Natural Convection In Rectangular Cavity Research Articles

A meticulous study of aspect ratio impacts on flow and heat of nanofluid in a cavity: Finite difference-based computations

The phenomenon of natural convection in rectangular cavities of different aspect ratios is considered. The water is considered a base fluid associated with copper nanoparticles. The flow is induced only due to buoyancy force that arises by heating the right side of the cavity. The left side is set cold while the other walls are assumed to be at zero flux temperature. The governing equations of the present communication are simulated by the finite difference method. This study explores the impacts of Rayleigh number (Ra), Prandtl number (Pr), nanoparticles volume fraction ([Formula: see text]), and aspect ratio (A). Different combinations of these parameters are investigated. Compared to other parameters, Rayleigh number (10[Formula: see text]), aspect ratio ([Formula: see text]), and volume fraction of nanoparticles ([Formula: see text]), A is found more effective on the flow field and isotherms. Regression curves are determined for the mean Nusselt number (Nuavg) as a function of Ra for different cases. It is found that Nuavg more precisely fits the exponential function. Also, it is found that Nuavg decreases as the values of A increase. But, [Formula: see text], shows the opposite behavior. It is noticed that when the A of the cavity grows, so does the mean heat transfer Nu. With rising Ra, the local heat transfer NuL decreases and the heat transfer rises. In the case of the square cavity, the regression coefficient for Nuavg is found to be 0.3673 and 0.2514 for an exponential function.

Machine Learning based algorithms for modeling natural convection fluid flow and heat and mass transfer in rectangular cavities filled with non-Newtonian fluids

The importance of studying double-diffusive fluid flows along with the significance of non-Newtonian fluids have been well recognized in the fluid dynamics field for scientific and practical purposes. However, and given the ever-rising complexity of such non-linear flows, the conventional simulation methods are confronted with problems related to accuracy and required computation time and resources. As a result, the Machine Learning approach qualifies as a promising solution to said limitations. The present study investigates the application of Machine Learning models to study double-diffusive natural convection in rectangular cavities filled with non-Newtonian fluids. The flow is governed by four dimensionless parameters, namely: thermal Rayleigh number RaT, Lewis number Le, buoyancy ratio N, and power-law behavior index n, employed as input features. To precisely model fluid flow, three characteristics are predicted: flow intensity |ψc|, average Nusselt number Nu¯, and average Sherwood number Sh¯ using four machine learning models: Artificial Neural Networks (ANN), Random Forests (RF), Gradient Boosted Decision Trees (GBDT), and Extreme Gradient Boosting (XGBoost). The analysis of investigated models’ fine-tuned architectures using various tools confirms the non-linear complexity of the problem and allows to explore and discuss in details the inner-workings of each model. The ANN predicts the test data with R2=0.9999,R2=0.9996, and R2=0.9999 followed by XGBoost with R2=0.9979,R2=0.9802, and R2=0.9979, and that for |ψc|, Nu¯, and Sh¯, respectively. The study shows the strong and correlated effects of RaT and n on the flow characteristics. The models’ generalization is further examined using fluids with power-law behavior indexes outside the learning range. The present paper validates the choice of Machine Learning approach as a promising solution to model non-Newtonian double-diffusive fluid flows and encourages future works in this direction.

Influence of aspect ratio on the natural convection and entropy generation in rectangular cavities with wavy-wall

The natural convection in rectangular cavities with different aspect ratios and hot wavy walls was investigated through numerical simulations. The undulation of the cavity is fixed to three (03) however the Rayleigh numbers is ranging from 105 to 108. Second law of thermodynamics was also applied to predict the nature of irreversibility in terms of entropy generation. Heat transfer between vertical walls occurs by laminar and turbulent natural convection. The computations have been performed using FLUENT 6.3.26 by employing the k–ε model for turbulence. Based on the obtained dimensionless velocity and temperature values, the distributions of local entropy generation due to heat transfer and fluid friction are determined. The distributions of the stream function, static temperature, the total entropy generation and the local Bejan number are plotted for different aspect ratios Rayleigh number, and irreversibility coefficients 10-4< <10-2. The total entropy generation is found to increase with increasing aspect ratios.

