Abstract
The unsteady flow of Jeffrey fluid along with a vertical plate is studied in this paper. The equations of momentum, energy, and generalized Fourier’s law of thermal flux are transformed to non-dimensional form for the proper dimensionless parameters. The Prabhakar fractional operator is applied to acquire the fractional model using the constitutive equations. To obtain the generalized results for velocity and temperature distribution, Laplace transform is performed. The influences of fractional parameters α , β , γ , thermal Grashof number Gr , and non-dimensional Prandtl number Pr upon velocity and temperature distribution are presented graphically. The results are improved in the form of decay of energy and momentum equations, respectively. The new fractional parameter contains the Mittag-Leffler kernel with three fractional parameters which are responsible for better memory of the fluid properties rather than the exponential kernel appearing in the Caputo–Fabrizio fractional operator. The Prabhakar fractional operator has advantage over Caputo–Fabrizio in the real data fitting where needed.
Highlights
Non-Newtonian fluids have recently become more appropriate for technical and scientific applications than Newtonian fluids
E solution for temperature and velocity profile is obtained using the Laplace transform. e graphical behavior for fluid temperature can be visualized for fractional parameters α, β, c and Prandtl number Pr. e influence of fractional parameters α, β, c and thermal Grashof number Gr is analyzed for velocity distribution. e comparison between the fractional derivatives Caputo–Fabrizio and Prabhakar fractional operator is justified
It is found that the new fractional parameter contains the Mittag-Leffler kernel with three fractional parameters which are responsible for better memory of the fluid properties rather than the exponential kernel appearing in Caputo–Fabrizio fractional operator
Summary
Non-Newtonian fluids have recently become more appropriate for technical and scientific applications than Newtonian fluids. Shahid [19] obtained the generalized solution for the equations of energy and momentum along with a vertical flat plate of free convection flow with the techniques of Caputo fractional derivative. Shah et al [31] obtained the generalized solution for the convective flow of Maxwell fluid for the stressshear rate and heat flux density vector along with a vertical heated wall via Prabhakar fractional operator. Elnaqeeb et al [32] used the Prabhakar fractional operator with constant wall temperature to study the carbon nanotube technique for viscous fluids and obtained results for a viscous fluid with the help of Laplace transform. In order to fill this research gap, we intended to obtain the natural convection flow of Prabhakar fractional derivative through generalized thermal flux of Jeffrey fluid along with an infinite vertical plate with a constant temperature. On the basis of generalized fractional constitutive equations, we present a mathematical model for the stress relaxation property. e analytical solutions are obtained with the Laplace transform method and compared with recent published work for the validation of the present results
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