Analysis of MHD Dusty Flow of non-Newtonian Liquids Through a slippery Inclined Heated Channel

Abstract This work addresses the magnetohydrodynamic (MHD) interfacial stability of dusty two different viscoelastic liquids with heat transfer analysis through a planar channel filled with a saturated medium of porous nature. For the purpose of heat transfer, the bottom and the top slip plates are maintained at two different and constant temperatures. The dust elements are imagined to own a spherical shape, a uniform volume, and a constant number density during the flow operation. The basic state solutions are obtained, and the role of some parameters on the basic velocities and temperature is illustrated by drawing some diagrams. The unsteady governing equations are solved using the perturbation method under certain boundary and interface conditions in the limit of long wave. The stability boundary is accomplished in terms of growth rate and neutral lines, in which stability boundary and instability range are quantified. The impact of emerging relevant quantities on flow characteristics has been investigated through graphs. The Hartmann number associated with the lower layer has been found to decrease both the horizontal and vertical speeds together, depending on the parameters chosen. The influence of the Peclet number associated with the upper layer also has a direct impact on the heat of both the liquid and the dust particles. The Reynolds number connected with the lower layer of the fluid has a stable influence on the movement of the channel, while the enlarge in Reynolds number related with the upper layer causes a regular increase in the rate of growth and can be destabilized the system. Furthermore, the impacts of Marangoni number and wall slip on the stability picture are shown graphically, and the influence of the viscosity ratio is discussed in the light of flow and thermal patterns, which are found to accelerate the movement. Comparative studies between existing results and those of the present study are considered, and it has been found to be in excellent harmony. It is hoped that the findings of this article will enhance the understanding of the interfacial stability of the dusty MHD flow process as established in various industrial applications.