https://doi.org/10.1140/epjp/s13360-023-04632-8
Regular Article
Semi-analytical solution of Graetz–Brinkman problem combined with non-Newtonian Ellis fluid flow in a passive channel
1
Department of Mathematics and Sciences, College of Humanities and Sciences, Prince Sultan University, 11586, Riyadh, Saudi Arabia
2
NUTECH, School of Applied Sciences and Humanities, National University of Technology, 44000, Islamabad, Pakistan
3
Department of Mathematics and Statistics, International Islamic University, 44000, Islamabad, Pakistan
4
Department of Medical Research, China Medical University Hospital, China Medical University, 40402, Taichung, Taiwan
5
Department of Mathematics, Faculty of Science, The Hashemite University, P.O. Box 330127, 13133, Zarqa, Jordan
6
Department of Mathematics and Sciences, Dhofar University, 211, Salalah, Oman
a
zasghar@psu.edu.sa
b
waris.saeed88@gmail.com
Received:
27
March
2023
Accepted:
26
October
2023
Published online:
4
November
2023
Heat transfer analysis of non-Newtonian fluids has numerous applications in the industrial and chemical engineering fields. Inspired by the prevalence of non-Newtonian liquids in chemical industries, this article aims to elaborate on the Graetz–Brinkman problem for an Ellis fluid inside the horizontal channel. The developed heat equation is first solved employing an analytical approach, i.e., the separation of variables, and then, the numerical solution of the eigenvalue problem is obtained by employing the MATLAB function bvp4c. The simulation is carried out for the situation of the isothermal walls. The temperature distribution under the impact of Brinkman number and model parameters is analyzed through various graphs. A comparison between the Ellis fluid and Newtonian fluid is also expounded. The results reveal that while using Ellis fluid, a higher heat transfer rate is achieved as compared to Newtonian fluid. The results may improve our comprehension of how non-Newtonian fluids transmit heat in a variety of situations. Furthermore, it is thought that this approach has made a significant contribution to the chemical sector in terms of developing and enhancing various types of thermal equipment.
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© The Author(s), under exclusive licence to Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2023. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
