Evolution Of Nusselt Number Research Articles

Heat transfer measurements in an inclined low aspect ratio Rayleigh–Bénard convection cell under feedback control

We report experimental results on the inclined Rayleigh–Bénard convection of a moderate aspect ratio convection cell using a high Prandtl aqueous solution of glycerol. The main goal of the present work is to measure continuously the transition from a convective condition into a purely conduction regime by a smooth quasi-static variation of the tilt angle of the convection cell with respect to the gravity vector in 180° at Rayleigh numbers just above of convection onset. Flow circulation inside the convection cell is indirectly detected by temperature sensors located at the bounding active plates. Changes in the temporal evolution of the heat transfer curve appear directly related to flow transitions between characteristic flow patterns from transversal rolls evolving into an unicellular single roll convective pattern and then a conductive state. For small tilt angles 6°≤γ≤20° time signal fluctuations on both the Nusselt number and temperature readings were observed. Flow visualizations and PIV measurements provided a complementary view of the convective flow pattern being associated to transitions in the Nusselt number evolution with the tilt angle of the cell. For small tilt angle transitions, we observed a loss of rolls process followed by a reorganization of the flow which might be the responsible of the Nusselt unsteadiness.

Large-eddy simulation of a planar offset wall-jet with heat transfer: Characterization, turbulent kinetic energy and Reynolds shear stress budgets

Planar wall-attaching offset jets can be found in a variety of engineering applications. In the present work, a planar turbulent offset wall-jet, at a Reynolds number of 7500 and an offset-ratio of 5, with heat transfer is numerically studied using large-eddy simulation (LES). First, a grid sensitivity study is performed and the quality of the mesh used is assessed using LES index of quality of resolution and an appropriate mesh is selected. Next, the solver is validated for mean streamwise velocity, streamwise Reynolds normal stress, and the evolution of coefficient of pressure on the wall, using reference experimental data from the literature. Thereafter, the unsteady flow features of the jet, maximum velocity decay and jet-spread, statistical features of flow and temperature, and turbulent kinetic energy (TKE) budgets and in-plane component of Reynolds shear stress are studied. The streamwise evolution of Nusselt number on the wall shows three distinct peaks and the location of these peaks correlates with a change-of-sign of the wall skin-friction coefficient. The domain can be categorized into three distinct regions namely, the recirculation, impingement and wall-jet regions. Distinct flow and thermal characteristics are observed depending on the region of interest. The peak magnitudes of Reynolds normal and shear stresses increase as one moves from the recirculation region to the impingement region and decreases thereafter attaining a lowest value in the wall-jet region. The heat transfer from the wall is observed to be most effective in the recirculation region. The production of TKE is dominant in all the three regions of the flow, whereas the Reynolds shear stress budgets indicate that the production and velocity–pressure-gradient terms are dominant and balance each other in all the three regions of the flow.

Galerkin finite element analysis of Darcy–Brinkman–Forchheimer natural convective flow in conical annular enclosure with discrete heat sources

This numerical study is intended for the analysis of thermal convection induced by buoyancy forces generated within a conical annular porous gap. The annulus was vertically positioned, it contains a discrete heat source and is filled with a Single-Walled Carbon Nanotubes-Water (SWCNT-H2O) nanoliquid exposed to a Lorentz force. To describe the porous medium in question, we have adopted the Darcy–Forchheimer model. Galerkin Finite Element Method (GFEM) has been used in this study to predict both thermal and hydrodynamic fields in the physical model. An extensive range of parameters are explored, i.e., the Rayleigh number (103 to 106), Hartman number Ha (1 to 100), and the volume fraction of nanoparticles (0 ≤ϕ≤0.08). For the purpose of exterminating the effects of heat source location on thermal and hydrodynamic fields, three locations (bottom, middle and upper) have been considered. Findings include current lines, isotherms, and Nusselt number evolution according to the previously stated variables. Predictably, our findings prove that heat transfer rate exhibits a decreasing function of Ha and an increasing function of Da and ϕ. Also, it was revealed that the convective regime is preponderant when the heat source was located in the bottom wall.

