulent square duct by focusing on heat transfer effects, considering the case of unit Prandtl number. Reynolds numbers up to $Re_τ\approx 2000$ are considered which are much higher than in previous studies, and which yield clear scale separation between inner- and outer-layer dynamics. Close similarity between the behavior of the temperature and the streamwise velocity fields is confirmed as in previous studies related to plane channels and pipes. Just like the mean velocity, the mean temperature is found to exhibit logarithmic lay…
When boiling occurs in a liquid flow field, the phenomenon is known as forced-convection boiling. We numerically investigate such a boiling system on a cylinder in a flow at a saturated condition. To deal with the complicated liquid-vapor phase-change phenomenon, we develop a numerical scheme based on the pseudopotential lattice Boltzmann method (LBM). The collision stage is performed in the space of central moments (CMs) to enhance numerical stability for high Reynolds numbers. The adopted forcing scheme, consistent with the CMs-based LBM, leads to a concise yet robust algorithm. Furthermore,…
We report a new thermal boundary layer equation for turbulent Rayleigh-Benard convection for Prandtl number Pr>1 that takes into account the effect of turbulent fluctuations. These fluctuations are neglected in existing equations, which are based on steady-state and laminar assumptions. Using this new equation, we derive analytically the mean temperature profiles in two limits: (a) Pr>1, Pr~1 and (b) Pr>>1. These two theoretical predictions are in excellent agreement with the results of our direct numerical simulations for Pr=4.38 (water) and Pr=2547.9 (glycerol) respectively.
We numerically investigate the structures of the near-plate temperature profiles close to the bottom and top plates of turbulent Rayleigh-Bénard flow in a cylindrical sample at Rayleigh numbers Ra=10^8 to Ra=2\times10^{12} and Prandtl numbers Pr=6.4 and Pr=0.7 with the dynamical frame method [Q. Zhou and K.-Q. Xia, Phys. Rev. Lett. 104, 104301 (2010)] thus extending previous results for quasi-2-dimensional systems to 3D systems for the first time. The dynamical frame method shows that the measured temperature profiles in the spatially and temporally local frame are much closer to the temperatu…
Turbulent mixed convection in channel flows with heterogeneous surfaces is studied using direct numerical simulations. The relative importance between buoyancy and shear effects, characterized by the bulk Richardson number $Ri_b$, is varied in order to cover the flow regimes of forced, mixed and natural convection, which are associated with different large-scale flow organization. The heterogeneous surface consists of streamwise-aligned ridges, which are known to induce secondary motion in case of forced convection. The large-scale streamwise rolls emerging under smooth-wall mixed convection c…
We conducted direct numerical simulations (DNSs) of turbulent flow over three-dimensional sinusoidal roughness in a channel. A passive scalar is present in the flow with Prandtl number $Pr=0.7$, to study heat transfer by forced convection over this rough surface. The minimal channel is used to circumvent the high cost of simulating high Reynolds number flows, which enables a range of rough surfaces to be efficiently simulated. The near-wall temperature profile in the minimal channel agrees well with that of the conventional full-span channel, indicating it can be readily used for heat-transfer…
Turbulent flow past an equilateral triangular cylinder with splitter plate inserted downstream is numerically tested for different gap ratios (0, 0.5, 1, 1.5, 2) and plate dimensions (0, 1, 1.5) on the flow field and heat transfer characteristics. Unsteady flow simulations are carried out at Re=22,000 in a finite volume based collocated framework, on a two-dimensional unstructured mesh. Reynolds averaged momentum and energy equations are solved in conjunction with the standard $κ$-$ε$ model. In this study, cylinder and control plate are subjected to constant wall temperature. It is observed th…
The structure of the boundary layers in turbulent Rayleigh-Benard convection is studied by means of three-dimensional direct numerical simulations. We consider convection in a cylindrical cell at an aspect ratio one for Rayleigh numbers of Ra=3e+9 and 3e+10 at fixed Prandtl number Pr=0.7. Similar to the experimental results in the same setup and for the same Prandtl number, the structure of the laminar boundary layers of the velocity and temperature fields is found to deviate from the prediction of the Prandtl-Blasius-Pohlhausen theory. Deviations decrease when a dynamical rescaling of the dat…
This article presents a study of the influence of electromagnetically (EM) forced convection on segregation formation. As a reference case the solidification of Sn-5 wt pct Pb alloy from the Hebditch and Hunt experiment is taken. Applied forcing of convective flow is determined by the dimensionless electromagnetic forcing parameter $F$. The study was carried out in the range $-3.5\times 10^6<F<3.5\times 10^6$. Velocity profiles and flow patterns in the liquid phase are obtained for different applied EM forcing conditions. As a result of parametric analysis, the dependence of the Reynolds numbe…
The shape of velocity and temperature profiles near the horizontal conducting plates in turbulent Rayleigh-Bénard convection are studied numerically and experimentally over the Rayleigh number range $10^8\lesssim Ra\lesssim3\times10^{11}$ and the Prandtl number range $0.7\lesssim Pr\lesssim5.4$. The results show that both the temperature and velocity profiles well agree with the classical Prandtl-Blasius laminar boundary-layer profiles, if they are re-sampled in the respective dynamical reference frames that fluctuate with the instantaneous thermal and velocity boundary-layer thicknesses.
