Abstract
In this paper, we use a model of non-Newtonian second grade fluid which having three partial differentialequations of momentum, heat and mass transfer with initial condition and boundary condition. Wedevelop the modified Laplace transform of this model with fractional order generalized Caputo fractional operator.We find out the solutions for temperature, concentration and velocity fields by using modified Laplacetransform and investigated the impact of the order α and ρ on temperature, concentration and velocity fieldsrespectively. From the graphical results, we have seen that both the α and ρ have reverse effect on the fluidflow properties. In consequence, it is observed that flow properties of present model can be enhanced nearthe plate for smaller and larger values of ρ. Furthermore, we have compared the present results with theexisting literature for the validation and found that they are in good agreement.
Highlights
The fractional calculus and its applications in assorted fields of science and engineering is considered
We develop the modified Laplace transform of this model with fractional order generalized Caputo fractional operator
We find out the solutions for temperature, concentration and velocity fields by using modified Laplace transform and investigated the impact of the order α and ρ on temperature, concentration and velocity fields respectively
Summary
The fractional calculus and its applications in assorted fields of science and engineering is considered. Qi Haitao and Xu Mingyu discussed about the fractional derivative Maxwell model (FDMM) which contained viscoelastic fluid with unsteady flow [32]. Shaowei Wang and Moli Zhao gave analytical solutions of generalized fractional Maxwell fluid which has transient electro-osmotic flow with help of fractional derivative [33]. Amir Mahmood and Saima Parveen discussed generalized fractional Maxwell fluid which has torsional oscillatory flow and find its exact analytic solutions [34]. Jarad and Jawad [35] defined a modified Laplace transform for particulargeneralized fractional operators namely, Riemann and generalized Caputo fractional operators. We have applied the modified Laplace transform for generalized Caputo fractional derivative operator to some fluid flow problem in transport phenomena.
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