Convection In Square Cavity Research Articles

Comment on: “Fluid flow and heat transfer characteristics of natural convection in square cavities due to discrete source-sink pairs” [International Journal of Heat and Mass Transfer 51 (2008) 5949–5957]

The following observations report incorrect/missing information, inaccurate mathematical expressions, and incorrect findings in the above-mentioned paper.

Effect of Wavy Interface on Natural Convection in Square Cavity Partially Filled with Nanofluid and Porous Medium using Buongiorno Model

nvective heat transfer improvement from wavy surfaces presents a new solution in industrial engineering for composite materials, including porous medium, and nanofluids to address the wavy irregular surfaces in heat transfer devices such as a wavy solar collector, energy absorption and filtration, thermal insulation, and geothermal power plants. This technique enables the performance of engineering applications. The numerical study is performed to examine the effects of a wavy interface separating two layers in the enclosure on heat exchange rates. This paper investigates numerically the natural convection flow in a square cavity partially filled with nanofluid-porous layers separated by a wavy horizontal interface. The left and right walls of the cavity are maintained at constant hot and cold temperatures, whereas the other walls are adiabatic. The Buongiorno model is used to describe nanofluid motion, taking into account the brownian and thermophoresis effects in the cavity. The Galerkin finite element method was applied to solve the differential governing equations. The dynamic, thermal field and heat transfer have been analyzed for various parameters such as Rayleigh number (10^3 ≤ Ra ≤ 10^6), the amplitude of interface (0 ≤ A ≤ 0.1), and undulation number (0 ≤ n ≤ 9). The results reveal that the flow intensity induced by buoyancy forces is more significant in the nanofluid layer than in the porous layer, since the heat transfer is enhanced while the flow is not sensitive to variations in amplitude and number undulation, and accordingly, the decline of average Nusselt and Sherwood numbers is insignificant. The effects of controlled parameters on the structure of nanofluid flow, heat, and mass transfer rate are insignificant.

INFLUENCE OF HYBRID NANOFLUIDS AND SOURCE CONFIGURATION ON NATURAL CONVECTION IN SQUARE CAVITY

A numerical investigation was conducted of steady laminar natural convection within a heated square enclosure filled with a mixture of water, carbon nanotubes (CNT), and aluminum oxide (Al<sub>2</sub>O<sub>3</sub>) (hybrid CNT-Al<sub>2</sub>O<sub>3</sub>/water nanofluid). Various heat source configurations and different volume fractions for the hybrid nanofluids were examined. The obtained results were analyzed through numerical simulation using ANSYS Fluent software. Thermal and dynamic fields were acquired, along with the Nusselt number (Nu). The influence of parameters such as Rayleigh number (Ra), nanofluid type, and heat source configuration was taken into account. Correlations between the Nusselt number and the various control parameters of our configuration were also established. The acquired findings clearly indicate that the introduction of nanoparticles has notably amplified heat transfer within the cavity (φ = 0.09). Furthermore, the heat source configuration has proven to be a pivotal element that effectively expedites the heat transfer process. Additionally, a direct correlation is observed between the increase in average Nusselt number and the augmentation in volume fraction. Notably, the most favorable outcomes are derived from the implementation of the (CNT-Al<sub>2</sub>O<sub>3</sub>)/water hybrid nanofluid.

Hybrid-nanofluid mixed convection in square cavity subjected to oriented magnetic field and multiple rotating rough cylinders