Assessment of subgrid-scale models for large-eddy simulation of a planar turbulent wall-jet with heat transfer

In the present work, five different subgrid-scale (SGS) models and implicit large-eddy simulation (LES) are evaluated and compared against the DNS for the simulation of the planar turbulent wall-bounded jet with heat transfer. The SGS models tested are the classical constant coefficient Smagorinsky model and its dynamic version, the wall-adaptive local eddy-viscosity (WALE) model, the turbulent kinetic energy one-equation model, and its dynamic version. The effects of using variable turbulent Prandtl number and the near-wall damping function are also studied in these models. The mean, second-order flow and heat-transfer statistics with the evolution of Nusselt number along the jet downstream are used to assess the different SGS models. The quality of resolution of the present LES are evaluated using the activity parameter and the index of resolution quality. Among the models tested, the constant coefficient Smagorinsky model together with Van-Driest damping predicts the solution accurately in the near-wall region as well as in estimating the thermal parameters. However, the dynamic models performed better in evaluating the Reynolds stress profiles away from the wall in the outer region. Capabilities of the models to predict the turbulent kinetic energy budgets, pressure-velocity gradient correlations and triple velocity correlations are also studied. The implemented variable Prandtl number algorithm is noted to have minimal influence on the evolution of the solution.

Study of mixed convection in closed enclosure with a ceiling fan

This paper presents a numerical study of heat transfer by convection in a square cavity. The vertical walls of the cavity are differentially heated and the horizontal ones are considered adiabatic. A fan is placed in the middle of the cavity and releases a jet down. Numerical simulation was performed using the lattice Boltzmann method to show the flow patterns and the heat flux depending on the Rayleigh number (thermal convection intensity) and the Reynolds number (fan-driven flow intensity). A parametric study was performed presenting the influence of Reynolds number (20 ≤ Re ≤ 500), Rayleigh number (10 ≤ Ra ≤ 106) and the fan position (0.2 ≤ HF ≤ 0.8). In forced convection mode, the flow structure has been mapped according to the position and the power of the fan. Three structures have emerged: two symmetrical cells, four symmetrical cells and asymmetrical structure. It has been observed that the heat transfer rate increases with the rise of Reynolds number and the reduction of the distance of the fan position from the ceiling. For the latter one, an unfavorable evolution of Nusselt number is observed for Ra > 104.

Turbulent Rayleigh-Bénard convection of cold water near its maximum density in a vertical cylindrical container

In order to understand the effects of density inversion parameter and Rayleigh number on the fluid motion and heat transfer characteristics of penetrative Rayleigh-Bénard convection in a cylindrical container, a series of large eddy simulations were performed. The working fluid is cold water and Prandtl number is 11.57. Rayleigh number up to 1011 is considered and the density inversion parameter ranges from 0 to 0.7. The results indicate that the effect of cold plumes on the larger scale circulation gradually diminishes and finally disappears with the increase of density inversion parameter. Furthermore, an increase of the temperature within the bulk region and a decrease of the penetration depth are also certified with the increase of density inversion parameter. With the increase of Rayleigh number, soft and hard turbulent states are successively observed. In the soft turbulence state, the evolution of Nusselt number shows a weak fluctuation, the corresponding histogram has a Gaussian distribution, and the penetration depth increases sharply with the increase of Rayleigh number. In the hard turbulence state, the evolution of Nusselt number presents a much stronger fluctuation than that in the soft turbulence state, the corresponding histogram fits more exponential distribution, and the variation of the penetration depth with Rayleigh number is small. A single power law between the heat transfer efficiency (Nusselt number) and Rayleigh number that covers soft and hard turbulence states is developed for each density inversion parameter. It is found that the average Nusselt number decreases linearly with the increase of density inversion parameter.

