Nusselt number correlation for natural convection from vertical cylinders with triangular fins

Highlights

• We propose a correlation for the Nusselt number based on experimental data.

• The correlation is applicable to vertical cylinders with triangular fins.

• The correlation is applicable only for natural convection.

Abstract

In this study, natural convection from vertical cylinders with triangular fins was experimentally investigated with various fin numbers, fin heights, and base temperatures. From the experimental data, we propose a correlation for estimating the Nusselt number, which is applicable when the Rayleigh number, ratio of the fin height to fin length, and fin number are in the ranges of 1000–120,000, 0.2–0.6, and 9–72, respectively. Using this correlation, a contour map depicting the thermal resistance as a function of the fin number and fin thickness is presented. This contour map shows the existence of the fin number and fin thickness, at which the thermal resistance is minimized.

Introduction

Since the introduction of semiconductor technology, heat generation from electronic devices has significantly increased with continuously rising demands for high performance, low cost, and miniaturization of the devices [1], [2], [3], [4]. For instance, heat generation density (heat flux) from silicon microprocessors has reached 100 W/cm² and is approaching that of the surface of the sun [1]. Despite the high heat generation, the device temperature must be maintained at a relatively low level for the following reasons. (a) The rate of thermal failures increases exponentially with the device temperature [5]. These failures include thermal runaway, junction failure, metallization failure, corrosion, resistor drift, and electromigration diffusion. (b) The lifetime and performance of the device also decrease exponentially with increasing junction temperature [6], [7]. Therefore, to prevent catastrophic thermal failure and to extend the useful lifetime of the device, thermal management of electronic devices is essential [8], [9].

A number of cooling methods for thermal management have been proposed; among these, natural-convective heat sinks have proven to be appropriate because of their inherent simplicity, reliability, and low long-term cost [10]. As summarized by Martynenko and Khramtsov [11] and Raithby and Hollands [12], many previous researchers investigated natural convection from extended surfaces, as shown in Fig. 1. These studies are motivated by the fact that the heat transfer rate from extended surfaces differs greatly from that at the base surfaces. For example, Harahap and McManus performed a comprehensive experimental investigation of natural-convection heat transfer from rectangular fins on a horizontal surface and suggested a Nusselt number correlation (Fig. 1a) [13]. Welling and Wooldridge experimentally investigated the effects of various fin geometries on heat transfer from the vertical surface of a base finned by parallel vertical plates (Fig. 1b) [10]. Joo and Kim analytically compared the thermal performances of optimized plate-fin and pin-fin heat sinks with a vertically oriented base plate under natural convection [14]. Ledezma and Bejan experimentally and numerically investigated the overall thermal conductance of heat sinks with sloped plate fins [15]. Some previous investigations focused on natural-convective heat transfer from a cylindrical heat sink, which consists of a cylindrical body with fins attached. Sparrow and Bahrami performed an experiment based on the naphthalene sublimation technique to determine the heat transfer rate from square vertical fins attached to a horizontal tube (Fig. 1c) [16]. Chen and Chou suggested the use of the finite difference method in conjunction with the least-squares scheme to predict the heat transfer coefficient of square vertical fins attached to a horizontal tube, and proposed a Nusselt number correlation [17]. Yildiz and Yüncü experimentally investigated the heat transfer from annular fin arrays mounted on a horizontal cylinder (Fig. 1d) [18]. Hahne and Zhu also conducted an experimental study of horizontal cylinders with annular fins [19]. Yu et al. experimentally and numerically investigated natural convection in a radial heat sink composed of a horizontal circular base and rectangular fins [20]. Jang et al. numerically optimized the cooling performance of a radial heat sink with pin fins [21]. Recently, our group proposed an empirical correlation for estimating the Nusselt number for natural convection from cylinders with rectangular fins (Fig. 1e) [22]. Presently, cylindrical heat sinks with vertical triangular fins are being widely used for cooling light-emitting diode (LED) lighting. However, to the best of our knowledge, natural convection from these vertical cylinders with triangular fins has not been experimentally investigated yet. Therefore, there is no general correlation by which Nusselt numbers can be obtained for natural convection from vertical cylinders with vertical triangular fins. Therefore, there is no way to obtain the thermal resistance of vertical cylinders with vertical triangular fins quantitatively.

The purpose of the present study is to propose a Nusselt number correlation for estimating the thermal performance of a natural-convective cylindrical heat sink with vertically oriented triangular fins. We have conducted extensive experiments for various fin numbers, fin heights, and base temperatures. Based on these results, we suggest a Nusselt number correlation, which is applicable when the Rayleigh number, ratio of the fin height to fin length, and fin number are in the ranges of 1000–120,000, 0.2–0.6, and 9–72, respectively. From this correlation, a contour map that depicts the thermal resistance as a function of fin number and fin thickness is obtained, which shows the fin number and fin thickness at which the thermal resistance is minimized.