Free convection flow of second grade dusty fluid between two parallel plates using Fick’s and Fourier’s laws: a fractional model

Abstract

AbstractThe paper aims to investigate the channel flow of second grade visco-elastic fluid generated due to an oscillating wall. The effect of heat and mass transfer has been taken into account. The phenomenon has been modelled in terms of PDEs. The constitutive equations are fractionalized by using the definition of the Caputo fractional operator with Fick’s and Fourier’s Laws. The system of fractional PDEs is non-dimensionalized by using appropriate dimensionless variables. The closed-form solutions of thermal and concentration boundary layers are obtained by using the Laplace and finite Fourier-Sine transforms, while the momentum equation is solved by a numerical approach by Zakian using $$\textit{PYTHON}$$ PYTHON . Furthermore, the parametric influence of various embedded physical parameters on momentum, temperature, and concentration distributions is depicted through various graphs. It is observed that the fractional approach is more convenient and realistic as compared to the classical approach. It is worth noting that the increasing values of $$M$$ M , $$Sc$$ Sc and $$Re$$ Re retard the boundary layer profile. For instance, this behaviour of $$M$$ M is significant where boundary control is necessary. That is, in the case of resonance, the physical solution may be obtained by adding the effect of MHD. The Reynolds number is useful in characterising the transport properties of a fluid or a particle travelling through a fluid. The Reynolds number is one of the main controlling parameters in all viscous flow. It determines whether the fluid flow is laminar or turbulent. The evolution of the rate of heat, mass transfer, and skin friction on the left plate with various physical parameters are presented in tables. These quantities are of high interest for engineers. Keeping in mind the effect of various parameters on these engineering quantities, they make their feasibility reports.