Eur. Phys. J. Plus (2017) 132: 540
https://doi.org/10.1140/epjp/i2017-11809-9

Regular Article

On the applications of nanofluids to enhance the performance of solar collectors: A comparative analysis of Atangana-Baleanu and Caputo-Fabrizio fractional models

¹ Computational Analysis Research Group, Ton Duc Thang University, Ho Chi Minh City, Vietnam
² Faculty of Mathematics and Statistics, Ton Duc Thang University, Ho Chi Minh City, Vietnam
³ Department of Mathematics, City University of Science and Information Technology, Peshawar, Khyber Pakhtunkhwa, Pakistan
⁴ Basic Engineering Sciences Department, College of Engineering Majmaah University, 11952, Majmaah, Saudi Arabia

^* e-mail: farhad.ali@tdt.edu.vn

Received: 29 October 2017
Accepted: 28 November 2017
Published online: 27 December 2017

Abstract

In the modern era, solar energy has gained the consideration of researchers to a great deal. Apparently, the reasons are twofold: firstly, the researchers are concerned to design new devices like solar collectors, solar water heaters, etc. Secondly, the use of new approaches to improve the performance of solar energy equipment. The aim of this paper is to model the problem of the enhancement of heat transfer rate of solar energy devices, using nanoparticles and to find the exact solutions of the considered problem. The classical model is transformed to a generalized model using two different types of time-fractional derivatives, namely the Caputo-Fabrizio and Atangana-Baleanu derivatives and their comparative analysis has been presented. The solutions for the flow profile and heat transfer are presented using the Laplace transform method. The variation in the heat transfer rate has been observed for different nanoparticles and their different volume fractions. Theoretical results show that by adding aluminum oxide nanoparticles, the efficiency of solar collectors may be enhanced by 5.2%. Furthermore, the effect of volume friction of nanoparticles on velocity distribution has been discussed in graphical illustrations. The solutions are reduced to the corresponding classical model of nanofluid.