THERMAL SCIENCE

International Scientific Journal

Muhammad Imran Asjad

,

Muhammad Zahid

,

Yu-Ming Chu

,

Dumitru Baleanu

PRABHAKAR FRACTIONAL DERIVATIVE AND ITS APPLICATIONS IN THE TRANSPORT PHENOMENA CONTAINING NANOPARTICLES

ABSTRACT
In this paper, a new approach of analytical solutions is carried out on the thermal transport phenomena of Brinkman fluid based on Prabhakar's fractional derivative with generalized Fourier's law. The governing equations are obtained through constitutive relations and analytical solutions obtained via Laplace transform technique. Solutions for temperature and velocity field were analyzed through graphical description by MathCad software. The fluid properties revealed various aspects for different flow parameters as well as fractional parameter values and found important results. As a result, it is found that fluid properties can be enhanced by increasing the values of fractional parameters and can be useful in some experimental data where suitable.
KEYWORDS
Prabhakar's fractional derivative, Mittag-Leffler kernel, heat transfer, Brinkman fluid, nanoparticles
PAPER SUBMITTED: 2021-07-01
PAPER REVISED: 2021-07-18
PAPER ACCEPTED: 2021-08-01
PUBLISHED ONLINE: 2021-12-18
DOI REFERENCE: https://doi.org/10.2298/TSCI21S2411A
CITATION EXPORT: view in browser or download as text file
THERMAL SCIENCE YEAR 2021, VOLUME 25, ISSUE Special issue 2, PAGES [411 - 416]
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Prabhakar fractional derivative and its applications in the transport phenomena containing nanoparticles

© 2024 Society of Thermal Engineers of Serbia. Published by the Vinča Institute of Nuclear Sciences, National Institute of the Republic of Serbia, Belgrade, Serbia. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution-NonCommercial-NoDerivs 4.0 International licence