Fig.3 illustrates that the unsteadiness parameter reduces the dimensionless film thickness . Also, for critical value of the unsteadiness parameter the film thickness tends to zero. This implies the film thickness vanishes that this critical value and then the motion becomes impossible.
One of the main objectives of this study is to discuss the surface tension effect, according to thermosolutal Marangoni convection effect, on the motion. The increase of the temperature surface tension parameter and the concentration surface tension parameter means a decrease in the surface tension according to the negative values of the coefficients and . So, the reduction of the surface tension, at the free surface, reduces the free surface rigidity …show more content…
It is assumed that and throughout the boundary layer. Physically, increasing both the temperature and the concentration gradients provokes a higher instability at the interface according to reducing the surface tension. This means that increasing both the temperature and the concentration surface tension coefficients and reduces the temperature and the concentration profiles, as shown in Figs.8 and 11. Similar result was obtained experimentally by Aubeterre et al.[26]. This experimental study deduced that the temperature gradient destabilizes the free surface. This means that when the temperature gradients occur the substance tends to evaporate easily. This provokes a higher instability at the interface (which means a decrease in the surface tension). Also, depending on the alcohol studying, in this article, turbulence begins at the interface at different temperature gradients. The instability starts near the interface and causes a sinuous movement to the interface. At higher temperature gradients, the instabilities increase and the movement becomes continuous. When temperature gradients are a sinuous wave was observed [26]. Also, when the concentration at the interface is less than the concentration at the slot the surface tension at the free surface accordingly reduces. This implies that the surface tension is inversely proportional …show more content…
This resistive force retards the motion of the fluid and enhances its temperature. This effect is clear for the velocity in Fig.5 and for the temperature as well as the concentration in Figs. 8 and 10, respectively. Also, these figures illustrate that the magnetic field decreases the film thickness.
The effect of the Schmidt number is highlighted in Figs.7 and 12 for the temperature and concentration distributions, respectively. The relative effect of momentum diffusion to particles diffusion is presented by Schmidt number. For , the particles diffusivity dominates. Decreasing the particles diffusivity produces an increase in the temperature gradients and means an increase in Schmidt number. So, it is observed that Schmidt number enhances the temperature. Meanwhile, the higher values of Schmidt number correspond to a reduction in the particles diffusion. So, the concentration decreases with increasing .
Fig.6 illustrates that, the Prandtl number reduces the temperature. An increase of Prandtl number means a slow rate of thermal-diffusion. This physically implies a decrease in the thermal boundary layer thickness. While, Prandtl number enhances the concentration profiles as shown in
One of the main objectives of this study is to discuss the surface tension effect, according to thermosolutal Marangoni convection effect, on the motion. The increase of the temperature surface tension parameter and the concentration surface tension parameter means a decrease in the surface tension according to the negative values of the coefficients and . So, the reduction of the surface tension, at the free surface, reduces the free surface rigidity …show more content…
It is assumed that and throughout the boundary layer. Physically, increasing both the temperature and the concentration gradients provokes a higher instability at the interface according to reducing the surface tension. This means that increasing both the temperature and the concentration surface tension coefficients and reduces the temperature and the concentration profiles, as shown in Figs.8 and 11. Similar result was obtained experimentally by Aubeterre et al.[26]. This experimental study deduced that the temperature gradient destabilizes the free surface. This means that when the temperature gradients occur the substance tends to evaporate easily. This provokes a higher instability at the interface (which means a decrease in the surface tension). Also, depending on the alcohol studying, in this article, turbulence begins at the interface at different temperature gradients. The instability starts near the interface and causes a sinuous movement to the interface. At higher temperature gradients, the instabilities increase and the movement becomes continuous. When temperature gradients are a sinuous wave was observed [26]. Also, when the concentration at the interface is less than the concentration at the slot the surface tension at the free surface accordingly reduces. This implies that the surface tension is inversely proportional …show more content…
This resistive force retards the motion of the fluid and enhances its temperature. This effect is clear for the velocity in Fig.5 and for the temperature as well as the concentration in Figs. 8 and 10, respectively. Also, these figures illustrate that the magnetic field decreases the film thickness.
The effect of the Schmidt number is highlighted in Figs.7 and 12 for the temperature and concentration distributions, respectively. The relative effect of momentum diffusion to particles diffusion is presented by Schmidt number. For , the particles diffusivity dominates. Decreasing the particles diffusivity produces an increase in the temperature gradients and means an increase in Schmidt number. So, it is observed that Schmidt number enhances the temperature. Meanwhile, the higher values of Schmidt number correspond to a reduction in the particles diffusion. So, the concentration decreases with increasing .
Fig.6 illustrates that, the Prandtl number reduces the temperature. An increase of Prandtl number means a slow rate of thermal-diffusion. This physically implies a decrease in the thermal boundary layer thickness. While, Prandtl number enhances the concentration profiles as shown in