Contents lists available at ScienceDirect Applied Thermal Engineering journal homepage: www.elsevier.com/locate/apthermeng Numerical simulation of non-Fourier heat conduction in fins by lattice Boltzmann method Yi Liu a,b , Ling Li a,b, ⁎ , Yuwen Zhang c a School of Energy and Power Engineering, University of Shanghai for Science and Technology, Shanghai 200093, China b Shanghai Key Laboratory of Multiphase Flow and Heat Transfer in Power Engineering, Shanghai, China c Department of Mechanical and Aerospace Engineering, University of Missouri, Columbia, MO 65211, USA HIGHLIGHTS • Lattice Boltzmann method calculate the non-Fourier heat conduction in fin. • Factors affecting the non-Fourier heat transfer of fins are discussed. • Under the non-Fourier condition, the efficiency of rectangular fin is higher. • Extending periodic heat transfer’s lag time can enhance fin’sefficiency. ARTICLE INFO Keywords: Lattice Boltzmann method Non-Fourier heat conduction Heat transfer and efficiency of fin ABSTRACT The addition of fin to the surface of microelectronic elements is a very effective way to enhance their heat transfer rate. Since the heat generation of the microelectronic elements is very fast, the Fourier law is no longer valid and the non-Fourier effect must be considered when designing a fin. Cattaneo – Vernotte model (CV model) is the most common model that is used to describe the non-Fourier effect in heat conduction. The mathematical expression of the CV model is essentially a wave equation. The lattice Boltzmann method (LBM) can be used to solve the wave equation in the CV heat conduction problem. In this paper, LBM is used to solve the non-Fourier heat conduction in a fin under periodic boundary conditions. Effects of relaxation time, shape and the frequency of the base temperature oscillations on heat transfer efficiency are analyzed. 1. Introduction In modern personal computers, microelectronic elements such as integrated circuit (IC) chips are important components. A large amount of heat is generated when the microelectronic elements are used [1]. In order to ensure the safety of the computer, how to dissipate the gen- erated heat into the environment efficiently is an urgent problem that needs to be addressed. Generally, the heat transfer rate can be enhanced by increasing the temperature difference, surface heat transfer coeffi- cient, and heat exchange area. Increasing the temperature difference is limited by the technology, and increasing the heat transfer coefficient is more difficult to control. Therefore, increasing the heat exchange area is the most common method for increasing the heat exchange rate. The use of fin is an effective method of increasing the heat exchange area [2]. Some of the classic heat transfer problems in a fin has been studied by many scholars based on the conditions established by Fourier's law [3]. It has been shown that for microelectronic elements, the heat flux density is close to the heat flux density produced by nuclear fusion [4] and Fourier's law no longer holds under this condition. When analyzing the heat transfer problem of the fin in microelectronic elements, the non-Fourier effect should be considered. The most widely used non- Fourier heat transfer equation is the hyperbolic heat conduction model proposed by Cattaneo [5,6] and Vernotte [7], which is known as CV model. In the recent years, the non-Fourier heat transfer in a fin has gained attention from many scholars, and various solving methods have been proposed. Lin, who first explored this problem, found that the non- Fourier effect in the fins cannot be ignored under periodic conditions [8]. Huang and Wu studied the inverse problem of non-Fourier heat conduction in fins under periodic conditions [9]. Kundu et al. solved the non-Fourier heat conduction problem when the heat source contained in the fin by the separation of variable method [1]. Singh et al. analyzed the difference between Fourier and non-Fourier heat conductions in the https://doi.org/10.1016/j.applthermaleng.2019.114670 Received 23 April 2019; Received in revised form 2 November 2019; Accepted 10 November 2019 ⁎ Corresponding author. E-mail address: liling@usst.edu.cn (L. Li). Applied Thermal Engineering 166 (2020) 114670 Available online 13 November 2019 1359-4311/ © 2019 Elsevier Ltd. All rights reserved. T