TY - JOUR
T1 - Applications of Prabhakar-like Fractional Derivative for the Solution of Viscous Type Fluid with Newtonian Heating Effect
AU - Raza, Ali
AU - Khan, Umair
AU - Zaib, Aurang
AU - Mahmoud, Emad E.
AU - Weera, Wajaree
AU - Yahia, Ibrahim S.
AU - Galal, Ahmed M.
N1 - Publisher Copyright:
© 2022 by the authors. Licensee MDPI, Basel, Switzerland.
PY - 2022/5
Y1 - 2022/5
N2 - This article examines a natural convection viscous unsteady fluid flowing on an oscillating infinite inclined plate. The Newtonian heating effect, slip effect on the boundary wall, and constant mass diffusion conditions are also considered. In order to account for extended memory effects, the semi-analytical solution of transformed governed partial differential equations is attained with the help of a recent and more efficient fractional definition known as Prabhakar, like a thermal fractional derivative with Mittag-Leffler function. Fourier and Fick’s laws are also considered in the thermal profile and concentration field solution. The essentials’ preliminaries, fractional model, and execution approach are expansively addressed. The physical impacts of different parameters on all governed equations are plotted and compared graphically. Additionally, the heat transfer rate, mass diffusion rate, and skin friction are examined with different numerical techniques. Consequently, it is noted that the variation in fractional parameters results in decaying behavior for both thermal and momentum profiles while increasing with the passage of time. Furthermore, in comparing both numerical schemes and existing literature, the overlapping of both curves validates the attained solution of all governed equations.
AB - This article examines a natural convection viscous unsteady fluid flowing on an oscillating infinite inclined plate. The Newtonian heating effect, slip effect on the boundary wall, and constant mass diffusion conditions are also considered. In order to account for extended memory effects, the semi-analytical solution of transformed governed partial differential equations is attained with the help of a recent and more efficient fractional definition known as Prabhakar, like a thermal fractional derivative with Mittag-Leffler function. Fourier and Fick’s laws are also considered in the thermal profile and concentration field solution. The essentials’ preliminaries, fractional model, and execution approach are expansively addressed. The physical impacts of different parameters on all governed equations are plotted and compared graphically. Additionally, the heat transfer rate, mass diffusion rate, and skin friction are examined with different numerical techniques. Consequently, it is noted that the variation in fractional parameters results in decaying behavior for both thermal and momentum profiles while increasing with the passage of time. Furthermore, in comparing both numerical schemes and existing literature, the overlapping of both curves validates the attained solution of all governed equations.
KW - fractional derivative
KW - natural convection
KW - Prabhakar fractional derivative
KW - viscous flow
UR - http://www.scopus.com/inward/record.url?scp=85130386840&partnerID=8YFLogxK
U2 - 10.3390/fractalfract6050265
DO - 10.3390/fractalfract6050265
M3 - Article
AN - SCOPUS:85130386840
SN - 2504-3110
VL - 6
JO - Fractal and Fractional
JF - Fractal and Fractional
IS - 5
M1 - 265
ER -