In this study, mixed convective hybrid-nanofluid flow in a partially heated square cavity with two rotating rough cylinders in presence of an external magnetic field is numerically investigated. A pair of rotating rough cylinders is placed at different locations inside the cavity. The cavity is permeated by an external magnetic field at different inclination angles. Maxwell's thermal conductivity model is modified incorporating Brownian motion of hybrid nanoparticles. The conservation equations of the flow and thermal fields are simulated using finite element method. The effects of different influential parameters such as cylinders rotation velocity (0 ≤ ω ≤ 50), Hartmann number (0 ≤ Ha ≤50), hybrid nanoparticle volume fraction (0% ≤ φ ≤ 5%) and magnetic inclination angle (0° ≤ α ≤ 135°) on the flow and thermal fields are explored via streamlines, isotherms and bar charts of average Nusselt number. The simulated results ensure that mixed convective flow is accelerated with cylinders rotation speed but declines with higher magnetic field strength and hybrid-nanoparticle volume fraction. Heat transfer enhancement is recorded up to 261.29% at highest rotating speed of rough cylinders (ω: 0–50, φ = 1%, Ha = 10). Enhancement of heat transfer rate is found decreasing for increasing magnetic field strength. Lowest heat transfer rate is occurred at highest magnetic field impact (Ha = 50) which is 144.62% less than that of heat transfer in absence of magnetic field (Ha = 0). Optimum heat transfer is found for 5% hybrid nanoparticle volume fraction which is 101.2% more compared to base fluid water. The presence of triangular rough components accelerates the fluid flow and heat transfer rate significantly. In addition, 48.89% more heat transfer is obtained for rotating rough cylinders with triangular components compared to smooth cylinders. Moreover, maximum heat transfer is achieved at magnetic inclination angle of 90°. It is also observed that the flow and thermal fields strongly depend on the cylinders arrangements.

Development of unsteady natural convection in a square cavity under large temperature difference

To investigate how the nonuniform fluid density distribution caused by large temperature variations affects the development of unsteady natural convection, we perform a series of direct numerical simulations of two-dimensional compressible natural convection in an air-filled square cavity. The cavity has a hot wall on the left and a cold wall on the right, and two horizontal walls are adiabatic. The simulations are done using a kinetic approach based on a modeled Boltzmann equation, from which the fully compressible Navier–Stokes–Fourier equations are recovered. No Boussinesq approximation or low Mach number approximation is made. An extra source term is introduced to adjust the fluid Prandtl number. Simulations are performed for a range of Rayleigh numbers (107−109) with a fixed dimensionless temperature difference of ε=0.6 to determine the critical Rayleigh number and study the development of unsteady flow. To illustrate the instability mechanism, instantaneous fluctuation field, time trace of temperature, and velocity at selected monitoring points, the spectrum and other statistics are presented and discussed. As expected, significant differences are observed between the instability of compressible natural convection and the Boussinesq-type natural convection. With a large temperature difference, the transition to unsteady flow is asymmetric for the flows near the hot wall and cold wall. For the Rayleigh number range we studied, the cold wall region is dominated by low-frequency impact instability of the boundary thermal jet at the bottom corner. For the hot wall region, besides the upper corner impact instability, a boundary layer instability featuring high-frequency oscillations is observed.

Natural convection in a square cavity containing two heat-generating cylinders with different geometries

This work presents a numerical study of laminar natural convection in an air-filled square cavity (Pr = 0.71). Inside this cavity, there are two cylinders having the same surface and different geometric shapes (square, circular, and elliptical). These two cylinders generate uniform volume powers represented by two Rayleigh numbers. The right wall of the cavity is cooled uniformly with a constant temperature Tc, while the other walls are assumed to be perfectly insulated. Numerical simulations are performed with an in-house CFD code using the Finite Volume Method (FVM) based on the SIMPLE algorithm. The objective of this study is to determine the effects of the two studied Rayleigh numbers (ranging from 103 to 107) and the effect of the cylinders’ geometry on the temperature and flow fields, as well as on the local heat transfer. The results obtained show that Rayleigh numbers significantly affect the flow and heat transfer in the cavity.

A combined method for simulating MHD convection in square cavities through localized heating by method of line and penalty-artificial compressibility

A new combined technique is developed for studying free convection of magnetohydrodynamic unsteady incompressible flow in a square cavity that partially heated from lower wall and regular cooling from lateral walls. Convection has been studied for several lengths of heat source, Hartman and the Rayleigh numbers. The local and average Nusselt numbers are calculated and presented graphically along the heat source portion. The proposed technique is a combination of the method of lines (MOL) and a developed penalty-artificial compressibility technique (PACT). Unsteady penalty compressibility governing equations are used instead of solving steady-state balances. The penalty and artificial compressibility factors are estimated using a deduced stability restriction. The validation of the MOL-PACT is verified by comparing the current data with other numerical and experimental ones existing in the literature. The proposed technique provides a new choice through the investigation of MHD mass and heat transfer.