Natural convection in rectangular cavities with one active vertical wall

Natural convection in rectangular cavities has been studied. One of the vertical walls of the cavity is active. The opposing vertical wall is inactive and insulated from the back. The other four walls are adiabatic. Heat transfer is by convection only because surface emissivities of the walls have been reduced. Experiments are performed on rectangular cavities with aspect ratios of 1, 2.09, 3, 4, 5 and 6. All six cavities have a height of 340mm and a depth of 210mm. The cavity length is changed to obtain different rectangular cavities. The cavity is closed and filled with air. Thermocouples are used to measure the temperature. For each cavity, the temperature distribution between the vertical walls of the cavity is obtained at 35 positions in the length, three positions in the height and one position in the depth directions. Three regions are observed along the cavity length. In the central region, the temperature changes slightly. The isotherms are concentrated near the active wall. The variation of local Nusselt number along the cavity height is obtained. Heat transfer correlations are presented for the Rayleigh number range of 2.16×105 to 5.06×107, and for the aspect ratio range of 1–6.

Numerical Study of Entropy Generation for Natural Convection in Rectangular Cavity with Circular Corners

This article numerically studies entropy generation due to natural convection in a rectangular cavity with circular corners. In this work, in order to solve the governing equations, an explicit finite-volume procedure and a time-marching method are utilized. Also, instead of the conventional algorithms of SIMPLE, SIMPLEM, and SIMPLEC, an artificial compressibility technique is applied for coupling the continuity to the momentum equations. Entropy generation, as a representation of irreversibility and efficiency loss in engineering heat transfer processes, is analyzed in detail. In this work, effects of the radius of walls corner, Rayleigh number, and distribution ratio on total entropy generation, Nusselt number, and Bejan number are also evaluated. The results show that entropy generation decreases with the increase of the radius of the walls’ corner and increases with the increase of Rayleigh number, aspect ratio, and irreversibility ratio.

A Study on the Importance of Natural Convection During Solidification in Rectangular Geometry

In this study, solidification process inside a water filled rectangular cavity is numerically investigated. The mathematical model is validated by comparing the current numerical predictions with the available analytical, numerical, and experimental results for three different test cases: one-dimensional conduction dominated solidification, natural convection in rectangular cavity, and natural convection dominated solidification in rectangular cavity. For all three cases, some good agreements are achieved in terms of isotherms, interface positions, and streamlines. After validation, time-wise ice formations are represented, and comparisons are made between bare and finned wall cases. In addition to these, further analyses are carried out by neglecting the buoyancy forces to introduce the differences between natural convection dominated and conduction dominated models. The results emphasize that natural convection has a critical effect in actual phase change processes.

The effects of Reduced Temperature and Pressure on Natural Convection in Rectangular Cavity Filled with a Supercritical Water: a Benchmark Numerical Solution

In this paper, natural convection heat transfer of supercritical water in rectangular enclosure has been investigated in various values of reduced temperature (0.955 1.205) and pressure (1.2 2.0). The right and left sides of enclosure considered to be isotherm with a temperature difference of , while the lower and upper sides of the enclosure was thermally insulated. The width of enclosure is 0.004m. Calculations were performed for Rayleigh number ( ), Prandtl number ( ). The values of Ra and Pr are governed by the fluid temperature and pressure which are controlled by reduced temperature( ) and reduced pressure ( ). Streamlines, isotherms and mean Nusselt numbers are presented. It is found that the temperature distribution and flow field are affected by the reduced temperature and pressure. The results also show that the maximum Nusselt number could be obtained at the same specification of geometry and temperature difference increases as the pressure reach the critical pressure. Keyword: Natural convection, supercritical Water, reduced temperature and pressure

High Rayleigh Number Laminar-Free Convection in Cavities: New Benchmark Solutions

The fully matrix-inversion-free artificial compressibility (AC), characteristic based split (CBS) algorithm is used to produce a stable and accurate solution for high Rayleigh number natural convection in rectangular cavities. Two benchmark problems are solved using the AC-CBS scheme: the classical differentially heated (DH) cavity, and a cavity subject to temperature boundary conditions on its sides, which is proposed here as a new benchmark. For the DH cavity problem, the dependence of the solution on the computational grid is highlighted, and it is shown how the horizontal velocity is more sensitive than the other calculated quantities. For the newly proposed benchmark, the numerical results are compared to experimental data that has recently appeared in the open literature.

