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The purpose of this study is to numerically investigate the geometric influence of different corrugation profiles (rectangular, trapezoidal and triangular) of varying heights on the flow and the natural convection heat transfer process over isothermal plates.

This work is an extension and finalization of previous studies of the leading author. The numerical methodology was proposed and experimentally validated in previous studies. Using OpenFOAM® and other free and open-source numerical-computational tools, three-dimensional numerical models were built to simulate the flow and the natural convection heat transfer process over isothermal corrugation plates with variable and constant heights.

The influence of different geometric arrangements of corrugated plates on the flow and natural convection heat transfer over isothermal plates is investigated. The influence of the height ratio parameter, as well as the resulting concave and convex profiles, on the parameters average Nusselt number, corrected average Nusselt number and convective thermal efficiency gain, is analyzed. It is shown that the total convective heat transfer and the convective thermal efficiency gain increase with the increase of the height ratio. The numerical results confirm previous findings about the predominant effects on the predominant impact of increasing the heat transfer area on the thermal efficiency gain in corrugated surfaces, in contrast to the adverse effects caused on the flow. In corrugations with heights resulting in concave profiles, the geometry with triangular corrugations presented the highest total convection heat transfer, followed by trapezoidal and rectangular. For arrangements with the same area, it was demonstrated that corrugations of constant and variable height are approximately equivalent in terms of natural convection heat transfer.

The results allowed a better understanding of the flow characteristics and the natural convection heat transfer process over isothermal plates with corrugations of variable height. The advantages of the surfaces studied in terms of increasing convective thermal efficiency were demonstrated, with the potential to be used in cooling systems exclusively by natural convection (or with reduced dependence on forced convection cooling systems), including in technological applications of microelectronics, robotics, internet of things (IoT), artificial intelligence, information technology, industry 4.0, etc.

To the best of the authors’ knowledge, the results presented are new in the scientific literature. Unlike previous studies conducted by the leading author, this analysis specifically analyzed the natural convection phenomenon over plates with variable-height corrugations. The obtained results will contribute to projects to improve and optimize natural convection cooling systems.

The purpose of this study is to numerically and experimentally investigate the natural convection heat transfer in flat plates and plates with square, trapezoidal and triangular corrugations.

This work is an extension of the previous studies by Verderio et al. (2021a, 2021b, 2021c, 2021d, 2022a). An experimental apparatus was built to measure the plates’ temperatures during the natural convection cooling process. Several physical parameters were evaluated through the experimental methodology. Free and open-source computational tools were used to simulate the experimental conditions and to quantitatively and qualitatively evaluate the thermal plume characteristics over the plates.

The numerical results were experimentally validated with reasonable accuracy in the range of studied RaLP for the different plates. Empirical correlations of Nu¯LPexp=f(RaLP), h¯conv=f(RaLP) and Nu¯LPexp⋅(A/AP)=f(RaLP), with good accuracy and statistical representativeness, were obtained for the studied geometries. The convective thermal efficiency of corrugated plates (Δη), as a function of RaLP, was also experimentally studied quantitatively. In agreement with the findings of Oosthuizen and Garrett (2001), the experimental and numerical results proved that the increase in the heat exchange area of the corrugations has a greater influence on the convective exchange and the thermal efficiency than the disturbances caused in the flow (which reduce h¯conv). The plate with trapezoidal corrugations presented the highest convective thermal efficiency, followed by the plates with square and triangular corrugations. It was also proved that the thermal efficiency of corrugated plates increases with RaLP.

The results demonstrate that corrugated surfaces have greater thermal efficiency than flat plates in heating and/or cooling systems by natural convection. This way, corrugated plates can reduce the dependence on auxiliary forced convection systems, with application in technological areas and Industry 4.0.

The empirical correlations obtained for the corrected Nusselt number and thermal efficiency for the corrugated plate geometries studied are original and unpublished, as well as the experimental validation of the developed three-dimensional numerical code.

The purpose of this study is to analyze the influence of the main physical–numerical parameters in the computational evaluation of natural convection heat transfer rates in isothermal flat square plates in the laminar regime. Moreover by experimentally validate the results of the numerical models and define the best parameter settings for the problem situation studied.

The present work is an extension of the study by Verderio Junior et al. (2021), differing in the modeling, results analysis and conclusions for the laminar flow regime with Rade=1×105. The analysis of the influence and precision of the physical–numerical parameters: boundary conditions, degree of mesh refinement, refinement layers and κ – ω SST and κ – ε turbulence models, occurred from the results from 48 numerical models, which were simulated using the OpenFOAM® software. Comparing the experimental mean Nusselt number with the numerical values obtained in the simulations and the analysis of the relative errors were used in the evaluation of the advantages, restrictions and selection of the most adequate parameters to the studied problem situation.

The numerical results of the simulations were validated, with excellent precision, from the experimental reference by Kitamura et al. (2015). The application of the κ – ω SST and κ – ε turbulence models and the boundary conditions (with and without wall functions) were also physically validated. The use of the κ – ω SST and κ – ε turbulence models, in terms of cost-benefit and precision, proved to be inefficient in the problem situation studied. Simulations without turbulence models proved to be the best option for the physical model for the studies developed. The use of refinement layers, especially in applications with wall functions and turbulence models, proved unfeasible.

Use of the physical–numerical parameters studied and validated, and application of the modeling and analysis methodology developed in projects and optimizations of natural convection thermal systems in a laminar flow regime. Just like, reduce costs and the dependence on the construction of experimental apparatus to obtain experimental results and in the numerical-experimental validation process.

Exclusive use of free and open-source computational tools as an alternative to feasible research in the computational fluid dynamics area in conditions of budget constraints and lack of higher value-added infrastructure, with applicability in the academic and industrial areas.

The results and discussions presented are original and new for the applied study of laminar natural convection in isothermal flat plate, with analysis and validation of the main physical and numerical influence parameters.

This paper aims to study, experimentally validate and select the main physical and numerical parameters of influence in computational numerical simulations to evaluate mean heat flux by natural convection on square flat plates.

Several numerical models were built to study the influence of physical and numerical parameters about the predictions of the natural convection heat transfer rates on the surface of a flat plate with aspect ratio = 1, in isothermal conditions, turbulent regime and using the free and open-source software OpenFOAM®. The studied parameters were: boundary conditions (using or not using wall functions in properties ε, κ, ν_t and ω), degree of mesh refinement, refinement layers and turbulence models [κ – ε and κ – ω Shear Stress Transport (SST)]. From the comparison of the values of the mean Nusselt number, obtained from numerical simulations and literature experimental results, the authors evaluated the precision of the studied parameters, validating and selecting the most appropriate to the analyzed problem situation.

The validation and agreement of the numerical results could be proven with excellent precision from experimental references of the technical scientific literature. More refined meshes with refinement layers were not suitable for the studies developed. The κ – ε and κ – ω SST turbulence models, in meshes without refinement layers, proved to be equivalent. Whether or not to use wall functions in turbulent boundary conditions proved to be irrelevant as to the accuracy of results for the problem situation studied.

Use of the physical and numerical parameters is studied and validated for various applications in natural convection heat transfer of technology and industry areas.

Use of free and open-source software as a research tool in the Computational Fluid Dynamics (CFD) area, especially in conditions without large financial resources or state-of-the-art infrastructure.

To the best of the authors’ knowledge, this work is yet not available in existing literature.