  A model for three-dimensional Rayleigh-B\'{e}nard convection in
low-Prandtl-number fluids near onset with rigid horizontal boundaries in the
presence of a uniform vertical magnetic field is constructed and analyzed in
detail. The kinetic energy $K$, the convective entropy $\Phi$ and the
convective heat flux ($Nu-1$) show scaling behaviour with $\epsilon = r-1$ near
onset of convection, where $r$ is the reduced Rayleigh number. The model is
also used to investigate various magneto-convective structures close to the
onset. Straight rolls, which appear at the primary instability, become unstable
with increase in $r$ and bifurcate to three-dimensional structures. The
straight rolls become periodically varying wavy rolls or quasiperiodically
varying structures in time with increase in $r$ depending on the values of
Prandtl number $Pr$. They become irregular in time, with increase in $r$. These
standing wave solutions bifurcate first to periodic and then quasiperiodic
traveling wave solutions, as $r$ is raised further. The variations of the
critical Rayleigh number $Ra_{os}$ and the frequency $\omega_{os}$ at the onset
of the secondary instability with $Pr$ are also studied for different values of
Chandrasekhar's number $Q$.