CFD investigation on the offset ratio effect on thermal characteristics of a combined wall and offset jets flow

The present paper deals with CFD simulation of a two-dimensional, steady, incompressible and turbulent flow combining a wall jet and an offset jet (this combination will be denoted wall offset jet) in order to study the heat transfer phenomenon in this type of flow. Several turbulence models were tested including standard k–ω, SST k–ω, standard k–e, RNG k–e and realizable k–e models. A parametric study was also presented to investigate the offset ratio H and the Reynolds number Re effect on the local (Nu) and average \( \left( {\overline{{\text{Nu}}} } \right) \) Nusselt number evolution along the wall. Constant wall heat flux boundary condition is considered. The Reynolds number and the offset ratio have been varied respectively from 10,000 to 40,000 and from 5 to 20 and Pr = 0.7 is adopted for all computation. Correlations that predict the average Nusselt number as a function of both the offset ratio H and the Reynolds number Re are also provided. This study has allowed us to conclude that the heat transfer exchanged between the flow and the wall is intensified when decreasing the offset ratio H and increasing the Reynolds number Re.

Laminar aiding and opposing mixed convection in a vertical channel with an asymmetric discrete heating at one wall

Detailed numerical simulations are carried out for aiding/opposing mixed convection in a rectangular channel with an asymmetric discrete heating. The governing equations were solved by the finite volume method using OpenFoam? open source code. Based on streamline patterns, temperature maps, velocity and thermal profiles, and Nusselt number evolution an extensive analysis on the effects of Richardson number in the range ?5 to +5 for both opposed and aided buoyancy on the fluid flow and heat transfer characteristics is presented and discussed.

Impact of Square Fuel Assemblies Arrangement on Fluid Flow and Heat Transfer Enhancement inside Water Filled Enclosures

Through this paper, the hydrodynamic and thermal characteristics of a Newtonian fluid within a square cold enclosure containing four inner heaters, arranged in different manners, are numerically investigated. To do so, a developed computer code based on the finite volume method and the SIMPLER algorithm is used. The validity of the latter was ascertained after the comparison between the obtained results and the experimental and numerical ones already available in the literature. To make clear the effect of pertinent parameters such the Rayleigh number and the distance between these heaters, the phenomenon was reported by means of Streamlines, Isotherm plots, velocity and temperature profiles, with a special attention to the local and average Nusselt number evolution. As shown in the latter, taking into account the heaters’ arrangement into the enclosure leads to a significant improvement of the overall transfer. Consequently, powerful correlations predicting the heat transfer ratio into the cold square as a function of the heaters’ disposition are proposed which predict within ±1% the numerical results.

Natural Convection Heat Transfer of a Nanofluid into a Cubical Enclosure: Lattice Boltzmann Investigation

Through this paper, the hydrodynamic and thermal characteristics of Ag–water nanofluid, filling a differentially heated cubic enclosure, are numerically investigated. To do so, a developed computer code based on the lattice Boltzmann approach coupled with the finite-difference method is used. The later has been validated after comparison between the obtained results and experimental and numerical ones already found in the literature. To make clear the effect of main parameters such as the Rayleigh number, the nanoparticle volume fraction, and the enclosure inclination angle, the convection phenomenon was reported by means of streamlines, temperature iso-surfaces, and velocity and temperature profiles. A special attention was paid to the Nusselt number evolution. Compared to a 2D investigation, and when the convection mode dominates, taking into account the third direction leads to significant modifications on the nanofluid motion and heat transfer as well. As the conductive regime dominates, the use of a 2D configuration is found to be valid to predict the studied phenomenon. It is to note that the three-dimensional D3Q19 model was adopted based on a cubic lattice, where each pattern of the later is characterized by 19 discrete speeds.

Impact of Square Fuel Assemblies Arrangement on Fluid Flow and Heat Transfer Enhancement inside Water Filled Enclosures

Through this paper, the hydrodynamic and thermal characteristics of a Newtonian fluid within a square cold enclosure containing four inner heaters, arranged in different manners, are numerically investigated. To do so, a developed computer code based on the finite volume method and the SIMPLER algorithm is used. The validity of the latter was ascertained after the comparison between the obtained results and the experimental and numerical ones already available in the literature. To make clear the effect of pertinent parameters such the Rayleigh number and the distance between these heaters, the phenomenon was reported by means of Streamlines, Isotherm plots, velocity and temperature profiles, with a special attention to the local and average Nusselt number evolution. As shown in the latter, taking into account the heaters’ arrangement into the enclosure leads to a significant improvement of the overall transfer. Consequently, powerful correlations predicting the heat transfer ratio into the cold square as a function of the heaters’ disposition are proposed which predict within ±1% the numerical results.