Effects of porous medium and wavy surface on heat transfer and entropy generation of Cu-water nanofluid natural convection in square cavity containing partially-heated surface

This article analyzes the natural convection of nanofluid within a porous cavity containing a partially-heated vertical wall and wavy lower and upper walls. Numerical simulations are performed to explore the effects of the Rayleigh number (Ra), Darcy number (Da), porosity (ε), volume fraction of nanoparticles (φ), amplitude of wavy surface (αw), length of partially-heated wall surface (LH∗), and irreversibility distribution ratio (χ) on the Bejan number (Be), total entropy generation (St), mean Nusselt number (Num), and energy-flux-vector distribution. The results show that for high values of Da and Ra, circulation regions are developed in the energy-flux-vector distribution and hence convection heat transfer dominates. Consequently, Num and St both increase, while Be reduces as Ra, ε and Da increase. For low values of Da and Ra, the effects of Da, Ra and ε on Num and St are insignificant, and Be approaches unity since conduction heat transfer dominates. As φ and αw increase, Num and Be increase, but St decreases. Moreover, as LH∗ increases, Num and St also increase. For a high value of Ra, St increases and Be reduces as χ is increased. Finally, for a low value of Ra, the effect of χ on St is insignificant and Be ≈ 1.

Coupled solid-liquid phase change and thermal flow simulation by particle method

Abstract This paper applied the Particle Method on the coupled simulation of phase change process and thermal fluid flow. An enthalpy-based heat and mass transfer model was approximated by SPH discretization, and the temperature and liquid fraction evaluation during phase change can then be calculated. Besides, a particle shifting was adopted to decrease the particle irregularity on thermal flow. To verify the capability of proposed model, two benchmarks without fluid flow were first presented: 1D Stefan Problem with constant temperature or specific heat flux on the boundary and 2D solidification example. The interface evaluation and temperature distribution by proposed method agreed well with the analytical solution. After the validation of proposed model on thermal flow, phase change process coupled with natural convection in square cavity was then simulated and consistent results were obtained compared with previous work.

Numerical simulation of entropy generation due to natural convection heat transfer using Kernel Derivative-Free (KDF) Incompressible Smoothed Particle Hydrodynamics (ISPH) model

This paper develops and applies a Kernel Derivative-Free (KDF) Incompressible Smoothed Particle Hydrodynamics (ISPH) model for analysis of entropy generation and heat transfer in fluid-structure coupling problems. A modified high order Laplacian operator is applied for the treatment of pressure-velocity coupling (Poisson's equation), while an explicit third-order TVD Runge-Kutta scheme is used for time integration of the momentum, energy and displacement equations. To improve the consistency and stability of the model, a new particle regularization technique based on the particle shifting is also introduced for simulating free-surface flows. The developed KDF-ISPH model is validated and evaluated for a series of challenging benchmark cases, including, dam break, stretching water drop, rotating square patch of fluid, and natural convection in square cavity. Accuracy and applicability of the method are further validated by analyzing entropy generation due to the natural convection heat transfer in three well-known geometries including: square cavity with hot obstacle inside, C-shaped enclosure, and square enclosure containing a pair of hot and cold horizontal pipes (heat exchanger). The results are found to be in good agreement with available numerical and experimental data. The accuracy of the developed KDF-ISPH with new Laplacian operator, for use in prediction of fluid flow and heat transfer characteristics is also proven. Finally, by combining the cosine and signal functions, a new high order smoothing kernel is constructed. The evaluation of this new kernel for the propagation of shock wave in 1D tube demonstrates better global stability and consistency properties compared to two frequently used SPH kernels (i.e. cubic and quintic spline functions).

