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The purpose of this paper is to consider natural convection of a nanofluid inside of a C-shaped cavity using Lattice Boltzmann method (LBM).

Effects of some geometry and flow parameters consisting of the aspect ratio of the cavity, aspect ratio of the heat source; Rayleigh number (Ra = 10³ − 10⁶) have been investigated. The validity of the method is checked by comparing the present results with ones from the previously published work.

The results demonstrate that for Ra = 10³, the aspect ratio of the heat source has more influence on the average Nusselt number in contrast to the case of Ra = 10⁶. Contrary to the fact that the average Nusselt number increases non-linearly more than twice because of the increase of the aspect ratio of the enclosure at Ra = 10³, the average Nusselt number has a linear relation with the aspect ratio for of Ra = 10⁶. Therefore, upon increasing the Rayleigh number, the efficiency of the aspect ratio of the cavity on the thermal convection, gradually diminishes.

The authors believe that all the results, both numerical and asymptotic, are original and have not been published elsewhere.

A numerical study of the flow in and heat transfer across a vertical cavity containing pure water when the aspect ratio of the cavity is low, i.e. 1 or less, has been undertaken. One vertical wall of the cavity is kept at a temperature that is below the freezing point of water while the opposite wall is kept at a temperature that is above this freezing temperature. Ice therefore forms in part of the cavity, the conditions being such that there can be significant natural convection in the water. The upper surface of the cavity is open i.e. the water has a free surface, heat transfer from this surface being assumed negligible. The lower surface of the cavity is assumed to be adiabatic. Only the steady state has been considered here. It has been assumed that the flow is laminar and two‐dimensional and that liquid and solid properties are constant except for the water density change with temperature which gives rise to the buoyancy forces. The governing equations have been written in dimensionless form and these equations have been solved using a finite element‐based procedure in which the position of the solid‐liquid interface is obtained using an iterative approach. Solutions have been obtained for modified Rayleigh numbers of between 10³ and 10⁸ for various degrees of under‐cooling and for cavity aspect ratios of between 0.25 and 1. The density inversion that occurs with water has been shown to have a large effect on the steady state freezing of water in a cavity. The aspect ratio of the cavity has also been shown to have a significant influence on the results when the aspect ratio is less than 0.5.

The purpose of this paper is to apply lattice Boltzmann equation method (LBM) with multiple relaxation time (MRT) model, to investigate lid‐driven flow in a three‐dimensional (3D), rectangular cavity, and compare the results with flow in an equivalent two‐dimensional (2D) cavity.

The second‐order MRT model is implemented in a 3D LBM code. The flow structure in cavities of different aspect ratios (0.25‐4) and Reynolds numbers (0.01‐1000) is investigated. The LBM simulation results are compared with those from numerical solution of Navier‐Stokes (NS) equations and with available experimental data.

The 3D simulations demonstrate that 2D models may predict the flow structure reasonably well at low Reynolds numbers, but significant differences with experimental data appear at high Reynolds numbers. Such discrepancy between 2D and 3D results are attributed to the effect of boundary layers near the side‐walls in transverse direction (in 3D), due to which the vorticity in the core‐region is weakened in general. Secondly, owing to the vortex stretching effect present in 3D flow, the vorticity in the transverse plane intensifies whereas that in the lateral plane decays, with increase in Reynolds number. However, on the symmetry‐plane, the flow structure variation with respect to cavity aspect ratio is found to be qualitatively consistent with results of 2D simulations. Secondary flow vortices whose axis is in the direction of the lid‐motion are observed; these are weak at low Reynolds numbers, but become quite strong at high Reynolds numbers.

The findings will be useful in the study of variety of enclosed fluid flows.

Sets out to discuss laminar free convection characteristics of air confined to a square cavity and a horizontal rectangular cavity (aspect ratio A=2) along with the viable isosceles triangular cavities and right‐angle triangular cavities that may be inscribed inside the two original cavities.

The three distinct cavities shared the base wall as the heated wall, while the remaining sides and upper walls are cold. The finite volume method is used to perform the numerical computation of the transient conservation equations of mass, momentum and energy. The methodology takes into account the second‐order‐accurate quick scheme for the discretization of the convective term, whereas the pressure‐velocity coupling is handled with the simple scheme. The working fluid is air, which is not assumed as a Boussinesqian gas, so that all influencing thermophysical properties of air are taken as temperature‐dependent. The cavity problem is examined over a variety of height‐based Grashof numbers ranging from 10³ to 10⁶.

Numerical results are reported for the velocity fields, the temperature field as well as the local and mean wall heat fluxes along the heated base wall. It was found that the airflow remains symmetric for the isosceles triangular cavity with aspect ratio A=1 even at high Grashof numbers. In contrast, for an isosceles triangular cavity with an aspect ratio A=2, a pitchfork bifurcation begins to form at a critical Grashof number of 2 × 10⁵, breaking the airflow symmetry. The computed local and mean heat fluxes along the hot base wall are compared for the three configurations under study and the corresponding maximum heat transfer levels are clearly identified for the two aspect ratios A=1 and 2.

As a continuity of this work, there are two avenues that future research could explore and indeed are presently being explored by the authors within these geometries. The first deals with heat transfer enhancement using mixture of gases. The second is to re‐examine the problem under turbulent conditions.

The present study seeks to maximize the convection heat transport in cavities and minimize their sizes. The peculiarity of the derived cavities is their cross‐section area being half of the cross‐section area of the basic cavities.

