Free Convective Heat Transfer in a Closed Gap between Concentric Semi-Hemispheres

Abderrahmane Baïri,Alexander Martín-Garín,Kemi Adeyeye,José-Antonio Millán-García,Nacim Alilat,Luis Roseiro

doi:10.3390/en14227479

Abderrahmane Baïri, Alexander Martín-Garín + Show 4 more

Open Access

https://doi.org/10.3390/en14227479

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Abstract

Free convective heat transfer in the closed gap between concentric semi-hemispheres is quantified by means of a numerical approach based on the volume control method using the SIMPLE algorithm. The average Nusselt number is determined for several configurations obtained by varying the cavity’s aspect ratio between 0.15 and 1.5, while the Rayleigh number varies within the 5.33 × 103–4.50 × 108 range. The results show that the correlations available in the literature dealing with concentric whole spheres cannot be used for the configuration treated here. The new correlation between the Nusselt and Rayleigh numbers proposed in this work can be applied in various engineering sectors, such as in the electronic packaging considered in this present work, buildings, and architecture.

Highlights

Several works dealing with quantification of heat transfer by free convection have been carried out in both variable regime and steady state
The dynamic and thermal steady state phenomena have been determined for whole concentric spheres, and heat transfer was quantified via Nusselt–Rayleigh type correlations in several studies, such as [16,17,18,19,20]
A numerical approach based on the volume control method using the SIMPLE algorithm was used to quantify the convective exchanges occurring in an open air-filled cavity of semi-hemispherical shape

Summary

Introduction

Several works dealing with quantification of heat transfer by free convection have been carried out in both variable regime and steady state. The influence of various physical parameters on heat transfer are examined, such as thermal conditions, thermophysical characteristics of the considered fluid, Rayleigh number range, and the enclosure’s inclination angle with respect to the gravity’s direction. The study [13] quantifies the free convective heat transfer between inclined concentric hemispheres, separated by different nanofluids whose volume fraction varies in different ranges depending on the concerned engineering application. The proposed correlations allow determination of the average Nusselt number for various combinations of some influencing physical parameters. The dynamic and thermal steady state phenomena have been determined for whole concentric spheres, and heat transfer was quantified via Nusselt–Rayleigh type correlations in several studies, such as [16,17,18,19,20]. A correlation is proposed, allowing determination of the average Nusselt number

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Conclusion