Abstract
Increasing efficiency, improving energy consumption, and optimizing energy in industries are more than ever considered by researchers. Some methods such as nanoparticles use and porous medium are used to increase the heat transfer rate. For this reason, in this paper, simulation and optimization of a two-dimensional tube with the presence of water-silver nanofluid and porous media have been performed to improve heat transfer. Different profiles of the rate, pressure, and temperature of the two-dimensional tube at volume fraction, porosity coefficient and Darcy numbers have been obtained and finally, the results are compared. Then, the Nusselt number and the friction coefficient in the range of Darcy numbers, porosity coefficient, different R1, and R2 were investigated. The results show that the Nusselt number and the friction coefficient increases and decreases with increasing the Darcy number, respectively and also, the Nusselt number and the friction coefficient reduces by increasing the porosity coefficient. Particle swarm algorithm method is used to optimize the results. Three methods of Shannon entropy, LINMAP and TOPSIS were examined to obtain the best solutions for the two objective functions studied in this study. The results showed that the Shannon entropy method show more optimal results. Finally, we can say that the best final value for the Nusselt number is 387.42 and for the coefficient friction is -0.02469. These values are obtained by taking the porosity, internal radius, external radius, and friction coefficient as 0.98, 0.05, 0.9, and 0.00228, respectively. (C) 2019 Elsevier B.V. All rights reserved.