Presents a numerical study on heat transfer by natural convection in porous media in vertical enclosures with side wall heating. The model for porous media includes inertia terms and also the Brinkman extension in addition to the Darcy resistance term. A semi‐implicit finite element scheme based on operator splitting method is adopted for solving the time‐dependent system of equations. The first half of the investigations is confined to the low permeability regime where Darcy law holds good. Presents the results for annular and rectangular cavities and proposes correlations for two types of boundary conditions, namely constant wall temperature case and uniform wall heat flux case. In the second half of the investigations, the scheme is applied in a high permeability regime, where the validity of Darcy law becomes questionable. Employs plane rectangular cavities with the two types of boundary conditions mentioned earlier. Highlights the influence of Rayleigh number (Ra) and Darcy number (Da) as separate parameters and proposes correlations for a square cavity for the first time in terms of Ra and Da as separate parameters. Discusses a qualitative study of the effect of aspect ratio on heat transfer as the permeability changes.

The purpose of this paper is to carry out a comprehensive review of some latest studies devoted to natural convection phenomenon in the enclosures because of its significant industrial applications.

Geometries of the enclosures have considerable influences on the heat transfer which will be important in energy consumption. The most useful geometries in engineering fields are treated in this literature, and their effects on the fluid flow and heat transfer are presented.

A great variety of geometries included with different physical and thermal boundary conditions, heat sources and fluid/nanofluid media are analyzed. Moreover, the results of different types of methods including experimental, analytical and numerical are obtained. Different natures of natural convection phenomenon including laminar, steady-state and transient, turbulent are covered. Overall, the present review enhances the insight of researchers into choosing the best geometry for thermal process.

A comprehensive review on the most practical geometries in the industrial application is performed.

This work is devoted to the numerical analysis of laminar natural convection in two-dimensional vertical cavities, filled with air and of high aspect ratios. One of the sidewalls is cooled isothermally while the other is heated by a uniform or linear heat flux whose average is located at mid-height of the wall. The paper aims to discuss these issues.

The governing equations are discretized by the finite volume method and solved, in transient regime, by using the SIMPLE algorithm.

The flow structure, air temperature field, local convective heat flux on the cold wall, variation of the temperature along the heated wall as well as its average and its maximum are analyzed for various combinations of the controlling parameters. These parameters are the linear heat flux slope γ (γ=0, 1 and −1, for a uniform, increasing and decreasing heat flux, respectively), the average Rayleigh number Ra _m (103Ra _m 3×104) and the aspect ratio A (10A80). It was found that for a given A and Ra _m , the highest (lowest) mean temperature of the hot wall is obtained when the linear heating is descending (ascending). While the maximum temperature increases with the three controlling parameters.

Accurate correlations which allow calculating the average and maximum temperatures of the heated wall are developed for each type of heating. Also, an empirical relationship for the position of the maximum temperature is provided for γ=−1.

Despite its fundamental and practical interest, natural convection in cavities with 10A80 and submitted to non-uniform heat flux was not examined before. Development of original correlations.

A finite element method based on the Eulerian velocity correction method has been used to analyse the laminar natural convection in an annular cavity. Unsteady, incompressible, axisymmetric Navier‐Stokes equations have been made use of. Different radius ratios of the annular cavity have been considered to investigate the effect of the radius of curvature on the heat transfer coefficient.

The purpose of this paper is to focus on the numerical analysis of transient free convection heat transfer in partially porous cylindrical domains. The authors analyze the dependence of velocity and temperature fields on the geometry, by analyzing transient flow behavior for different values of cavity aspect ratio and radii ratio; both inner and outer radius are assumed variable in order to not change the difference r_o-r_i. Moreover, several Darcy numbers have been considered.

A dual time-stepping procedure based on the transient artificial compressibility version of the characteristic-based split algorithm has been adopted in order to solve the transient equations of the generalized model for heat and fluid flow through porous media. The present model has been validated against experimental data available in the scientific literature for two different problems, steady-state free convection in a porous annulus and transient natural convection in a porous cylinder, showing an excellent agreement.

For vertically divided half porous cavities, with Rayleigh numbers equal to 3.4×106 for the 4:1 cavity and 3.4×105 for the 8:1 cavity, the numerical results show that transient oscillations tend to disappear in presence of cylindrical geometry, differently from what happens for rectangular one. The magnitude of this phenomenon increases with radii ratio; the porous layer also affects the stability of velocity and temperature fields, as oscillations tend to decrease in presence of a porous matrix with lower value of the Darcy number.

A proper analysis of partially porous annular cavities is fundamental for the correct estimation of Nusselt numbers, as the formulas provided for rectangular domains are not able to describe these problems.

The proposed model represents a useful tool for the study of transient natural convection problems in porous and partially porous cylindrical and annular cavities, typical of many engineering applications. Moreover, a fully explicit scheme reduces the computational costs and ensures flexibility.

This is the first time that a fully explicit finite element scheme is employed for the solution of transient natural convection in partially porous tall annular cavities.

A numerical study is conducted for natural convection dominated melting inside discretely heated rectangular enclosures. This study finds applications in the design and operation of thermal energy storage units and the cooling of electric equipment. Results show the benefits of discrete heating over uniform heating for optimizing the melting process. For enclosures of high aspect ratios (A ∼> 4), configurations leading to well controlled heat source temperatures and long melting times are obtained. For cavities of low aspect ratios (A ∼< 4), it is found that the source span η is the most influential parameter. For η ∼ < 0.45, the melting times are shorter and the heat source temperatures remain equal and moderate during the entire melting process. A map for determining the cavity size and the source distribution that optimizes the melting process is presented.