Theoretical investigation of thermal and mass stratification effects on unsteady flow across a vertical oscillating plate with periodic temperature variation and variable mass diffusion

This research paper examines the combined effects of thermal and mass stratification on unsteady flow past a vertical oscillating plate with periodic temperature variation and variable mass diffusion. The Laplace transform technique is introduced to deal with the linear coupled parabolic equations satisfying initial as well as boundary conditions and obtained solutions in closed form for concentration, temperature, and velocity. For example, to find the Laplace transform of an exponentially ordered piece wise continuous function $n\left(t\right)$, one can uses the formula $L\left\{n\left(t\right)\right\}={\int }_0^{\infty }{e}^{-st}n\left(t\right)dt=\overline{n}\left(s\right)$, t being the time and s is a parameter. In this study, we explore the effects of different factors such as plate amplitude, plate frequency, thermal Grashof number, and the mass Grashof number on the concentration, velocity, and temperature profiles and shows them graphically. We see a decline in the fluid's velocity for thermal and mass stratification. Most interestingly, in presence of higher temperature gradient, as the frequency of the oscillations increases close to the plate surface, the fluid velocity declines. The reason behind this is that the flow system has a plate with very high fluctuations. We have found that the fluid's temperature goes up while the concentration goes down when there is a decrease in the thermal stratification and a rise in the mass stratification.