Eur. Phys. J. Plus (2021) 136: 315
https://doi.org/10.1140/epjp/s13360-021-01294-2

Regular Article

Dynamics of multiple solutions of Darcy–Forchheimer saturated flow of Cross nanofluid by a vertical thin needle point

¹ College of Science, Hunan City University, 413000, Yiyang, People’s Republic of China
² Department of Mathematics, Quaid-i-Azam University, 45320, Islamabad, Pakistan
³ Department of Mathematics, Huzhou University, 313000, Huzhou, People’s Republic of China
⁴ Hunan Provincial Key Laboratory of Mathematical Modeling and Analysis in Engineering, Changsha University of Science and Technology, 410114, Changsha, People’s Republic of China
⁵ Department of Mathematics and Statistics, Riphah International University I-14, 44000, Islamabad, Pakistan
⁶ Davangere University, Davangere, Karnataka, India

^c chuyuming@zjhu.edu.cn

Received: 13 February 2021
Accepted: 3 March 2021
Published online: 12 March 2021

Abstract

Nanofluids have exposed a significant promise in the thermal development of several industrial systems, and at the same time, the flow via needle has major applications in modern construction systems including microstructure electric gadgets and microscale cooling gadgets for thermal migration applications. According to these applications, the current investigation concentrates to deliberate on 2D steady, laminar and incompressible flow of magneto-Cross nanofluid towards the region of moving thin needle in the occurrence of Darcy–Forchheimer porous medium, Ohmic and viscous dissipation with chemical reaction and mixed convection. The new dimensionless similarity variables are introduced to convert the nonlinear expressions governing the flow and transfer of heat. The change in velocity, thermal and concentration profiles for various non-dimensional parameters is deliberated briefly and illustrated with the help of suitable plots. Further, analysis of skin friction and rate of heat transfer is done through graphs. The results obtained are validated by existing works and are found to have a good agreement. The result outcome reveals that advanced values of magnetic parameter and Weissenberg number slowdown the fluid velocity motion. Also, upshot in Brownian motion and thermophoresis parameters improves the thermal profile.