| Abstract: We investigate the global transonic solution for a relativistic, magnetized, viscous, dissipative, and advective accretion flow around a rotating black hole (BH), including the effects of mass and angular momentum loss through winds. In doing so, we consider dominant toroidal magnetic fields, with synchrotron radiation serving as the primary cooling mechanism inside the disk. To account for mass loss, we adopt the mass accretion rate to decrease inward as a power-law function of the disk radius. Within this framework, we solve the governing equations that describe accretion flows in the presence of winds and obtain the flow structure as a function of the inflow parameters, namely energy $\mathcal{E}$, angular momentum $\lambda$, plasma-$\beta$ (=$P_{\rm gas}/P_{\rm mag}$, $P_{\rm gas}$ and $P_{\rm mag}$ being the gas and magnetic pressure), accretion rate $\dot{m}$, and viscosity $\alpha_{\rm B}$; the wind parameters governing mass loss ($p$) and angular momentum extraction ($l$); and the black hole spin ($a_{\rm k}$). Our results show that winds substantially modify the accretion dynamics, leading to a significant reduction in disk luminosity. We identify global solutions that admit standing shocks and demonstrate that winds have a strong influence on shock characteristics, including the shock radius ($x_{\rm s}$), compression ratio ($R$), and shock strength ($S$). Furthermore, we determine the critical wind parameter $p^{\rm crit}$ beyond which steady shock solutions no longer exist. We find that enhanced viscosity and more efficient angular momentum removal by winds systematically reduce $p^{\rm crit}$. These findings reveal the intricate interplay between viscosity and wind parameters in governing the dynamics of shock formation in accretion disk. |
