  We develop the framework of boundary derivative expansion (BDE) formalism of
fluid/gravity correspondence in compactified D4-brane system, which is a
nonconformal background used in top-down holographic QCD models. Such models
contain the D4-D6 model and the Sakai-Sugimoto (SS) model, with the background
of the compactified black D4 branes under the near horizon limit. By using the
dimensional reduction technique, we derive a 5D Einstein gravity minimally
coupled with 3 scalar fields from the 10D D4-brane background. Following the
BDE formalism of fluid/gravity correspondence in the conformal background, we
directly derive all the first order transport coefficients for nonconformal
gluonic matter. The results of the ratio of the bulk to shear viscosity and the
sound speed agree with those obtained from the Green-Kubo method. This
agreement guarantees the validity of the BDE formalism of fluid/gravity duality
in the nonconformal D-brane background, which can be used to calculate the
second order transport coefficients in nonconformal background.
