Closed-form solution of oscillating Maxwell nano-fluid with heat and mass transfer

Aamir Farooq; Sadique Rehman; Abdulaziz N Alharbi; Muhammad Kamran; Thongchai Botmart; Ilyas Khan

doi:10.1038/s41598-022-16503-w

Closed-form solution of oscillating Maxwell nano-fluid with heat and mass transfer

Sci Rep. 2022 Jul 16;12(1):12205. doi: 10.1038/s41598-022-16503-w.

Authors

Aamir Farooq^{1

2}, Sadique Rehman³, Abdulaziz N Alharbi⁴, Muhammad Kamran⁵, Thongchai Botmart⁶, Ilyas Khan⁷

Affiliations

¹ Department of Mathematics, Zhejiang Normal University, Jinhua, 321004, Zhejiang, China.
² Department of Mathematics, Abbottabad University of Science and Technology, Abbottabad, Pakistan.
³ Department of Pure and Applied Mathematics, University of Haripur, Haripur, KPK, Pakistan.
⁴ Department of Physics, College of Science, Taif University, P.O.Pox 11099, Taif, 21944, Saudi Arabia.
⁵ Department of Mathematics, COMSATS University Islamabad, Wah Campus, Islamabad, 47040, Pakistan.
⁶ Department of Mathematics, Faculty of Science, Khon Kaen University, Khon Kaen, 40002, Thailand. thongbo@kku.ac.th.
⁷ Department of Mathematics, College of Science Al-Zulfi, Majmaah University, Al-Majmaah, 11952, Saudi Arabia.

Abstract

The primary goal of this article is to analyze the oscillating behavior of Maxwell Nano-fluid with regard to heat and mass transfer. Due to high thermal conductivity of engine oil is taken as a base fluid and graphene Nano-particles are introduced in it. Coupled partial differential equations are used to model the governing equations. To evaluate the given differential equations, certain dimensionless factors and Laplace transformations are used. The analytical solution is obtained for temperature, concentration and velocity. The temperature and concentration gradient are also finds to analyze the rate of heat and mass transfer. As a special case, the solution for Newtonian fluid is discussed. Finally, the behaviors of various physical factors are studied graphically for both sine and cosine oscillation and give physical meanings to the parameters.