A time fractional second-grade magnetohydrodynamic dusty fluid flow model with variable conditions: Application of Fick's and Fourier's laws

Non-Newtonian fluids along with magnetohydrodynamic flow have numerous applications in the purification of mineral oil, MHD pumps and motors, polymer fabrication, and aerodynamic heating. Thermal engineering and welding mechanics include the application of heat injectors or sinks to the abovementioned flows for heating and cooling processes. The present study deliberated comprehensively the generalized hydromagnetic dusty flow of the viscoelastic second-grade fluid between vertical plates with variable conditions. The fluid motion is induced by the oscillations of the left plate. Heat and mass transport, along with particle temperature, are considered. Partial differential equations are used to model the given flow regime. Unlike the previous published studies, the momentum equation is fractionalized from their constitutive equations before dimensionalization. The dimensionless energy and concentration equations have been fractionalized using Fick's and Fourier's laws. The fractionalized dimensionless system of equations is then solved by using the Laplace and finite Fourier-Sine transforms. To find the final solution, the Laplace inverse is found by the numerical approach of Zakian via PYTHON software. It is worth noting that the fluid's velocity accelerate with increasing t, K-1 , Gr, and Gm and the parameters Pe, R, and t enhance the heat transfer rate. Furthermore, the parametric impact on the engineering interest quantities has been detailed in the Tables.