Aided Mixed Convection past a Heated Square Cylinder at Low Blockage Ratio

This paper investigates numerically the flow and heat transfer in air (Pr=0.71) by mixed convection past a heated square cylinder under aiding buoyancy effect in a confined channel. The numerical simulations are performed in the range of parameters 20≤Re≤45 and 1.61x10 3 ≤Gr≤6.33x10 3 for a fixed blockage ratio D/L of 0.1. The combination in the present study of these two Re and Gr parameters is reduced so that the Richarson number varies from 0,8 to 8, in order to neglect neither free convection (Ri 10). The steady two-dimensional governing equations are solved by the finite volume formulation using the open source OpenFoam® code. The representative flow structure, isotherm patterns and local Nusselt number evolution are presented and discussed. The effect of both the Reynolds number and the buoyancy parameter on the fluid flow and the heat transfer are also analyzed. It is found that the wake region size strongly depends on both Reynolds and Grashof numbers and this region is shown to increase in size increasing the Reynolds number and/or decreasing the Grashof number. Moreover, increasing the Reynolds number leads to a heat transfer enhancement more pronounced on the front face of the obstacle, whereas increasing the Grashof number leads to a heat transfer enhancement more pronounced on the side faces.

TiO2-water nanofluid within a tilted triangular enclosure including a square heater: optimum heat transfer

Into this paper, natural convection of TiO2 -water nanofluid is numerically investigated around a square isothermal heater, found into a two-dimensional cold enclosure of an isosceles triangle form. To do so, a computer code based on the finite volume method and the velocity-pressure correction approach, namely SIMPLER, is used. This code has been validated for cases of a base fluid and a Nanofluid, after comparison between the obtained results and the numerical (or experimental) ones already available in the literature. To make clear the effect of main parameters such the Rayleigh number, the solid volume fraction as well as the cavity’ inclination angle, the convection phenomenon is reported by means of Streamlines and isotherm plots; with a special attention to the Nusselt number evolution. The results show that the mean Nusselt number is an increasing function of the Rayleigh number and the solid volume fraction, whereas the inclination angle of the cavity has no significant effect on heat transfer. Then, useful correlations which predicting the latter as a function of the solid volume fraction for various Rayleigh values are proposed, which predicts within ±0.4% the numerical results.

Laminar Forced Convection of a Pseudoplastic Thermo dependent Fluid in an Annular Horizontal Duct

In this work, the problem of thermal development for laminar forced convection of a pseudoplastic thermo dependent fluid in a concentric annular horizontal duct is numerically addressed. Three thermal conditions are assumed: inner cylinder subjected to an imposed heat flux while the outer is insulated; then the inverse; and finally both cylinders are heated with the same heat flux densities. All computations are carried out from the entrance up to the thermal fully developed stage for a flow already developed dynamically. The study objective is to illustrate the effects of the rheological index (n), aspect ratio (r1), thermodependency (Pn) and heating mode on velocity profiles and Nusselt number evolution in addition to thermal entrance length. The results show an improvement in heat exchange with the shear-thinning of the fluid. The outer Nusselt decreases as r1 decreases while the inner one improves. Overall, the thermodependency has a similar effect to that of the shear-thinning. A very important result shows the reduction in thermal length with increasing n and/or Pn. Simple, accurate and widely valid correlations are provided for Nusselt number and thermal entrance length under different conditions.

Experimental study of the natural convection flow around an array of heated horizontal cylinders

Natural convection heat transfer from an array of heated cylinders has recently attracted much attention. However, in almost all of the investigations, attention has been restricted to the influence of geometrical parameters on the overall heat transfer. The present work deals with an experimental study of natural convection flow from a vertical array of two heated horizontal cylinders. A detailed analysis of the local temperature and velocity fields is performed. The modifications of the average Nusselt number evolution compared with the single cylinder are explained in terms of velocity and temperature fields of the flow around the cylinders. Results that are obtained for a variety of combinations of spacings and Rayleigh numbers are compared with known numerical results. The comparison shows a satisfactory agreement.

