  We investigated accretion on to black holes in presence of viscosity and
cooling, by employing an equation of state with variable adiabatic index and
multi-species fluid. We obtained the expression of generalized Bernoulli
parameter which is a constant of motion for an accretion flow in presence of
viscosity and cooling. We obtained all possible transonic solutions for a
variety of boundary conditions, viscosity parameters and accretion rates. We
identified the solutions with their positions in the parameter space of
generalized Bernoulli parameter and the angular momentum on the horizon. We
showed that a shocked solution is more luminous than a shock-free one. For
particular energies and viscosity parameters, we obtained accretion disc
luminosities in the range of $10^{-4}-1.2$ times Eddington limit, and the
radiative efficiency seemed to increase with the mass accretion rate too. We
found steady state shock solutions even for high-viscosity parameters, high
accretion rates, and for wide range of composition of the flow, starting from
purely electron-proton to lepton-dominated accretion flow. However, similar to
earlier studies of inviscid flow, accretion shock was not obtained for
electron-positron pair plasma.
