Eur. Phys. J. Plus (2020) 135: 850
https://doi.org/10.1140/epjp/s13360-020-00857-z

Regular Article

Numerical analysis of unsteady flow of three-dimensional Williamson fluid-particle suspension with MHD and nonlinear thermal radiations

¹ Department of Mathematics, Quaid-i-Azam University, 44000, Islamabad, Pakistan
² Department of Mathematics, 150 N. University Street, Purdue University, 47907, West Lafayette, IN, USA
³ Department of Mathematics and Statistics, FBAS, International Islamic University, 44000, Islamabad, Pakistan
⁴ Department of Mathematics, College of Sciences, King Khalid University, 61413, Abha, Saudi Arabia

^a madihabibi@math.qau.edu.pk

Received: 12 August 2020
Accepted: 10 October 2020
Published online: 19 October 2020

Abstract

In this study, the time-dependent incompressible 3D solid–liquid Williamson non-Newtonian fluid for momentum and heat flow is evaluated. Flow is generated through a sheet in both x and y directions and effected by MHD, dust particles and nonlinear thermal radiations. Problem controlling partial differential equations are converted into ordinary differential equations by using appropriate transformations. The finalized mathematical model is evaluated by ‘bvp4c method’. Numerical results are compared with already published data. Non-dimensional parameters such as first- and second-ordered radiation parameter, the interaction parameter between fluid and particles, the unsteadiness parameter, the stretching parameter, and others are discussed that how they affect the velocity and heat distribution. Physical quantities nusselt number and skin friction are also analyzed numerically as well as graphically.