Natural 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.

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.

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.

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.

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.

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.

Moment-based boundary conditions for lattice Boltzmann simulations of natural convection in cavities

We study a multiple relaxation time lattice Boltzmann model for natural convection with moment-based boundary conditions. The unknown primary variables of the algorithm at a boundary are found by imposing conditions directly upon hydrodynamic moments, which are then translated into conditions for the discrete velocity distribution functions. The method is formulated so that it is consistent with the second order implementation of the discrete velocity Boltzmann equations for fluid flow and temperature. Natural convection in square cavities is studied for Rayleigh numbers ranging from 103 to 108. An excellent agreement with benchmark data is observed and the flow fields are shown to converge with second order accuracy.

Numerical Study of Natural Convection in Square Cavity with Inner Bodies Using Finite Element Method

A numerical study of heat transfer problem by natural convection of a fluid inside a square cavity with two inner bodies is presented. This subject is of great interest in the engineering area, mainly in applications involving development of heat exchangers and cooling or heating systems of bodies by natural convection mechanism. Two cases have been studied. The inner bodies are square in case 1 and circular in case 2. In both cases, the bodies are solid and thermally conductive, the cavity lower and upper horizontal surfaces are isothermal with high temperature Th and low temperature Tc, respectively. Both vertical surfaces are adiabatic. A FORTRAN code using Finite Element Method (FEM) is developed to simulate the problem and solve the governing equations. The distributions of stream function, ψ, dimensionless temperature, θ, and vorticity, ω, are determined. Heat transfer is evaluated by analyzing the behavior of the average Nusselt number. The Grashof number and thermal diffusivity ratio are considered in range from 2 × 104 to 105 and from 0.1 to 100, respectively. The fluid is air with Prandtl number fixed in 0.733.

A three dimensional lattice model for thermal compressible flow on standard lattices

A three-dimensional double distribution function thermal lattice Boltzmann model has been developed for simulation of thermal compressible flows in the low Mach number limit. Both the flow field and energy conservation equation are solved by LB approach. A higher order density distribution function on standard lattices is used to solve the flow field, while an energy distribution function is employed to compute the temperature field. The equation of state of thermal perfect gas is recovered by higher order Hermite polynomial expansions in Navier–Stokes–Fourier equations. The equilibrium distribution functions of D3Q15, D3Q19 and D3Q27 lattices are obtained from the Hermite expansion. They exhibit slight differences originating in differences in the discrete lattice symmetries. The correction terms in LB models for third order derivation are added using an external force in orthogonal polynomials form. Present models are successfully assessed considering several test cases, namely the thermal Couette flow, Rayleigh–Bénard convection, natural convection in square cavity and a spherical explosion in a 3D enclosed box. The numerical results are in good agreement with both analytical solution and results given by previous authors.

Natural convection in square cavity with heat generating baffles

A numerical study of natural convection in an air filled differentially heated square cavity containing two vertical thin heat generating baffles is presented. The baffles are kept centrally separated by a distance d in the cavity and assumed to generate heat uniformly. A variety of thermal boundary conditions are imposed on the vertical walls while the horizontal walls are considered to be insulated. The Grashof number and Prandtl number are fixed at 107 and 0.71, respectively. A steady state results for the vorticity–stream function formulation are presented in the form of streamline and isotherm plots and average Nusselt numbers. The effects of various thermal boundary conditions on the vertical walls and different position of the baffles on heat transfer and fluid flow are investigated.

Numerical simulations of the effect of an isotropic heat field on the entropy generation due to natural convection in a square cavity

Entropy generation associated with laminar natural convection in an infinite square cavity, subjected to an isotropic heat field with different intensities; was numerically investigated for different values of Rayleigh number. The numerical work was carried out using, an in-house CFD code written in FORTRAN, which discretizes non-dimensional forms of the governing equations using the finite volume method and solves the resulting system of equations using Gauss-Seidal method utilizing a TDMA algorithm. Proper code validation was undertaken in order to establish the entropy generation calculations. It was found that the increase in the isotropic heat field intensity resulted in a corresponding exponential increase of the entropy augmentation number, and promoted high values of Bejan number within the flow. The entropy generation due to heat transfer was approximately one order of magnitude higher than the entropy generation due to fluid friction. The spatial uniformity of the Bejan number was more sensitive to the change in Rayleigh number than to the heat field intensity. The thermodynamic penalty of the isotropic heat field is shown by means of global integrals of the entropy source terms over the entire flow domain.

Entropy generation and natural convection in square cavities with wavy walls

The aim of the present work is to study the entropy generation in the natural convection process in square cavities with hot wavy walls through numerical simulations for different undulations and Rayleigh numbers, while keeping the Prandtl number constant. The results show that the hot wall geometry affects notably the heat transfer rate in the cavity. It has been found in the present numerical study that the mean Nusselt number in the case of heat transfer in a cavity with wavy walls is lower, as compared to heat transfer in a cavity without undulations. Based on the obtained dimensionless velocity and temperature values, the distributions of the local entropy generation due to heat transfer and fluid friction, the local Bejan number, and the local entropy generation are determined and plotted for different undulations and Rayleigh numbers. The study is performed for Rayleigh numbers 103 < Ra < 105, irreversibility coefficients 10−4 < φ < 10−2, and Prandtl numbers Pr = 0.71. The total entropy generation is found to increase with increasing undulation number.