Generalized Mittag-Leffler Kernel Form Solutions of Free Convection Heat and Mass Transfer Flow of Maxwell Fluid with Newtonian Heating: Prabhakar Fractional Derivative Approach
Fractal and Fractional
; 6(2):98, 2022.
Article
in English
| ProQuest Central | ID: covidwho-1715226
ABSTRACT
In this article, the effects of Newtonian heating along with wall slip condition on temperature is critically examined on unsteady magnetohydrodynamic (MHD) flows of Prabhakar-like non integer Maxwell fluid near an infinitely vertical plate under constant concentration. For the sake of generalized memory effects, a new mathematical fractional model is formulated based on a newly introduced Prabhakar fractional operator with generalized Fourier’s law and Fick’s law. This fractional model has been solved analytically and exact solutions for dimensionless velocity, concentration, and energy equations are calculated in terms of Mittag-Leffler functions by employing the Laplace transformation method. Physical impacts of different parameters such as α, Pr, β, Sc, Gr, γ, and Gm are studied and demonstrated graphically by Mathcad software. Furthermore, to validate our current results, some limiting models such as classical Maxwell model, classical Newtonian model, and fractional Newtonian model are recovered from Prabhakar fractional Maxwell fluid. Moreover, we compare the results between Maxwell and Newtonian fluids for both fractional and classical cases with and without slip conditions, showing that the movement of the Maxwell fluid is faster than viscous fluid. Additionally, it is visualized that both classical Maxwell and viscous fluid have relatively higher velocity as compared to fractional Maxwell and viscous fluid.
Mathematics; Prabhakar derivative; magnetic effect; slip conditions; analytical solution; Mittag-Leffler functions; physical aspect via graphs; Non-Newtonian fluids; Calculus; Velocity; Maxwell fluids; Mass transfer; Partial differential equations; Viscosity; Mathematical models; Wall slip; Operators (mathematics); Magnetohydrodynamics; Free convection; Fluid flow; Exact solutions; Newtonian fluids; Approximation; Heat; Polymer melts; Viscoelasticity; Coronaviruses; Boundary conditions; Viscous fluids; Convection heating; COVID-19
Full text:
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Collection:
Databases of international organizations
Database:
ProQuest Central
Language:
English
Journal:
Fractal and Fractional
Year:
2022
Document Type:
Article
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