  In this work, the quark-hadron phase transition in a chameleon Brans-Dicke
model of brane world cosmology within an effective model of QCD is
investigated. Whereas, in the chameleon Brans-Dicke model of brane world
cosmology, the Friedmann equation and conservation of density energy are
modified, resulting in an increased expansion in the early Universe. These have
important effects on quark-hadron phase transitions. We investigate the
evolution of the physical quantities relevant to quantitative descriptions of
the early times, namely, the energy density, $\rho$, temperature, $T$, and the
scale factor, $a$, before, during, and after the phase transition. We do this
for smooth crossover formalism in which lattice QCD data is used for obtaining
the matter equation of state and first order phase transition formalism. Our
analyses show that the quark-hadron phase transition has occurred at
approximately one nanosecond after the big bang and the general behavior of
temperature is similar in both of two approaches.
