Fate of an Accretion Disc around a Black Hole when both the Viscosity and Dark Energy is Effecting

This paper deals with the viscous accretion flow of modified Chaplygin gas towards a black hole as the central gravitating object. Modified Chaplygin gas is a particular type of dark energy model which mimics of radiation era to phantom era depending on the different values of its parameters. We compare the drak energy accretion with the flow of adiabatic gas. An accretion disc flow around a black hole is an example of a transonic flow. To make the model, we consider three components of Navier Stokes' equation, the equation of continuity and the modified Chaplygin gas's equation of state. As a transonic flow passes through the sonic point, the velocity gradient being apparently singular there, gives rise to two flow branches : one infalling, the accretion and the other outgoing, the wind. We show that the wind curve is stronger and wind speed reaches to that of light at a finite distance from the black hole when dark energy is considered. Besides, if we increase the viscosity, accretion disc is being shortened. This two process acting together deviates much from adiabatic accretion case. It shows a weakening process for the accretion procedure by the works of viscous system influenced angular momentum transport and the repulsive force of the modified Chaplygin gas together.