The effects of Soret and variable porosity on an unsteady magnetohydrodynamic flow of an upper convected Maxwell fluid through an expanding or contracting channel are explored in this article. The temperature and concentration at the walls are maintained at different values. The gravitational forces arising from temperature and concentration gradients are also considered. The behaviour of velocity components, skin friction, temperature and concentration with respect to various non-dimensional parameters has been numerically computed by using anefficient shooting method. Newtonian case has been studied using the current algorithm and the present results are compared with earlier literature. At the boundaries, the heat and mass transfer rates are studied using local Nusseltand Sherwood numbers. The results show that both the variable permeability and wall expansion have dominant effects on skin friction at the plates. The Prandtl and Soret numbers have dominating effect on mass transfer when compared with variable permeable parameter.

Due to the unique electro-optical and thermal properties of atomically thin molybdenum disulphide (MoS$_2$), it has the potential to transport excess heat in advanced electronic devices to ensure the efficient working of the device. The present article investigates the impact of adding blade-shaped, brick-shaped, cylinder-shaped and platelet-shaped MoS$_2$ nanoparticles on the heat transport characteristics of viscoelastic ethylene glycol (EG). The time-dependent MHD non-Newtonian nanofluid flow is studied in the presence of temperature- and space-dependent heat source. The influence of different shapes of MoS$_2$ nanoparticles on entropy generation as well as heat transport characteristics of viscoelastic boundary layer flow is studied in depth by plotting comparative graphical profiles.This numerical study will help in achieving the enhancement of heat transfer rate in various industrial processes by opting a suitable nanoparticle shape and adjusting the associated parameters to an appropriate value as suggested by the study.