In thermal convection for very large Rayleigh numbers ($Ra$), the thermal and viscous boundary layers (BL) undergo a transition from a classical state to an ultimate state. In the former state, the BL thicknesses follow a laminar-like Prandtl-Blasius-Polhausen scaling, whereas in the latter, the BLs are turbulent with log-corrections in the sense of Prandtl and von Kármán. Here, we report evidence of this transition via changes in the BL structure of vertical natural convection (VC), which is a buoyancy driven flow between differentially heated vertical walls. The dataset spans $Ra$-values fro…
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…
It is shown, using results of direct numerical simulations, that the spontaneous breaking of local reflectional symmetry (and corresponding localized kinetic and magnetic helicities) can dominate chaotic dynamics of the small-scale MHD dynamo in the Rayleigh-B{é}nard convection, in kinetically forced flows under strong stratification, in the near-surface solar convection, and in kinetically forced flows at large magnetic Reynolds numbers. The notions of deterministic and helical distributed chaos have been used for this purpose. The coexistence of large- and small-scale dynamo mechanisms and a…
The effect of the wind of Rayleigh-Benard convection on the boundary layers is studied by direct numerical simulation of an L/H=4 aspect-ratio domain with periodic side boundary conditions for Ra={10^5, 10^6, 10^7} and Pr=1. It is shown that the kinetic boundary layers on the top- and bottom plate have some features of both laminar and turbulent boundary layers. A continuous spectrum, as well as significant forcing due to Reynolds stresses indicates undoubtedly a turbulent character, whereas the classical integral boundary layer parameters -- the shape factor and friction factor (the latter is…
We study the velocity field in a horizontal (x-y) plane 1.5 mm above the hot plate in turbulent natural convection using PIV at a Rayleigh number Raw=106 and Prandtl number Pr=5.2. The plane of measurement is inside the velocity boundary layer estimated from the natural convection boundary layer equations[7] as well as inside the velocity boundary layer due to the large scale flow[2, 5].The boundary layer comprises of line plumes with sinking fluid between them. The instantaneous velocity variation from the center of the sinking fluid to the line plumes is found to deviate with the classical P…
We report measurements of the instantaneous viscous boundary layer (BL) thickness $δ_v(t)$ in turbulent Rayleigh-Bénard convection. It is found that $δ_v(t)$ obtained from the measured instantaneous two-dimensional velocity field exhibits intermittent fluctuations. For small values, $δ_v(t)$ obeys a lognormal distribution, whereas for large values the distribution of $δ_v(t)$ exhibits an exponential tail. The variation of $δ_v(t)$ with time is found to be driven by the fluctuations of the large-scale mean flow velocity and the local horizontal velocities close to the plate can be used as an in…
Transonic buffet is commonly associated with self-sustained flow unsteadiness involving shock-wave/boundary-layer interaction over aerofoils and wings. The phenomenon has been classified as either laminar or turbulent based on the state of the boundary layer immediately upstream of the shock foot and distinct mechanisms for the two types have been suggested. The turbulent case is known to be associated with a global linear instability. Herein, large-eddy simulations are used for the first time to make direct comparisons of the two types by examining free- and forced-transition conditions. Corr…
The problem of forced convection along an isothermal moving plate is a classical problem of fluid mechanics that has been solved for the first time in 1961 by Sakiadis (1961). It appears that the first work concerning mixed convection along a moving plate is that of Moutsoglou and Chen (1980). Thereafter, many solutions have been obtained for different aspects of this class of boundary layer problems. In the previous works the fluid properties have been assumed constant. Ali (2006) in a recent paper treated, for the first time, the mixed convection problem with variable viscosity. He used the …
We study Rayleigh-Benard convection in the high-Rayleigh-number and high-Prandtl-number regime, i.e., we consider a fluid in a container that is exposed to strong heating of the bottom and cooling of the top plate in the absence of inertia effects. While the dynamics in the bulk are characterized by a chaotic convective heat flow, the boundary layers at the horizontal container plates are essentially conducting and thus the fluid is motionless. Consequently, the average temperature exhibits a linear profile in the boundary layers. In this article, we rigorously investigate the average temperat…
We study the evolution of a melting front between the solid and liquid phases of a pure incompressible material where fluid motions are driven by unstable temperature gradients. In a plane layer geometry, this can be seen as classical Rayleigh-Bénard convection where the upper solid boundary is allowed to melt due to the heat flux brought by the fluid underneath. This free-boundary problem is studied numerically in two dimensions using a phase-field approach, classically used to study the melting and solidification of alloys, which we dynamically couple with the Navier-Stokes equations in the …
