Three-dimensional free convective flow between two parallel vertical plates moving in opposite directions (Q2455837)

This paper presents an analysis of steady three-dimensional free convective flow of a viscous incompressible fluid between two infinite vertical parallel porous plates moving in opposite directions with uniform velocity. The plate moving vertically upwards along \(x\)-axis is subjected to a transverse sinusoidal injection velocity of non-dimensional form \(v(z)=1+\varepsilon\cos(\pi z)\), where \(\varepsilon\) is a small positive constant quantity (\(\varepsilon\ll1\)). The other plate is moving in opposite direction and is subjected to a constant suction velocity. The problem becomes three-dimensional due to the transverse sinusoidal injection velocity. A series solution in small \(\varepsilon\) is used to solve the non-dimensional partial differential equations of motion and energy. The main flow velocity component \(u\) along with the main flow components \((\tau_x)_{y=0}\) and \((\tau_x)_{y=1}\) of the skin friction is shown graphically for some values of parameters \(Gr\), the Grashof number, \(\lambda\), the suction parameter and \(Pr\), the Prandtl number. It is found that the main flow velocity \(u\) increases with the increase in both parameters \(Gr\) and \(\lambda\). It is also found that \((\tau_x)_{y=0}\) increases with \(Gr\) and decreases with \(Pr\). However, \((\tau_x)_{y=1}\) decreases with \(Gr\) and with \(Pr\). Further, it is shown that \((\tau_x)_{y=0}\) increases with increasing the parameter \(\lambda\) for \(Gr>0\) but decreases for \(Gr<0\). On the other hand, \((\tau_x)_{y=1}\) decreases with increasing \(\lambda\) for \(Gr>0\) but increases for \(Gr<0\). The results of this paper seem to be important from technological point of view, but there is no mentioned any application of the obtained results.