Pseudoplastic fluid flows for different Prandtl numbers: Steady and time-dependent solutions

In this work, a variational multiscale (VMS) finite element formulation is used to approximate numerically the natural convection in square cavity with differentially heated from sidewalls problem for Newtonian and power-law fluids. The problem is characterized for going through a Hopf bifurcation when reaching high enough Rayleigh numbers, which initiates the transition between steady and time dependent behavior, however, results found in the literature are only for air Prandtl number. The presented VMS formulation is validated using existing results, and is used to study highly convective cases, to determine the flow conditions at which it becomes time dependent, and to establish new benchmark solutions for non-Newtonian fluid flows for different Pr and power-law indexes n. The range of solutions were found in the range 0.6<n<1 and 0.01<Pr<1,000, and the critical Rayleigh number (Rac) where Hopf bifurcations appear were identified for all cases. Obtained results have good agreement with those previously reported in the specific literature, and new data related to the heat transfer capabilities of pseudoplastic fluids and its oscillatory behavior was identified. This non-Newtonian influence of the fluid is later checked in a 3D model of a simplified heat exchanger, where the capability of pseudoplastic fluids for energy transport proved to be enhanced when compared to the Newtonian case.

Natural Convection Study with Internal Heat Generation on Heat Transfer and Fluid Flow Within a Differentially Heated Square Cavity Filled with Different Working Fluids and Porous Media

To study the intricate natural convection in square cavity filled with porous medium with an electrically conductive fluid in the presence of internal heat source, a numerical methodology based on the finite volume method and a full multigrid acceleration is utilized in this paper. The Darcy–Brinkman is adopted to model the fluid flow and energy transport equations in order to predict the heat transfer process in the porous medium. Numerical solutions are generated for representative combinations of the controlling Grashof number (103 ≤ Gr ≤ 106), the Prandtl number (0.015 ≤ Pr ≤ 0.054), and the Darcy number (10−5 ≤ Da ≤ 10−2). Typical sets of streamlines, isotherms, and average Nusselt number profiles are presented to analyze the flow patterns set up by the competition between homogenous and porous medium. It is revealed that average Nusselt number values are strongly affected by the increase of Prandtl number and the presence of homogeneous medium overestimates the rate of heat transfer better than the presence of a porous medium. Correlations of heat transfer rates in porous medium cases are established in the current investigation.

Natural Convection in a Square Cavity with Uniformly Heated and/or Insulated Walls Using Marker-and-Cell Method

In this paper, a numerical Harlow–Welch MAC (Marker and Cell) method is developed to investigate the unsteady free convection in lid-driven square cavity. The constant heat flux is considered over left wall and remaining walls are kept thermally insulated. The structure of thermal convection patterns analysed via streamline, vorticity, pressure and temperature contour plots. The influence of the thermo-physical parameters, Reynolds number (Re), thermal Grashof number (Gr) Prandtl number (Pr) and Peclet number (Pe = PrRe), on these distributions are described in detail. Validation of solutions with earlier studies is included. Mesh independence is also conducted. It is observed that an increase in Prandtl number intensifies the primary circulation whereas it reduces the heat transfer rate. Increasing thermal Grashof number also decreases heat transfer rates. Furthermore, the isotherms are significantly compressed towards the left (constant flux) wall with a variation in Grashof number while Peclet number is fixed. The study is relevant to solar collector heat transfer simulations and also crystal growth technologies.

基于Soret和Dufour效应的方腔内双扩散自然对流振荡特性研究

The lattice Boltzmann method was adopted to study the oscillating characteristics of double diffusive natural convection in square cavities with Soret and Dufour effects. The inner heating cylinder with high concentration was located at the center of the cavity and the 4 surrounding walls were assumed to be at low concentrations and temperatures. The impacts of buoyancy ratio B_r(2.0≤B_r≤10.0), Soret number S_r(-0.6≤S_r≤0.0) and Dufour number D_f(-0.6≤D_f≤0.0) on the oscillating characteristics in the cavity were analyzed with the time history method and the power spectrum method. The results show that the flow state is steady at S_r=0.0 and D_f=0.0. With decreasing S_rand D_f from 0.0 to -0.6, the state of double diffusive natural convection turns into the periodic state and in turn the aperiodic oscillatory state gradually. Moreover, the positive buoyancy ratio enhances the oscillating characteristics.

