Heat transfer of generalized second grade fluid with MHD, radiation and exponential heating using Caputo-Fabrizio fractional derivatives approach

Sehra Sehra; Afshan Noor; Sami Ul Haq; Saeed Ullah Jan; Ilyas Khan; Abdullah Mohamed

doi:10.1038/s41598-022-22665-4

Heat transfer of generalized second grade fluid with MHD, radiation and exponential heating using Caputo-Fabrizio fractional derivatives approach

Sci Rep. 2023 Mar 30;13(1):5220. doi: 10.1038/s41598-022-22665-4.

Authors

Sehra Sehra¹, Afshan Noor¹, Sami Ul Haq², Saeed Ullah Jan², Ilyas Khan³, Abdullah Mohamed⁴

Affiliations

¹ Shaheed Benazir Bhutto Women University Peshawar, Peshawar, 25000, Khyber Pakhtunkhwa, Pakistan.
² Department of Mathematics, Islamia College Peshawar, Peshawar, 25000, Khyber Pakhtunkhwa, Pakistan.
³ Department of Mathematics, College of Science Al-Zulfi, Majmaah University, Al-Majmaah, 11952, Saudi Arabia. i.said@mu.edu.sa.
⁴ Research Centre, Future University in Egypt, New Cairo, 11835, Egypt.

Abstract

The aim of the present work is to apply the Caputo-Fabrizio fractional derivative to the heat transformation of unsteady incompressible second grade fluid. The effects of magneto hydro dynamic and radiation are analyzed. In governing equation of heat transfer nonlinear radiative heat is examined. Exponential heating phenomena is considered at boundary. Firstly, the dimensional governing equations with the initial & boundary conditions are converted into non-dimensional form. Exact analytical solutions are obtained for dimensionless fractional governing equations which consist of momentum and energy equations by using Laplace transform method. Special cases are investigated of the obtained solutions and it is noticed that some well-known results are achieved published in literature from these special cases. At the end, for graphical illustration the influences of different physical parameters like radiation, Prandtl, fractional parameter, Grashof numbers and Magneto hydro dynamic are checked graphically.