Modeling of three dimensional Prandtl hybrid nano-material over a heated rotating cone involving hall and ion slip currents via finite element procedure

Muhammad Sohail; Umar Nazir; Essam R El-Zahar; Choonkil Park; Kanit Mukdasai; Amjad Iqbal

doi:10.1038/s41598-022-16555-y

Modeling of three dimensional Prandtl hybrid nano-material over a heated rotating cone involving hall and ion slip currents via finite element procedure

Sci Rep. 2022 Jul 16;12(1):12206. doi: 10.1038/s41598-022-16555-y.

Authors

Muhammad Sohail¹, Umar Nazir², Essam R El-Zahar^{3

4}, Choonkil Park⁵, Kanit Mukdasai⁶, Amjad Iqbal⁷

Affiliations

¹ Department of Mathematics, Khwaja Fareed University of Engineering and Information Technology, Rahim Yar Khan, 64200, Pakistan.
² Department of Applied Mathematics and Statistics, Institute of Space Technology, P.O. Box 2750, Islamabad, 44000, Pakistan.
³ Department of Mathematics, College of Science and Humanities in Al-Kharj, Prince Sattam Bin Abdulaziz University, P.O. Box 83, Al-Kharj, 11942, Saudi Arabia.
⁴ Department of Basic Engineering Science, Faculty of Engineering, Menoufia University, Shebin El-Kom, 32511, Egypt.
⁵ Research Institute for Natural Sciences, Hanyang University, Seoul, 04763, Korea.
⁶ Department of Mathematics, Faculty of Science, Khon Kaen University, Khon Kaen, 40002, Thailand. kanit@kku.ac.th.
⁷ Department of Materials Technologies, Faculty of Materials Engineering, Silesian University of Technology, 44-100, Gliwice, Poland.

Abstract

Flow in a rotating cone for magnetized Prandtl fluid model is inspected in this investigation. The momentum equation of Prandtl model is derived under the consideration of Hall and ion slip effects and heat transport phenomenon is considered with Joule heating and viscous dissipation effects. The model of Hamilton Crosser and Yamada Ota are considered for the empirical relations of nanofluid mixture. The flow presenting expression of Prandtl fluid model with thermal transport is modeled under boundary layer approximation in the form of partial differential equations (PDEs). The derived PDEs have been converted into set of coupled nonlinear ordinary differential equations (ODEs) by engaging an appropriate scaling group transformation and these converted nonlinear set of ODEs have been tackled numerically via finite element scheme (FES). Impact of different emerging parameters has been displayed graphically and the physics behind the observed phenomena is explained in detail. The convergence of FES is established by carrying the grid independent survey. From the performed investigation, it is recorded that the parameters appear due to Hall and Ion slip currents enhance the fluid velocity but the inverse behavior is recorded for temperature profile.