Technical Note Internal natural convection around a sphere in a rectangular chamber Daehoon Lee a,1 , Hosung Jang b,1 , Byeong Jun Lee c,⇑ , Wonjoon Choi d,⇑ , Chan Byon a,⇑ a School of Mechanical, Aerospace and Nuclear Engineering, Ulsan National Institute of Science and Technology, Ulsan 44919, Republic of Korea b Humidity Sealing Tech Lab, SL Corporation, Gyeongsan 38470, Republic of Korea c School of Mechanical Engineering, Yeungnam University, Gyeongsan 38541, Republic of Korea d School of Mechanical Engineering, Korea University, Seoul 02841, Republic of Korea article info Article history: Received 11 October 2018 Received in revised form 5 March 2019 Accepted 5 March 2019 Keywords: Natural convection Sphere Rectangle abstract In this study, a three-dimensional internal natural convection heat transfer between a cuboidal enclosure and a spherical surface placed in the enclosure, is investigated numerically. The effects of enclosure shape and Rayleigh number on the flow and heat transfer characteristics are analyzed for concentric and eccen- tric positions of sphere, respectively. The numerical results show that there exists a critical Rayleigh number beyond which the Nusselt number decreases as the temperature difference increases. This is attributable to the fact that the thermal diffusivity and kinematic viscosity of air both increases as the temperature increases, resulting in reduction of Rayleigh number with the temperature increases. Based on the numerical results, a correlation for predicting Nusselt number is proposed as a function of Rayleigh number and the enclosure shape for concentric and eccentric cases, respectively. Ó 2019 Elsevier Ltd. All rights reserved. 1. Introduction The natural convection heat transfer is of a significant scientific as well as technological issue due to its various industrial applica- tions and its rich academic value [1–4]. Especially, flow and heat transfer from a heated body within an enclosure, namely, the inter- nal natural convection, have been studied actively and received a significant attention due to many relevant applications such as pipes, solidification process, electronics, heat exchangers, buildings and vehicle-related applications [5]. The internal natural convec- tion distinguishes itself from the external natural convection in that the natural convective flow is highly constrained by the enclo- sure shape, resulting in complex flow and heat transfer character- istics depending on the geometry and Rayleigh number [6]. In this regards, the internal natural convection has long been studied and many correlations have been proposed for predicting the Nusselt number [7]. Cesini et al. studied a natural convection from a horizontal cylinder in a rectangular cavity [8]. Ramon et al. investigated the transition from conduction to convection regime in a cuboidal enclosure with a partially heated wall [9]. Varol et al. studied a nat- ural convection in a triangle enclosure with flush mounted heater on the wall and showed that the heat transfer performance is enhanced when the heater and cooler are placed closer to each other [10]. Cheikh et al. investigated the influence of thermal boundary conditions on natural convection in a square enclosure partially heated from below [11]. Koca et al. [12] conducted a numerical analysis of natural convection in shed roofs with eave of buildings for cold climates. Deng [13] studied fluid flow and heat transfer characteristics of natural convection in square cavities due to discrete source and sink pairs. Varol et al. [14] studied a natural convection in right-angle porous trapezoidal enclosure partially cooled from inclined wall. Anderson et al. studied the suppression effect of natural convection in an attic shaped enclosure [15]. Abouali and Ahmadi [16] numerically investigated the natural con- vective flow of a single phase nanofluid. Kumar et al. [17], Stafford and Egan [18], and Sedaghat et al. [19] studied natural convective flows and resulting heat transfer performance of cylinders or cylin- der pairs located inside an enclosure. Zhang et al. [20] investigated a natural convective flow around an elliptical cylinder in a cavity. Roslan et al. [5] investigated a natural convection in an enclosure containing a sinusoidally heated cylindrical source and proposed a correlation for estimating the heat transfer efficiency between the cylinder surface and the inner surface of the container in terms of Nusselt number. As shown above, numerous studies have been performed in regard to the internal natural convection. However, few studies considered three-dimensional configurations due to a huge computational cost, which ruins the applicability of literature in practical situations. For example, even though there are many literatures that consider the natural convection between a cylinder https://doi.org/10.1016/j.ijheatmasstransfer.2019.03.023 0017-9310/Ó 2019 Elsevier Ltd. All rights reserved. ⇑ Corresponding authors. E-mail addresses: bjlee@yu.ac.kr (B.J. Lee), wojchoi@korea.ac.kr (W. Choi), cbyon@unist.ac.kr (C. Byon). 1 Equally contributed to this work. International Journal of Heat and Mass Transfer 136 (2019) 501–509 Contents lists available at ScienceDirect International Journal of Heat and Mass Transfer journal homepage: www.elsevier.com/locate/ijhmt