Moving and Rotating Sphere in the Thermal Entrance Region of a Heated Pipe

Flow and unsteady heat transfer around a moving and rotating sphere is considered as it passes through the thermal entrance region of a heated pipe. The flow is incompressible and viscous with constant properties, and the heated pipe wall is kept at a constant temperature. Two Peclet numbers of 25 and 100 are considered along with two sphere-to-pipe-diameter ratios of 0.2 and 0.4. The flow is made three dimensional by an eccentric positioning of the sphere inside the pipe. The governing equations are solved by a validated numerical method which uses a finite volume formulation in a generalized body-fitted coordinate system. An overset (Chimera) grid scheme is used to resolve the two geometries of the pipe and sphere. The results are presented in terms of the steady pressure and viscous lift and drag forces on the sphere. In addition the unsteady heat transfer characteristics of the flow are presented in terms of the local and overall Nusselt number evolution around the sphere as it passes through the thermal entrance region of the pipe. Sphere heat-up is also given as the lumped mass sphere temperature as a function of distance from the thermal entrance. [S0022-1481(00)02402-6]

Numerical study of the laminar natural convection flow around an array of two horizontal isothermal cylinders

Natural convection heat transfer from an array of heated cylinders has received attention in recent years. However, most of the previous investigations has been experimental and has been restricted to the influence of geometrical parameters on the overall heat transfer. The present work is devoted to the numerical study of lanunar natural convection flow from an array of two horizontal isothermal cylinders. This work, that enters within the framework of general study dealing with an array of several cylinders, states the problem in Cartesian coordinates system, involves the use of a control-volume method and solves the full vorticity transport equation together with the stream function and energy equations. The modifications of the average Nusselt number evolution compared with the single cylinder are explained in terms of velocity and temperature fields of the flow around the cylinders. Results are obtained for variety of combinations of spacing and numbers of Rayleigh.

Convection mixte dans un écoulement de poiseuille vertical: Étude comparative de chauffage volumique et pariétal à flux constant

Numerical study of heat transfer in a laminar flow between two vertical parallel plates is reported. Two configurations are considered: the first consists of an imposed constant wall-heat-flux boundary conditions; the second corresponds to a bulk energy dissipation by direct electric-conduction (Joule effect) in the fluid In the two cases, we have kept the same average temperature-difference between the fluid at the entrance and at the exit of the channel. The flow rate is also the same in both cases. Comparison is made between the axial evolution of Nusselt number obtained from this computation and the Nusselt number given by a classical correlation, in forced convection regime. It has been found that they are in good agreement. Heat transfer enhancement in the mixed convection regime is analysed We show particularly that the temperature distribution at the exit section of the channel is more uniform in the bulk heating case than in the constant wall-heat-flux condition. The secondary-flow induced by free convection and its contribution to the temperature uniformity is also studied We show the similarity between the two configurations from the point of view of the secondary-flow structure. In both cases we cam observe two convective cells whose centres are located closer to the exit from the channel. It is explained that this phenomenon is due to the presence, in the two cases, of the wall temperature increase along the channel in the downstream direction.

Etude des structures convectives et du transfert thermique autour d'un cylindre en deuxième nappe dans une configuration en quinconce, en écoulement d'air chargé de gouttelettes d'eau

We describe an experimental study of the influence of longitudinal and transversal pitch on the convective transfer around a cylinder on the second row of a three cylinder staggered bank, operating in an airstream charged with sprayed water at moderate Reynolds number. The analysis of the wall velocity gradient and its fluctuation shows the effects of geometrical parameters on various characteristic zones of the flow: laminar boundary layer, separation and vortices. The modifications of local Nusselt number evolution compared with the single cylinder are explained. For the disposition which gives the highest heat transfer, a correlation of local Nusselt number is proposed.