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The purpose of this paper is to show a thermodynamic analysis to determine the contribution of each term of the total energy balance.

The thermodynamic analysis comprises a number of numerical simulations where some terms, typically ignored by the commonly used approximations, are removed from the total energy equation to quantify the effects in the flow and heat transfer fields. The case study is the differentially heated square cavity flow, in which the effects of work done by the pressure forces contribute significantly to the energy balance. Because local magnitudes are computed here for discussion, the dimensional form of the governing equations is preferred and a numerical model without any restrictive approximation about the role of the pressure is used.

The results show that the work of gravity forces term is in perfect balance with the work of pressure forces term, and thus, ignoring the contribution of one of them yields an incorrect solution. In addition, it is shown that the assumption of zero divergence of the Boussinesq approximation can be erroneous, even for a natural convection flow case where the temperature difference is very small.

As the flow and heat transfer governing equations are complex, simplifying assumptions are generally used; that is, the Boussinesq and low Mach number approximations. These assumptions are systematically adopted without any validation process and without considering that they modify the physical meaning of one or more of the thermodynamic quantities, particularly the pressure. This fact results in inconsistencies of the different forms of energy.

This is the first time that the terms of the total energy balance are quantified in such a way, in a differentially heated square cavity flow, which is a case study addressed by several authors.

In this study, Benchmark solutions are derived for the problem of two‐dimensional laminar flow of air in a square cavity which is heated on the left, cooled on the right and insulated on the top and bottom boundaries. The temperature differences between the hot and cold walls are large. Neither Boussinesq nor low‐Mach number approximations of the Navier‐Stokes equations are used. The ideal‐gas law is used and the viscosity is given by Sutherland's law. A constant Prandtl number is assumed. The computational method is completely described by Vierendeels et al. Grid converged results with an accuracy of 4 up to 5 digits are obtained for different Rayleigh numbers and temperature differences.

This paper aims to present and then resolve the thermodynamic inconsistencies inherent in the usual Boussinesq model, especially with respect to the second law, and to highlight the effects of the correction.

The Boussinesq model (i.e. still assuming ▽v=0) is made thermodynamically consistent by maintaining in the heat equation, primarily the work of pressure forces, secondarily the heat generated by viscous friction. Numerically speaking, the modifications are very easy and hardly affect the computing time. However, new non‐dimensional parameters arise, especially the non‐dimensional adiabatic temperature gradient, ϕ.

There are presented and interpreted results of systematic numerical simulations done for a two‐dimensional square differentially‐heated cavity filled with air at 300K, with Rayleigh number ranging from 3,000 to 10⁸ and ϕ ranging from 10⁻³ to 2. All configurations are stationary and the fluid is far from its critical state. Nevertheless, the pressure‐work effect (similar to the piston effect) enhances the heat transfer while diminishing the convection intensity. The magnitude of this effect is non‐negligible as soon as ϕ reaches 0.02.

The domain where the thermodynamic Boussinesq model must be used encompasses configurations relevant to building engineering.

Exact second‐law analyses can be developed with the so‐corrected model.

The generalized integral transform technique (GITT) is an hybrid numerical‐analytical method that has been successfully applied in convection‐diffusion problems, where the original potentials are replaced by eigenexpansion series, and the system of partial differential equations is transformed into a finite system of ordinary differential equations, allowing to obtain an error controlled solution without any kind of grid generation. This paper aims at the application of GITT to the transient version of the classical differentially heated square cavity problem, considering fluid properties as functions of temperature. Comparing results to some previously reported data for constant fluid properties validates the computational procedure. The solution for variable fluid properties with Boussinesq approximation is presented for several values of inclinations, at Rayleigh number of 10³ and a Prandtl number of 0.71, demonstrating GITT capability of capturing circulating cells formation and evolution at a low Rayleigh number. New correlations for leaning angle and aspect ratio are presented.

The purpose of this paper is to assess the Boussinesq approach for a wide range of Ra (10 × 6 to 10 × 11) in two-dimensional (square cavity) and three-dimensional (cubic cavity) problems for air- and liquid-filled domains.

The thermal behavior in “differentially heated cavities” filled with air (low and medium Rayleigh) and water (high Rayleigh) is solved using computational fluid dynamics (CFDs) (OpenFOAM) with a non-compressible (Boussinesq) and compressible approach (real water properties from the IAPWS database).

The results from the wide range of Rayleigh numbers allowed for the establishment of the limitation of the Boussinesq approach in problems where the fluid has significant density changes within the operation temperature range and especially when the dependence of density with temperature is not linear. For these cases, the symmetry behavior predicted by Boussinesq is far from the compressible results, thus inducing a transient heat imbalance and leading to a higher mean temperature.

The main limitation of the present research can be found in the shortage of experimental data for very high Rayleigh problems.

Practical implications of the current research could be use of the Boussinesq approach by carefully observing its limitations, especially for sensible problems such as the study of pressure vessels, nuclear reactors, etc.

