Abstract We study a global transonic solution for a relativistic, magnetized, viscous advective accretion flow around a rotating black hole, incorporating the effects of mass and angular momentum loss through winds. Our model considers dominant toroidal magnetic fields with synchrotron radiation as the primary cooling mechanism. To self-consistently model mass loss, the mass accretion rate is prescribed to decrease inward as a power law with disk radius. With this, we solve the governing equations that describe the accretion flows in presence of winds and obtain the flow structure in terms of the inflow parameters (energy E , angular momentum λ , plasma- β , accretion rate m ̇ , and viscosity α B ), the wind parameters ( p , governing mass loss; and l , governing angular momentum transport by winds), and the black hole spin ( a k ). Our analysis reveals that winds substantially modify the accretion flow, leading to a significant decrease in disk luminosity. We specifically identify global solutions that admit standing shocks and find that winds profoundly alter shock properties, such as the shock radius ( x s ), compression ratio ( R ), and shock strength ( S ). Furthermore, we determine the critical wind parameter p crit beyond which steady shock solutions cease to exist. We demonstrate that increased viscosity and strong angular momentum extraction by winds lead to a reduction in p crit . These findings evidently highlight a complex interplay between viscosity and winds in governing the dynamics of shock formation in accretion disks.
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