New agegraphic dark energy in Brans–Dicke theory with sign changeable interaction for flat universe

In the present study, we discuss a cosmological model considering interaction between new agegraphic dark energy and dark matter with sign changeable interaction term within the framework of Brans–Dicke theory of gravity for a flat universe. We assume the well motivated logarithmic form of Brans–Dicke scalar field in terms of the scale factor to find the cosmological parameters such as equation of state parameter, deceleration parameter and plot graphs to discuss their evolution against redshift parameter z. It is shown that the equation of state parameter may behave like cosmological constant for suitable values of parameters but it shows quintessence like behavior for different values of model parameters in future. The deceleration parameter shows observationally verified recent phase transition and accelerated expansion of the universe in future. The physical significance of well-known cosmological planes i.e. \(w-w^{\prime }\) and statefinder diagnostic is also explored for our model. The statefinder diagnostic shows that new agegraphic dark energy behaves like chaplygin gas in early time and behaves like quintessence in future. Moreover, for suitable values of parameters it behaves like cosmological constant at present. The analysis of \(w-w^{\prime }\) plane shows that our model shows freezing region and reaches in the vicinity of \(\Lambda \)CDM model in future. Further, we apply thermodynamic analysis and found that the generalized second law of thermodynamics is satisfied with in the model.