Entropy generation in turbulent natural convection due to internal heat generation Sheng Chen a, b, * , Manfred Krafczyk b a State Key Lab of Coal Combustion, Huazhong University of Science and Technology, Wuhan 430074, China b Institute for Computational Modeling in Civil Engineering, Technical University, Braunschweig 38106, Germany article info Article history: Received 31 August 2008 Received in revised form 12 February 2009 Accepted 13 February 2009 Available online 18 March 2009 Keywords: Entropy generation Turbulent natural convection Internal heat generation Lattice Boltzmann method abstract In this study numerical predictions of entropy generation in turbulent natural convection due to internal heat generation in a square cavity are reported for the first time. Results of entropy generation analysis are obtained by solving the entropy generation equation. The values of velocity and temperature, which are the inputs of the entropy generation equation, are obtained by an improved thermal lattice-BGK model proposed in this paper. The analyzed range is wide, varying from the steady laminar symmetric state to the fully turbulent state. Distributions of entropy generation numbers, for various Rayleigh numbers, Prandtl numbers, and Eckert numbers, are given. Ó 2009 Elsevier Masson SAS. All rights reserved. 1. Introduction Natural convection occurring in nature and many industrial devices are driven by internal heating [1,2], ranging from the mantle convection in the Earth [3,4] to the cooling of a molten nuclear reactor core [5,6]. Natural convection due to internal heat generation has been lately receiving increasing attention because of its relevance to nuclear safety issues [5–8]. As discussed in Refs. [6,8], an inadequate or prolonged absence of nuclear reactor core cooling may cause core melting to occur in a light water reactor. The core debris may heat up on account of the volumetric decay heat generation to form a molten pool in natural convection. Conse- quently, to predict the behavior of the convectional flow and to optimally design the thermal systems are necessary in the nuclear engineering [6,9]. The pioneers on this subject are Kulacki and his collaborators, who conducted several experiments using Joule heating as a volu- metric heat source [10,11]. In these experiments, which were primarily applicable to the nuclear industry, heat transfer through a horizontal fluid layer was assessed for different boundary cooling arrangements. Asfia et al. conducted experiments of natural convection in a spherical cavity [12]. The working fluid was Freon- 113, which was heated with microwaves. The range of the Rayleigh number (Ra) tested was between 2  10 10 and 1.1 10 14 at the Prandtl (Pr) number 8. Recently, Lee et al. studied high modified Rayleigh number natural convection with the aid of the simulant internal gravitated material apparatus rectangular pool [6]. The modified Ra based on the power input was varied from 10 9 to 10 14 . The Pr of working fluid ranged from 4 to 8 for water, and 0.7 for air. In their work, particular attention was paid to the influence of Pr on natural convection heat transfer in the pool. The relation between the Nusselt number (Nu) and the modified Ra was determined for different boundary conditions in the rectangular pool. However, it is still a challenge for experiments to capture the turbulent flow motion at high Ra. In fact, the highest Ra attainable in an apparatus of a given size is usually quite limited for a fluid such as water. Because of the unknown properties of the core melt at high temperatures, the researchers were unable to reproduce adequate accident conditions. Moreover, it is not a simple task to measure Pr dependence in convectional turbulence by experi- ments. Therefore, numerical simulations are required to predict the turbulent flows especially at very high Ra [7,8]. In Ref. [9], the effect of the Pr on the Nu distributions for different geometries was demonstrated. In their work, Ra spanned from 10 6 to 10 12 and Pr from 0.6 to 7. The authors found that the influence of Pr is small in convection-dominated regions and much more significant in * Corresponding author at: Institute for Computational Modeling in Civil Engi- neering, Technical University, Braunschweig 38106, Germany. E-mail addresses: chen@irmb.tu-bs.de (S. Chen), kraft@irmb.tu-bs.de (M. Krafczyk). Contents lists available at ScienceDirect International Journal of Thermal Sciences journal homepage: www.elsevier.com/locate/ijts 1290-0729/$ – see front matter Ó 2009 Elsevier Masson SAS. All rights reserved. doi:10.1016/j.ijthermalsci.2009.02.012 International Journal of Thermal Sciences 48 (2009) 1978–1987