Heat and mass transfer of generalized fourier and Fick's law for second-grade fluid flow at slendering vertical Riga sheet

Wasfi Shatanawi; Nadeem Abbas; Taqi A M Shatnawi; Fady Hasan

doi:10.1016/j.heliyon.2023.e14250

Heat and mass transfer of generalized fourier and Fick's law for second-grade fluid flow at slendering vertical Riga sheet

Heliyon. 2023 Mar 11;9(3):e14250. doi: 10.1016/j.heliyon.2023.e14250. eCollection 2023 Mar.

Authors

Wasfi Shatanawi^{1

2

3}, Nadeem Abbas¹, Taqi A M Shatnawi³, Fady Hasan¹

Affiliations

¹ Department of Mathematics and Sciences, College of Humanities and Sciences, Prince Sultan University, Riyadh, 11586, Saudi Arabia.
² Department of Medical Research, China Medical University, Taichung, 40402, Taiwan.
³ Department of Mathematics, Faculty of Science, The Hashemite University, P.O Box 330127, Zarqa, 13133, Jordan.

Abstract

In this analysis, the generalized Fourier and Fick's law for Second-grade fluid flow at a slendering vertical Riga sheet is examined along with thermophoresis and Brownian motion effects. Boundary layer approximations in terms of PDE's (Partial Differential Equations) are used to build the mathematical model. An appropriate transformation has been developed by using the Lie symmetry method. PDE's (Partial Differential Equations) are transformed into ODE's (Ordinary Differential Equations) by implementing the suitable transformation. A numerical method called bvp4c is used to explain the dimensionless system (ODE's). Graphs and tables are used to interpret the impact of the significant physical parameters. The curves of temperature function declined due to enchanting the values of the thermophoresis Parameter. The temperature is produced at a low level due to enchanting the values of thermophoresis because this force transports burn at a low 10 μm diameter so the temperature becomes lessor. Increments of thermophoresis parameter which enhanced the values of concentration Function. As the concentration boundary layer increased which declined the mass transfer due increment in thermophoresis. The curves of temperature function are increasing due to enhancing the values of the Brownian parameter because addition in the Brownian motion, improved the movement of particles ultimately increasing the kinematic energy of fluid which improved the heat transfer phenomena. Increments of Brownian parameter which declined the values of concentration function. Physically, the kinematic energy improved which declined the mass transfer rate near the surface.

Keywords: Buongiorno model; Fourier and Fick's law; Second-grade fluid; Slendering vertical riga sheet.