**Xing Tian 1, Jian Yang 1,2,\*, Zhigang Guo 1, Qiuwang Wang 1,\* and Bengt Sunden <sup>2</sup>**


Received: 27 February 2020; Accepted: 14 April 2020; Published: 16 April 2020

**Abstract:** In the present paper, the heat transfer of gravity-driven dense particle flow around five different shapes of tubes is numerically studied using discrete element method (DEM). The velocity vector, particle contact number, particle contact time and heat transfer coefficient of particle flow at different particle zones around the tube are carefully analyzed. The results show that the effect of tube shape on the particle flow at both upstream and downstream regions of different tubes are remarkable. A particle stagnation zone and particle cavity zone are formed at the upstream and downstream regions of all the tubes. Both the stagnation and cavity zones for the circular tube are the largest, and they are the smallest for the elliptical tube. As the particle outlet velocity (*v*out) changes from 0.5 mm/s to 8 mm/s at *d*p = 1.72 mm/s, when compared with the circular tube, the heat transfer coefficient of particle flow for the elliptical tube and flat elliptical tube can increase by 20.3% and 15.0% on average, respectively. The proper design of the downstream shape of the tube can improve the overall heat transfer performance more efficiently. The heat transfer coefficient will increase as particle diameter decreases.

**Keywords:** gravity-driven particle flow; discrete element method; heat transfer enhancement