Free Convection in a Porous Square Enclosure with Localized Sinusoidally Varying Temperature Profile on the Bottom Wall

This current study focuses on the simulation of free convection in square cavity filled with a porous medium considered homogenous, isotropic and saturated by a Newtonian fluid obeying the law of Darcy and the hypothesis of Boussinesq. The lower horizontal wall of the enclosure is subjected to a localized temperature varying sinusoidally with the space while the upper horizontal wall and rest of the bottom walls are insulated. The vertical walls are kept cold isotherm. In order to generalize the results, all governing equations are put into dimensionless form, discretized by the Finite Difference Method and solved by the relaxed Gauss Seidel (SUR) Algorithm. A code has been proposed in FORTRAN 95, in order to solve numerically the equations of the problem. The study parameters are the Rayleigh-Darcy number (Ra) and the amplitude (Ar) of the hot wall temperature. The effects of the Rayleigh-Darcy number, amplitude and length of source heating on the dynamic and thermal fields are investigated. On the other hand, the effects of the amplitude on the horizontal velocity distribution and the mean horizontal temperature distribution(y=0.5) were presented and discussed. It emerges from this study that the increasing of the amplitude and Rayleigh-Darcy number intensify the flow and the global heat transfer in our physical domain.

Numerical Study of Natural Convection in a Porous Square Enclosure with Sinusoidally Varying Temperature Profile on the Bottom Wall

This current study focuses on the simulation of natural convection in square cavity filled with a porous medium considered homogenous, isotropic and saturated by a Newtonian fluid obeying the law of Darcy and the hypothesis of Boussinesq. The lower horizontal wall of the enclosure is subjected to a temperature varying sinusoidally with the space while the upper horizontal wall is maintained adiabatic. The vertical walls are kept cold isotherm. In order to generalize the results, all governing equations are put into dimensionless form, discretized by the Finite Difference Method and solved by the relaxed Gauss Seidel (SUR) Algorithm. A code has been proposed in Fortran 95, in order to solve numerically the equations of the problem. The study parameters are the Rayleigh-Darcy number (Ra) and the amplitude (Ar) of the hot wall temperature. The effects of the Rayleigh-Darcy number and amplitude on the dynamic and thermal field, the horizontal velocity distribution and the mean horizontal temperature distribution (y = 0.5) were presented and discussed. It emerges from this study that the increases of the amplitude and Rayleigh-Darcy number intensify the flow and the global transfer of heat in our physical domain.

Parameter-free numerical method for modeling thermal convection in square cavities in a wide range of Rayleigh numbers

Some numerical results for the two- and three-dimensional de Vahl Davis benchmark are presented. This benchmark describes thermal convection in a square (cubic) cavity with vertical heated walls in a wide range of Rayleigh numbers (104 to 1014), which covers both laminar and highly turbulent f lows. Turbulent f lows are usually described using a turbulence model with parameters that depend on the Rayleigh number and require adjustment. An alternative is Direct Numerical Simulation (DNS) methods, but they demand extremely large computational grids. Recently, there has been an increasing interest in DNS methods with an incomplete resolution, which, in some cases, are able to provide acceptable results without resolving Kolmogorov scales. On the basis of this approach, the so-called parameter-free computational techniques have been developed. These methods cover a wide range of Rayleigh numbers and allow computing various integral properties of heat transport on relatively coarse computational grids. In this paper, a new numerical method based on the CABARET scheme is proposed for solving the Navier–Stokes equations in the Boussinesq approximation. This technique does not involve a turbulence model or any tuning parameters and has a second-order approximation scheme in time and space on uniform and nonuniform grids with a minimal computational stencil. Testing the technique on the de Vahl Davis benchmark and a sequence of refined grids shows that the method yields integral heat f luxes with a high degree of accuracy for both laminar and highly turbulent f lows. For Rayleigh numbers up to 1014, a several percent accuracy is achieved on an extremely coarse grid consisting of 20 × 20 cells refined toward the boundary. No definite or comprehensive explanation of this computational phenomenon has been given. Cautious optimism is expressed regarding the perspectives of using the new method for thermal convection computations at low Prandtl numbers typical of liquid metals.

