A mathematical Study of Magnetohydrodynamic Casson Fluid via Special Functions with Heat and Mass Transfer embedded in Porous Plate

TL;DR

This paper investigates heat and mass transfer in magnetohydrodynamic Casson fluid within a porous medium, deriving generalized solutions using special functions and analyzing effects through graphical illustrations.

Contribution

It introduces new generalized solutions for temperature, concentration, and velocity profiles using special functions like Robotnov-Hartley, Wright, and Mittag-Leffler functions.

Findings

Solutions satisfy boundary and initial conditions

Graphical analysis reveals parameter effects on flow

Fractional solutions reduce to classical forms

Abstract

This article is proposed to investigate the impacts of heat and mass transfer in magnetohydrodynamic casson fluid embedded in porous medium. The generalized solutions have been traced out for the temperature distribution, mass concentration and velocity profiles under the existence and non-existence of transverse magnetic field, permeability and porosity. The corresponding solutions of temperature distribution and mass concentration, velocity profiles are expressed in terms of newly defined generalized Robotnov-Hartley function, wright function and Mittage-Leffler function respectively. All the corresponding solutions fulfill necessary conditions (initial, natural and boundary conditions) as well. Caputo Fractionalized solutions have been converted for ordinary solutions by substituting {\zeta}=1. Some similar solutions for the temperature distribution, mass concentration and velocity profiles have been particularized form generalized solutions. Owing to the rheology of problem, graphical illustrations of distinct parameters are discussed in detail by depicting figures using Mathcad software (15).