The Effect of the Top Wall Temperature on the Laminar Natural Convection in Rectangular Cavities With Different Aspect Ratios

The effect of the top wall temperature on the laminar natural convection in air-filled rectangular cavities driven by a temperature difference across the vertical walls was investigated for three different aspect ratios of 0.5, 1.0, and 2.0. The temperature distributions along the heated vertical wall were measured, and the flow patterns in the cavities were visualized. The experiments were performed for a global Grashof number of approximately 1.8×108 and nondimensional top wall temperatures from 0.52 (insulated) to 1.42. As the top wall was heated, the flow separated from the top wall with an undulating flow region in the corner of the cavity, which resulted in a nonuniformity in the temperature profiles in this region. The location and extent of the undulation in the flow are primarily determined by the top wall temperature and nearly independent of the aspect ratio of the cavity. The local Nusselt number was correlated with the local Rayleigh number for all three cavities in the form of Nu=C⋅Ran, but the values of the constants C and n changed with the aspect ratio.

Natural convection in cavities with constant flux heating at the bottom wall and isothermal cooling from the sidewalls

Natural convection in rectangular cavities is studied numerically using a finite volume based computational procedure. In many applications, especially for cooling of electronic components, a natural convection configuration is encountered where a constant flux heating element at the bottom surface are cooled from the isothermal sidewalls while the top wall can be considered adiabatic. The present study is based on such a configuration where a constant flux heat source is symmetrically embedded at the bottom wall. The length of the heat source is varied from 20 to 80% of the total length of the bottom wall. The non-heated parts of the bottom wall are considered adiabatic. The Grashof number is varied from 10 3 to 10 6. The study includes computations for cavities at various aspect ratios, ranging from 0.5 to 2, and inclination angles of the cavity from 0° to 30°. The effects aspect ratio, inclination angles, and heat source length on the convection and heat transfer process in the cavity are analysed. Results are presented in the form of streamline and isotherm plots as well as the variation of the Nusselt number and maximum temperature at the heat source surface under different conditions.

Multiple states, stability and bifurcations of natural convection in a rectangular cavity with partially heated vertical walls

The multiplicity, stability and bifurcations of low-Prandtl-number steady natural convection in a two-dimensional rectangular cavity with partially and symmetrically heated vertical walls are studied numerically. The problem represents a simple model of a set-up in which the height of the heating element is less than the height of the molten zone. The calculations are carried out by the global spectral Galerkin method. Linear stability analysis with respect to two-dimensional perturbations, a weakly nonlinear approximation of slightly supercritical states and the arclength path-continuation technique are implemented. The symmetry-breaking and Hopf bifurcations of the flow are studied for aspect ratio (height/length) varying from 1 to 6

Heat transfer by natural convection in rectangular cavities with low grashof number and various heater locations.

The velocity profiles, temperature distributions, average Nusselt numbers near heating wall, and maximum velocities of a circulating flow were calculated numerically by fundamental equations under different operating conditions including changing the Grashof number (at low Gr range), the location and number of heating walls, and the temperature difference between heated and cooled walls.The number of circulating flows is one or two owing to the configurations of heated and cooled walls under the present operating condition. Generally, the circulating rate was very slow and the temperature distributions were similar to those of conduction alone. In the case of a heated top wall, a domain of cold temperature extended widely as the circulating flow rate was increased, and it could be seen that heat transfer was suppressed.To check these calculated results, the velocity profiles and temperature distributions in small enclosures were measured experimentally and observed by a tracer under the same operating conditions as those of theoretical analysis. The calculated results agreed closely with the experimental ones.

