Contents lists available at ScienceDirect International Communications in Heat and Mass Transfer journal homepage: www.elsevier.com/locate/ichmt Natural convection and entropy generation of a nanofluid in two connected inclined triangular enclosures under magnetic field effects Wi Liu a , Amin Shahsavar b , Azeez A. Barzinjy c,d , Abdullah A.A.A. Al-Rashed e , Masoud Afrand f,g, ⁎ a School of Mechanical and Electrical Engineering & Jiangsu Collaborative Innovation Center of Intelligent Mining Equipment, China University of Mining and Technology, Xuzhou 210008, China b Department of Mechanical Engineering, Kermanshah University of Technology, Kermanshah, Iran c Cihan Scientific Research Centre, Cihan University, Erbil, Kurdistan Region, Iraq d Physics Department, College of Education, Salahaddin University, Erbil, Kurdistan Region, Iraq e Department of Automotive and Marine Engineering Technology, College of Technological Studies, The Public Authority for Applied Education and Training, Kuwait f Laboratory of Magnetism and Magnetic Materials, Advanced Institute of Materials Science, Ton Duc Thang University, Ho Chi Minh City, Vietnam g Faculty of Applied Sciences, Ton Duc Thang University, Ho Chi Minh City, Vietnam ARTICLE INFO Keywords: Entropy generation Natural convection Nanofluid Triangular enclosure Magnetic field ABSTRACT The objective of this paper is to study the entropy generation and natural convection of water- Al2O3 nanofluid in an inclined cavity which consists of two connected inclined triangular enclosures under a horizontal magnetic field. The horizontal diameter of the cavity is small in thickness and has the temperature Tc. Half of the bottom wall and also the right wall are at the temperature Th. The rest of the walls are adiabatic. The governing equations of the nanofluid flow are algebrized and solved using the FVFEM method. The effective parameters are 103 < Ra < 105, 0 < Ha < 40, 0° < γ < 90°, and 0.00 < φ < 0.06. The results indicate that the rate of heat transfer increases by 12% and the entropy generation enhances by 13% through enhancing the Raleigh number. As the Hartmann number increases, the rate of heat transfer and the entropy generation decrease by 6.5% and 8%, respectively. The Bejan number also decreases for a higher Raleigh number and a lower Hartmann number. For a higher angle of the cavity, the average Nusselt number calculated on the right wall always reduces. Entropy generation decreases and Bejan number increases for a higher inclined angle. 1. Introduction Natural convection in closed enclosures has long been considered by researchers. The main reason is its different applications in applied and engineering industries. Studies on heat transfer rate in the enclosures have been seen using various fluids, such as water, air, or even non- Newtonian fluids [1–6]. Use of nanofluids instead of simple fluids in the enclosures leads to a higher heat transfer rate. The researchers in- vestigated the heat transfer of nanofluids in closed enclosures using different nanofluids instead of simple fluids such as air and water [7–13]. Nanofluids are a combination of nanoparticles and a base-fluid and, according to various experiments, have a higher thermal-con- ductivity coefficient than simple fluids [14]. Hence, many researchers have used nanofluids in various applications, and nanofluids have been used extensively in various industries [15,16]. Sheremet et al. [17] numerically assessed the natural convection heat transfer of alumina- water nanofluid through an inclined solar collector. They used an in- clined square cavity having time-sinusoidal temperature upper wall to model the solar collector and examined the impacts of different influ- ential parameters on the performance metrics of cavity. Pordanjani et al. [18] studied on alumina-water nanofluid in an enclosure in dif- ferent inclination angles using the control volume method. Magnetic field has been used in different industries including elec- tronics, geothermal energy, cooling of nuclear and metallurgical re- actors and solar collectors [19–23]. Thus, there have been lots of stu- dies on the effect of the magnetic field on nanofluids heat transfer in closed enclosures [24–29]. Pordanjani et al. [30] assessed the natural convection of alumina-water in a cavity. They evaluated the effect of the magnetic field on the heat transfer rate which results in a higher Hartmann number. Alnaqi et al. [31] analyzed the magnetic field effect on alumina-water in an inclined square cavity. Their results showed that the average Nusselt number enhances for a higher Rayleigh number and a lower Hartmann number. Considering the increasing consumption of human energy, it is re- quired to modify the energy efficiency. Hence, the researchers studied the efficiency of various devices. There are several methods for the https://doi.org/10.1016/j.icheatmasstransfer.2019.104309 ⁎ Correspondence to: M. Afrand, Ton Duc Thang University, Ho Chi Minh City, Vietnam E-mail addresses: azeez.azeez@su.edu.krd (A.A. Barzinjy), masoud.afrand@tdtu.edu.vn (M. Afrand). International Communications in Heat and Mass Transfer 108 (2019) 104309 0735-1933/ © 2019 Elsevier Ltd. All rights reserved. T