Soret and Dufour influences on forced convection of Cross radiative nanofluid flowing via a thin movable needle

M Israr Ur Rehman; Haibo Chen; Aamir Hamid; Sajid Qayyum; Wasim Jamshed; Zehba Raizah; Mohamed R Eid; El Sayed M Tag El Din

doi:10.1038/s41598-022-23563-5

Soret and Dufour influences on forced convection of Cross radiative nanofluid flowing via a thin movable needle

Sci Rep. 2022 Nov 4;12(1):18666. doi: 10.1038/s41598-022-23563-5.

Authors

M Israr Ur Rehman¹, Haibo Chen¹, Aamir Hamid², Sajid Qayyum³, Wasim Jamshed⁴, Zehba Raizah⁵, Mohamed R Eid^{6

7}, El Sayed M Tag El Din⁸

Affiliations

¹ School of Mathematics and Statistics, Central South University, Changsha, 410083, China.
² Department of Mathematics, Women University of Azad Jammu and Kashmir, Bagh, 12500, Azad Kashmir, Pakistan.
³ Department of Mathematics, University of Mianwali, Mianwali, Pakistan.
⁴ Department of Mathematics, Capital University of Science and Technology (CUST), Islamabad, 44000, Pakistan. wasiktk@hotmail.com.
⁵ Department of Mathematics, College of Science, King Khalid University, Abha, Saudi Arabia.
⁶ Department of Mathematics, Faculty of Science, New Valley University, Al-Kharga, 72511, Al-Wadi Al-Gadid, Egypt.
⁷ Department of Mathematics, Faculty of Science, Northern Border University, Arar, 1321, Saudi Arabia.
⁸ Electrical Engineering, Faculty of Engineering and Technology, Future University in Egypt, New Cairo, 11835, Egypt.

Abstract

The main feature of the current investigation is to analyze the magnetohydrodynamic mixed convection flow of Cross fluid. Flow is due to a movable thin needle with Soret and Dufour effect. Heat generation/absorption and nonlinear heat radiation are used in the energy equation. Characteristics of the chemical reaction and thermal activation are given special attention. Appropriate variables are introduced for the transformation of partial differential equations to ordinary differential equations. With the assistance of Runge-Kutta Fehlberg's fourth- fifth-order method with the shooting technique, we determined the prominent result numerically. The prominent examined parameters range is velocity and temperature ratios, heat generation, Dufour, Hartmann, Schmidt numbers ([Formula: see text]), needle thickness ([Formula: see text]), radiative parameter ([Formula: see text]), and Weissenberg number ([Formula: see text]), respectively. Graphs for velocity, thermal, concentration, Skin friction coefficient, and heat and mass transport rates are displayed and analyzed for physical parameters. A similar observation of mixed convection and needle thickness parameter is seen on the velocity field. Temperature and heat transfer rate are reverse behavior in the frame of the Dufour effect. Moreover, an enhancement in chemical reaction shows decay to the concentration field.