Eur. Phys. J. Plus (2019) 134: 119
https://doi.org/10.1140/epjp/i2019-12455-y

Regular Article

Exact solutions for the Atangana-Baleanu time-fractional model of a Brinkman-type nanofluid in a rotating frame: Applications in solar collectors

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

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

Received: 8 August 2018
Accepted: 7 December 2018
Published online: 26 March 2019

Abstract

Nanofluids are the next generation fluids that exhibit thermal properties superior to those of conventional fluids. Nanofluids play a vital role in various thermal applications such as automotive industries, heat exchangers, solar power generation, etc. Therefore, a generalized Brinkman-type fluid model has been developed to predict the heat transport properties of a flat-plate solar collector using a nanofluid in a rotating frame under the influence of transverse magnetic field B₀ and two cases are discussed. i) B₀ being fixed to the fluid (K = 0 ; ii) B₀ being fixed to the plate (K = 0). Thermal radiation and concentration are also taken into account. Furthermore, the classical model is converted to a generalized model using the Atangana-Baleanu (AB) fractional derivative and then the exact solutions are obtained via the Laplace transform method. A parametric study of all the governing parameters is carried out and some other important results are illustrated in tabular form. A comparison of several nano-sized solid particles, i.e. SWCNT, MWCNT, CuO, Al₂O₃ and TiO₂ has been done in the current investigation and it is concluded that adding SWCNT in the working fluid (water) can augment the heat transfer rate up to 36.61%, which consequently upgrades the working ability of flat-plate solar collectors by enhancing their absorption power of solar radiation.