Eur. Phys. J. Plus (2021) 136: 1026
https://doi.org/10.1140/epjp/s13360-021-02025-3

Regular Article

Optimized analysis and enhanced thermal efficiency of copper–aluminum oxide nanoparticles under the influence of Joule heating and viscous dissipation

¹ Department of Mathematics, University of Azad Jammu & Kashmir, 13100, Muzaffarabad, Pakistan
² Department of Mathematics, COMSATS University Islamabad, 57000, Sahiwal, Pakistan
³ Department of Mathematics and Statistics, Riphah International University, I-14, 44000, Islamabad, Pakistan
⁴ Mathematical Modelling and Applied Computation Research Group (MMAC), Department of Mathematics, King Abdulaziz University, Jeddah, Saudi Arabia

^d mikhan@math.qau.edu.pk

Received: 10 July 2021
Accepted: 3 October 2021
Published online: 12 October 2021

Abstract

With extraordinary thermal activities, the nanofluids play the important role in industrial and engineering sector. The phenomenon of optimized assessment is also quite important to reduce the energy loss and subsequently enhance the thermal pattern of heat transfer which is the pioneer phenomenon in almost all industries. This continuation presents the phenomenon of entropy generation for the flow of water-based hybrid nanofluid in the presence of copper $\left(\mathit{Cu}\right)$ and alumina $\left(A{l}_2{O}_3\right)$ nanoparticles through a porous channel. The effects of magnetic field, heat source, Joule heating, viscous dissipation are also taken into account. The radiative mode of heat transfer is also incorporated to improve the thermal rate of hybrid nanofluid. The lower wall of channel stretched uniformly. The fundamental conservations laws of mass, momentum and energy are used to formulate the problem in Cartesian coordinates. The equations obtained from conservation laws are simplified using the similarity transformations axial velocity, and temperature profile is numerically approximated via implicit finite difference scheme, namely Keller Box method. The effect of applied electric field and thermal radiation is shown on different flow and temperature characteristics through various graphs. The heat transfer coefficient is presented and compared for hybrid nanofluid and nanofluid.