Eur. Phys. J. Plus (2021) 136: 1142
https://doi.org/10.1140/epjp/s13360-021-02101-8

Regular Article

Effect of Newtonian heating on two-phase fluctuating flow of dusty fluid: Poincaré–Lighthill perturbation technique

¹ Department of Mathematics, College of Science Al-Zulfi, Majmaah University, 11952, Al-Majmaah, Saudi Arabia
² Department of Mathematics, City University of Science and Information Technology, 25000, Peshawar, Pakistan
³ Institute of Computer Sciences and Information Technology, The University of Agriculture, Peshawar, Pakistan

^a i.said@mu.edu.sa

Received: 22 September 2020
Accepted: 19 October 2021
Published online: 15 November 2021

Abstract

This article deals with the two phase fluctuating flow of dusty fluid and heat transfer in the presence of electrically conducting dust particles induces a strong magnetic field. The flow is considered between two parallel non-conducting plates, one at rest and the other in the state of fluctuation. Heat transfers due to free convection and Newtonian heating condition (NHC). The flow is generated due to plate fluctuation. In the sequence to scrutinize methodical solutions, we have used the Poincaré–Lighthill perturbation technique (PLPT). Results are obtained and plotted in graphs. The effect of pertinent parameters on the base fluid velocity such as Grashof number, magnetic parameter, radiation parameter and dusty fluid parameter has been studied. It is noticed that the velocity of the base fluid increases with the decrease in magnetic field and the applied shear stress, i.e., decreases up to some extent but gradually increases for the large magnetic parameter.