Contents lists available at ScienceDirect Solar Energy journal homepage: www.elsevier.com/locate/solener Numerical investigation of two-dimensional heat transfer of an absorbing plate of a ﬂat-plate solar collector using dual-reciprocity method based on boundary element Seyyed Mohsen Mortazavinejad ⁎ , Milad Mozafarifard Department of Mechanical Engineering, Shahid Chamran University of Ahvaz, Ahvaz, Iran ARTICLE INFO Keywords: Dual-reciprocity method Boundary element method Finite diﬀerence method Flat-plate solar collector ABSTRACT In this paper, heat transfer in an absorbing plate of a ﬂat plate solar collector has been investigated upon using dual-reciprocity method. In order to validate the boundary element method, the results of this method have been compared with the numerical results obtained by ﬁnite diﬀerence method. Due to the presence of non-homo- geneous terms in the governing equation, it has been numerically solved using the dual-reciprocity boundary element method. The temperature distribution in the absorbing plate is investigated upon considering diﬀerent values of mass ﬂow rate in the tube and the results obtained by the dual-reciprocity boundary element and ﬁnite diﬀerence methods are compared. Additionally, the ﬂuid temperature along the tube has been studied, using two numerical methods. After being compared, the results of two methods well coincide, which proves the accuracy of numerical methods. Moreover, eﬀect of changes in various parameters such as conductivity of the absorbing plate, mass ﬂow rate, distance between two tubes, the ﬂuid inlet temperature, as well as the change in the diameter of the tubes on the eﬃciency of the absorbing plate has been thoroughly investigated. Another notable point is that the boundary element method can lead to less computational cost, compared to other numerical methods such as ﬁnite diﬀerence method. The reason for this is connected to the capability of the boundary element method, without need for points within the computational domain. 1. Introduction In recent years, given the importance renewable resources and the fact of the fossil fuels coming to an end, using solar collectors to convert solar energy into heat energy has drawn much attention in the world. Consequently, studies regarding the heat transfer in absorbing plates, eﬃciency of solar collectors, changes in ﬂuid temperature in the tube, various proﬁles for absorbing plates and the boundary conditions governing solar collectors have always been of great importance. Rao et al. (1977) investigated the two-dimensional heat transfer in the absorbing plate of a ﬂat plate solar collector. They obtained the temperature distribution of the absorbing plate for diﬀerent values of mass ﬂow rate of the working ﬂuid in the tube, and showed that the temperature distribution in the absorbing plate is one-dimensional for high values of mass ﬂow rate. Also, eﬀect mass ﬂow rate, tube diameter and thermal conductivity of the absorbing plate on ﬂuid outlet tem- perature was thoroughly discussed. Finally, they studied the eﬀects of mass ﬂow rate and tube diameter on the eﬃciency of the solar collector. Having implemented the dynamic test method, Nayak and Amer (2000) examined the operating parameters of the solar collector, and indicated that due to the simplicity of the dynamic test method, it can be used to control the quality of production of solar collectors. Kundu (2002) examined the eﬀect of diﬀerent proﬁles such as rec- tangular, trapezoidal, and piecewise rectangular on an absorbing plate on the eﬃciency of the solar collector. It was shown that the piecewise rectangular proﬁle is more capable of producing higher eﬃciency and easier construction than the other ones. Moreover, the method pre- sented by Hollands and Stedman modiﬁed the piecewise rectangular proﬁle and indicated an optimal proﬁle for the absorbing plate. Dhariwal and Mirdha (2005) presented an analytical solution to study the thermal response of absorbing plate, considering various conditions such as the diﬀerent pumping conditions. They showed that upon ap- plying this method, the eﬃciency of the collector can be estimated in conditions close to reality. Kalogirou (2006) studied the operating parameters of solar collector using artiﬁcial intelligence network. In this study, he showed that the proposed method is more eﬃcient that the other methods based on higher speed, ease of use and network capability. Other researchers https://doi.org/10.1016/j.solener.2019.08.075 Received 7 April 2019; Received in revised form 14 July 2019; Accepted 29 August 2019 ⁎ Corresponding author. E-mail address: m.mortazavinejad1991@gmail.com (S.M. Mortazavinejad). Solar Energy 191 (2019) 332–340 Available online 10 September 2019 0038-092X/ © 2019 International Solar Energy Society. Published by Elsevier Ltd. All rights reserved. T