Power Law Kernel Analysis of MHD Maxwell Fluid with Ramped Boundary Conditions: Transport Phenomena Solutions Based on Special Functions
[ X ]
Date
2021
Journal Title
Journal ISSN
Volume Title
Publisher
Mdpi
Access Rights
info:eu-repo/semantics/openAccess
Abstract
In this paper, a new approach to find exact solutions is carried out for a generalized unsteady magnetohydrodynamic transport of a rate-type fluid near an unbounded upright plate, which is analyzed for ramped-wall temperature and velocity with constant concentration. The vertical plate is suspended in a porous medium and encounters the effects of radiation. An innovative definition of the time-fractional operator in power-law-kernel form is implemented to hypothesize the constitutive mass, energy, and momentum equations. The Laplace integral transformation technique is applied on a dimensionless form of governing partial differential equations by introducing some non-dimensional suitable parameters to establish the exact expressions in terms of special functions for ramped velocity, temperature, and constant-concentration fields. In order to validate the problem, the absence of the mass Grashof parameter led to the investigated solutions obtaining good agreement in existing literature. Additionally, several system parameters were used, such as as magnetic value M, Prandtl value Pr, Maxwell parameter lambda, dimensionless time tau, Schmidt number Sc, fractional parameter alpha, and Mass and Thermal Grashof numbers Gm and Gr, respectively, to examine their impacts on velocity, wall temperature, and constant concentration. Results are also discussed in detail and demonstrated graphically via Mathcad-15 software. A comprehensive comparative study between fractional and non-fractional models describes that the fractional model elucidate the memory effects more efficiently.
Description
Keywords
power law kernel, fractional derivative, memory effects, special functions base solutions, Maxwell fluid, ramped conditions, dynamical and fractional parameteres
Journal or Series
Fractal and Fractional
WoS Q Value
Q1
Scopus Q Value
Q1
Volume
5
Issue
4