Numerical experiments on laminar natural convection in rectangular cavities with and without honeycomb‐structures

Two‐dimensional finite difference calculations are carried out to study laminar flow in longitudinal and transverse convection rolls for three different geometries: a single rectangular cavity with high aspect ratio; a double cavity with a thin separation sheet; and a double cavity with a separation sheet and a honeycomb structure. The equations for the convection‐diffusion in the fluid and conduction in the solid region are solved simultaneously. Good agreement with experimental data is achieved for Rayleigh numbers not too high above the critical value for the onset of secondary convection rolls (Ra &lt; 8500 for vertical and Ra &lt; 2700 for horizontal cavities filled with air). Simulation fails for inclined cavities, where the flow structure is essentially three‐dimensional.

Convection Near the Temperature of Maximum Density for High Rayleigh Number, Low Aspect Ratio, Rectangular Cavities

Natural convection in rectangular cavities with the vertical endwalls differentially heated about the temperature of maximum density of water was studied in the laboratory. In order to control heat losses, the experiments were conducted in a large cold room with the air temperature maintained at 4°C. The Rayleigh number was varied over the range 105 to 108 and the aspect ratio over the range 0.1 to 0.5. The flow field consisted of a double cellular circulation, and the observed temperature field, flow field, and heat transfer rates were compared with analytical predictions in the diffusive regime. The experiments demonstrated that the interior sinking flow was unstable for Ra &gt; 107.

Buoyancy and surface tension driven natural convection in rectangular cavities during solidification.

Buoyancy and surface tension driven natural convection in horizontal rectangular liquid layers was investigated. One of the vertical walls of the container was heated and the opposite wall was cooled below the freezing point of the liquid. Solidification initiated at the cooled wall proceeded on toward the opposite wall under the influence of convection. Experimental observation and numerical analyses, both one-dimensional and two-dimensional, were carried out, and the limit of the one-dimensional approximation was made clear. It was found that the two-dimensional analysis making use of the boundary fixing method could predict fairly well the rate of solidification and the profile of the solid-liquid boundary, except for a region near the free surface, since the thermal conditions could not be specified exactly in this region. At the same time, the phenomenon under zero-g field was analyzed numerically, and the effect of pure thermocapillary convection on solidification was made clear.

Oscillatory Motion of Natural Convection in Rectangular Cavity

An oscillatory motion of natural convection in a rectangular cavity has been studied both experimentally and analytically. Experiments were conducted mainly in the case that the hot and cold surfaces were set up as the upper and lower half walls of a side plate, and the other walls were insulated. A periodic oscillation of the hot and cold cells was found to occur by the flow visualization in a certain range of the Rayleigh numbers. The influences of the Prandtl number and the aspect ratios of the cavity on the oscillation frequency were also examined. Unsteady two-dimensional equations, which govern a laminar natural convection, were solved numerically to simulate the oscillation. The calculated flow patterns and oscillation frequencies were in fairly good agreement with the experiments. From these facts, the applicability of above numerical schemes to the other systems of the oscillations was discussed.

Oscillatory Motion of Natural Convection in Rectangular Cavity

An oscillatory motion of the natural convection in a rectangular cavity has been studied both experimentally and analytically. Experiments were conducted mainly with the case that the hot and cold surfaces were set up as the upper and lower half wall of a side plate, and the other walls were insulated. Periodic oscillations of the hot and cold cell were found to exist by the flow visualization in the certain range of Rayleigh number. The influence of Prandtl number and aspect ratios of the cavity on the oscillation frequency were also examined. Unsteady two-dimensional equations, which govern the laminar natural convection, were solved numerically to simulate the oscillation. And the calculated flow patterns and oscillation frequency were fairly in good agreement with the experiments. From these fact, the adoptability of above numerical schemes to the other systems of the oscillations were also discussed.