In this paper, we have constructed the cosmological model of the universe in a two fluids environment with a newly developed mathematical formalism. In order to construct the model Binachi type V (BV) space time is considered with a time varying deceleration parameter. Both the fluids, the viscous fluid and the dark energy (DE) fluid have shown their dominance respectively in early time and late time of the cosmic evolution. The scale factor that simulates the cosmic transition based on the value of the bulk viscous coefficient. Within the developed formalism, a general form of the skewness parameters is also obtained as a functional form of the scale factor. The physical parameter of the model such as equation of state (EoS) parameter is also derived and analysed. The state finder diagnostic pair are also obtained to understand the geometrical nature of the model.
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