  In order to explore the generic properties of a backreaction model for
explaining the accelerated expansion of the Universe, we exploit two metrics to
describe the late time Universe. Since the standard FLRW metric cannot
precisely describe the late time Universe on small scales, the template metric
with an evolving curvature parameter $\kappa_{\mathcal{D}}(t)$ is employed.
However, we doubt the validity of the prescription for $\kappa_{\mathcal{D}}$,
which motivates us apply observational Hubble parameter data (OHD) to constrain
parameters in dust cosmology. First, for FLRW metric, by getting best-fit
constraints of $\Omega^{{\mathcal{D}}_0}_m = 0.25^{+0.03}_{-0.03}$, $n =
0.02^{+0.69}_{-0.66}$, and $H_{\mathcal{D}_0} = 70.54^{+4.24}_{-3.97}\ {\rm km
\ s^{-1} \ Mpc^{-1}}$, the evolutions of parameters are explored. Second, in
template metric context, by marginalizing over $H_{\mathcal{D}_0}$ as a prior
of uniform distribution, we obtain the best-fit values of
$n=-1.22^{+0.68}_{-0.41}$ and
${{\Omega}_{m}^{\mathcal{D}_{0}}}=0.12^{+0.04}_{-0.02}$. Moreover, we utilize
three different Gaussian priors of $H_{\mathcal{D}_0}$, which result in
different best-fits of $n$, but almost the same best-fit value of
${{\Omega}_{m}^{\mathcal{D}_{0}}}\sim0.12$. Also, the absolute constraints
without marginalization of parameter are obtained: $n=-1.1^{+0.58}_{-0.50}$ and
${{\Omega}_{m}^{\mathcal{D}_{0}}}=0.13\pm0.03$. With these constraints, the
evolutions of the effective deceleration parameter $q^{\mathcal{D}}$ indicate
that the backreaction can account for the accelerated expansion of the Universe
without involving extra dark energy component in the scaling solution context.
Nevertheless, the results also verify that the prescription of
$\kappa_{\mathcal{D}}$ is insufficient and should be improved.
