The role of axisymmetric flow configuration in the estimation of the analogue surface gravity and related Hawking like temperature

For axially symmetric flow of dissipationless inhomogeneous fluid onto a non rotating astrophysical black hole under the influence of a generalized pseudo-Schwarzschild gravitational potential, we investigate the influence of the background flow configuration on determining the salient features of the corresponding acoustic geometry. The acoustic horizon for the aforementioned flow structure has been located and the corresponding acoustic surface gravity $\kappa$ as well as the associated analogue Hawking temperature $T_{\rm AH}$ has been calculated {\it analytically}. The dependence of $\kappa$ on the flow geometry as well as on the nature of the back ground black hole space time (manifested through the nature of the pseudo-Schwarzschild potential used) has been discussed. Dependence of the value of $\kappa$ on various initial boundary conditions governing the dynamic and the thermodynamic properties of the background fluid flow has also been studied.