Natural convection in square cavity filled with ferrofluid saturated porous medium in the presence of uniform magnetic field

This article contains numerical results for free convection through square enclosure enclosing ferrofluid saturated porous medium when uniform magnetic field is applied upon the flow along x-axis. Heat is provided through bottom wall and a square blockage placed near left or right bottom corner of enclosure as a heat source. Left and right vertical boundaries of the cavity are considered insulated while upper wall is taken cold. The problem is modelled in terms of system of nonlinear partial differential equations. Finite element method has been adopted to compute numerical simulations of mathematical problem for wide range of pertinent flow parameters including Rayleigh number, Hartman number, Darcy number and Prandtl number.Analysis of results reveals that the strength of streamline circulation is an increasing function of Darcy and Prandtl number where convection heat transfer is dominant for large values of these parameters whereas increase in Hartman number has opposite effects on isotherms and streamline circulations. Thermal conductivity and hence local heat transfer rate of fluid gets increased when ferroparticles are introduced in the fluid. Average Nusselt number increases with increase in Darcy and Rayleigh numbers while it is decreases when Hartman number is increased.

Natural convection investigation in square cavity filled with nanofluid using dispersion model

A cooling achieved with compact and efficient device is one of the major challenges encountered in the promising technique of fuel cell stacks. The safe and reliable use of such a system is highly dependent on the efficiency of the assured heat transfer and consequently on the quality of the coolant used. To test the possible improvement of the coolant performances, laminar natural convection in square cavity filled with copper-water nanofluid is numerically carried out taking into account the thermal dispersion effect on the heat transfer intensity. The finite element method is used to solve the governing equations. The hydrodynamic structure of the flow and its thermal behavior are studied for a wide range of Rayleigh numbers. The obtained results showed an enhancement of heat transfer with an increase in nanoparticle volume fraction for all examined Rayleigh numbers. However, it is found that an increase in nanoparticle diameter enhances heat transfer only when thermal dispersion is significant. Correlation with 99.94% confidence coefficient is proposed to quantify the heat transfer intensity according to the Rayleigh number and particle diameter and concentration.

Тurbulent natural convection modeling in enclosed tall cavities

In our previous work on the parameter-free numerical method for modeling thermal convection in square cavities in a wide range of Rayleigh numbers (Computational Continuum Mechanics, 2015, vol. 8, no. 1, pp. 60-70), it was shown that using eddy-resolving parameter-free CABARET scheme for solution of both two and three dimensional Davis’ test leads to surprisingly good agreement of computational results on the coarse grids (20×20) and (20×20×20) with experimental results and accurate computations for Rayleigh numbers up to 10^14. Current work is devoted to sensitivity analysis of this phenomenon in terms of cavity form variation from cubical to highly stretched. Therefore, the computational regions with the aspect ratio 1:4, 1:10, and 1:28.6 were considered. Comparison of CABARET scheme results with the experimental data (for the aspect ratio 1:28,6), DNS results (for the ratio 1:4), and empirical relation (for the ratio 1:10) is presented. In all the cases CABARET method showed good agreement of integral parameters of the flow with the results of other authors. For CABARET calculations notably coarse grids were used with refining to the walls of the region. It is shown that acceptable computation accuracy on the extremely coarse grids is achieved for the aspect ratio up to 1:10. For the higher aspect ratio and the given accuracy the number of computational cells significantly grows