Journal of Mechanical Science and Technology 29 (7) (2015) 2995~3003 www.springerlink.com/content/1738-494x(Print)/1976-3824(Online) DOI 10.1007/s12206-015-0630-z Effects of heater location and heater size on the natural convection heat transfer in a square cavity using finite element method † Ich-Long Ngo and Chan Byon * School of Mechanical Engineering, Yeungnam University, Gyeongsan, 712-749, Korea (Manuscript Received September 19, 2014; Revised February 17, 2015; Accepted March 2, 2015) ---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- Abstract Finite element method was used to investigate the effects of heater location and heater size on the natural convection heat transfer in a 2D square cavity heated partially or fully from below and cooled from above. Rayleigh number (5Í10 2 ≤ Ra ≤ 5Í10 5 ), heater size (0.1 ≤ D/L ≤ 1.0), and heater location (0.1 ≤ x h /L ≤ 0.5) were considered. Numerical results indicated that the average Nusselt number (Nu m ) increases as the heater size decreases. In addition, when x h /L is less than 0.4, Nu m increases as x h /L increases, and Nu m decreases again for a larger value of x h /L. However, this trend changes when Ra is less than 10 4 , suggesting that Nu m attains its maximum value at the region close to the bottom surface center. This study aims to gain insight into the behaviors of natural convection in order to potentially improve internal natural convection heat transfer. Keywords: Finite element method; Heat transfer; Natural convection; Square cavity ---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- 1. Introduction Heat transfer through natural convection flow has received considerable interest because of its broad applications in many engineering systems, such as cooling devices for electronic instruments, energy storage systems, compartment fires, double- glazed windows, solar collectors, and gas-filled cavities around nuclear reactor cores [1-5]. For several years, researchers have investigated natural convection in a cavities, with various con- figurations for the heated position on the surrounding bounda- ries. Watson [6] was one of the pioneers in this topic. An ex- perimental and analytical investigation of natural convection heat transfer in a rectangular cavity heated and cooled from the side walls was later developed by Seki et al. [7], who studied the effects of vessel geometry and the temperature difference be- tween cold and hot walls on the average Nusselt number. Rudraiah et al. [8] also considered this cavity configuration but under the presence of a magnetic field. They showed that the magnetic field decreases the rate of convective heat transfer. By accounting for the effects of surface radiation, correla- tions of the Nusselt number with the Grashof number were proposed by Ramesh and Venkateshan [9] using a differential interferometer in experiments. Such a cavity configuration has been recently used for studies on heat transfer enhancement by adding nanoscale particles to the base fluid [10-14]. Natural convection in a corner region formed by a vertical hot wall and a cold horizontal wall was studied by Kimura and Bejan [15] using scale analysis and numerical simulations. Other configurations of a cavity heated from below and cooled from one side were numerically investigated in other studies [16- 18]. November and Nansteel [19] investigated the natural convection in a cavity heated partially from a vertical or hori- zontal wall in regard to the effects of the unheated length ratio on the average Nusselt number. Oztop and Abu-Nada [20] numerically studied the natural convection in rectangular en- closures partially heated from the side wall using the finite volume method. Their work indicated that heater size and the location of the heating section affect the flow and temperature field. However, few researchers have addressed the signifi- cance of these factors when the heater is placed partially or fully at the bottom or top surface. Finite element method (FEM) was used to determine the ef- fects of heater location and heater size on the natural convec- tion heat transfer in a 2D square cavity heated partially or fully from below and cooled from above. COMSOL was used for the FEM study. The Rayleigh number (5Í10 2 ≤ Ra ≤ 5Í10 5 ), heater size (0.1 ≤ D/L ≤ 1.0), and location of the heating sec- tion (0.1 ≤ x h /L ≤ 0.5) were considered. 2. Methodology 2.1 Numerical model Fig. 1 shows the schematic diagram of the model and the * Corresponding author. Tel.: +82 53 810 2452, Fax.: +82 53 810 4627 E-mail address: cbyon@ynu.ac.kr † Recommended by Associate Editor Ji Hwan Jeong © KSME & Springer 2015