The originality of this paper lies in addressing the limitations of the Boussinesq approach for high Rayleigh water systems. This fluid is commonly used in numerous industrial equipment. This work presents valuable conclusions about the limitations of the currently used models to carry out industrial simulations.

Modeling of multi-phase flows for Rayleigh-Taylor instability and natural convection in a square cavity has been investigated using an incompressible smoothed particle hydrodynamics (ISPH) technique. In this technique, incompressibility is enforced by using SPH projection method and a stabilized incompressible SPH method by relaxing the density invariance condition is applied. The paper aims to discuss these issues.

The Rayleigh-Taylor instability is introduced in two and three phases by using ISPH method. The author simulated natural convection in a square/cubic cavity using ISPH method in two and three dimensions. The solutions represented in temperature, vertical velocity and horizontal velocity have been studied with different values of Rayleigh number Ra parameter (103=Ra=105). In addition, characteristic based scheme in Finite Element Method is introduced for modeling the natural convection in a square cavity.

The results for Rayleigh-Taylor instability and natural convection flow had been compared with the previous researches.

Modeling of multi-phase flows for Rayleigh-Taylor instability and natural convection in a square cavity has been investigated using an ISPH technique. In ISPH method, incompressibility is enforced by using SPH projection method and a stabilized incompressible SPH method by relaxing the density invariance condition is introduced. The Rayleigh-Taylor instability is introduced in two and three phases by using ISPH method. The author simulated natural convection in a square/cubic cavity using ISPH method in two and three dimensions.

The purpose of this paper is to model mixed convection in a square cavity included circular cylinders motion using an incompressible smoothed particle hydrodynamics (ISPH) technique.

The problem is solved numerically by using the ISPH method.

The SPH tool shows robust performance to simulate the rigid body motion in the mixed convective flow with heat transfer, and it may apply easily to complicated problems in 2D and 3D problem without difficulties.

The application of the SPH method to mixed convective flow with heat transfer and its potential application easily to complicated 3D problems is original.

The purpose of this study is the hydrothermal analysis of the natural convection phenomenon within the heat exchanger containing nanofluids using the lattice Boltzmann method (LBM).

The thermal conductivity as well as dynamic viscosity of the CuO–water nanofluid is estimated using the Koo-Kleinstreuer-Li model. The LBM has been used with unique modifications to make it flexible with the curved boundaries. The local as well as total entropy generation assessment, local Nusselt variation, as well as heatline visualization are used.

The solid volume percentage of the CuO–water nanofluid, a range of Rayleigh numbers (Ra) and thermal settings of internal operational fins and bodies are all factors that have been thoroughly researched to determine their effects on entropy production, heat transfer efficiency and nanofluid flow.

The originality of this work is using a novel numerical method (i.e. curved boundary LBM) as well as the local/volumetric second law analysis for the application of heat exchanger hydrothermal analysis.

This study aims to show the importance of natural convection of supercritical fluid in an inclined cavity. The heat transfer performance of natural convection can be improved.

A model of an inclined cavity was set up to simulate the natural convection of supercritical fluid. The influence of inclined angles (30 to approximately 90°) and pressures (8 to approximately 12 MPa) are analyzed. To ascertain flow and heat transfer of supercritical fluid natural convection, this paper conducts a numerical investigation using the lattice Boltzmann method (LBM), which is proven to be precise and convenient.

The results show that the higher heat transfer performance can be obtained with an inclined angle of 30°. It is also presented that the heat transfer performance under pressure of 10 MPa is the best. In addition, common criterion number correlations of average Nusselt number are also fitted.

These study results can provide a theoretical reference for the study of heat transfer of supercritical fluid natural convection in engineering.

This paper aims to conduct numerical simulations of unsteady natural/mixed convection in a cavity with fixed and moving rigid bodies and different boundary conditions using the incompressible smoothed particle hydrodynamics (ISPH) method.

In the ISPH method, the pressure evaluation is stabilized by including both of divergence of velocity and density invariance in solving pressure Poisson equation. The authors prevented the particles anisotropic distributions by using the shifting technique.

The proposed ISPH method exhibited good performance in natural/mixed convection in a cavity with fixed, moving and free-falling rigid body. In natural convection, the authors investigated the effects of an inner sloshing baffle as well as fixed and moving circular cylinders on the heat transfer and fluid flow. The heated baffle has higher effects on the heat transfer rate compared to a cooled baffle. In the mixed convection, a free-falling circular cylinder over a free surface cavity and heat transfer in the presence of a circular cylinder in a lid-driven cavity are simulated. Fixed or moving rigid body in a cavity results in considerable effects on the heat transfer rate and fluid flow.

The authors conducted numerical simulations of unsteady natural/mixed convection in a cavity with fixed and moving rigid bodies and different boundary conditions using the ISPH method.