  In this work, we have considered the flat FRW model of the universe in
$(n+2)$-dimensions filled with the dark matter and the magnetic field. We
present the Hubble parameter in terms of the observable parameters
$\Omega_{m0}$ and $H_{0}$ with the redshift $z$ and the other parameters like
$B_{0},\omega, \mu_{0},\delta,n,w_{m}$. The natures of magnetic field $B$,
deceleration parameter $q$ and $Om$ diagnostic have also been analyzed for
accelerating expansion of the universe. From Stern data set (12 points), we
have obtained the bounds of the arbitrary parameters by minimizing the
$\chi^{2}$ test. The best-fit values of the parameters are obtained by 66%, 90%
and 99% confidence levels. Now to find the bounds of the parameters
($B_{0},\omega$) and to draw the statistical confidence contour, we fixed four
parameters $\mu_{0},\delta,n,w_{m}$. Here the parameter $n$ determines the
higher dimensions and we perform comparative study between three cases : 4D
$(n=2)$, 5D $(n=3)$ and 6D $(n=4)$ respectively. Next due to joint analysis
with BAO observation, we have also obtained the bounds of the parameters
($B_{0},\omega$) by fixing other parameters $\mu_{0},\delta,n,w_{m}$ for 4D, 5D
and 6D. The best fit of distance modulus for our theoretical model and the
Supernova Type Ia Union2 sample are drawn for different dimensions.
