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The effect of uniform magnetic field applied along a fixed horizontaldirection in Rayleigh-B\'enard convection in low-Prandtl-number fluids has beenstudied using a low dimensional model. The model shows the onset of convection(primary instability) in the form of two dimensional stationary rolls in theabsence of magnetic field, when the Rayleigh number $R$ is raised above acritical value $R_c$. The flow becomes three dimensional at slightly highervalues of Rayleigh number via wavy instability. These wavy rolls become chaoticfor slightly higher values of $R$ in low-Prandtl-number ($P_r$) fluids. Auniform magnetic field along horizontal plane strongly affects all kinds ofconvective flows observed at higher values of $R$ in its absence. As themagnetic field is raised above certain value, it orients the convective rollsin its own direction. Although the horizontal magnetic field does not changethe threshold for the primary instability, it affects the threshold forsecondary (wavy) instability. It inhibits the onset of wavy instability. Thecritical Rayleigh number $R_o (Q,P_r)$ at the onset of wavy instability, whichdepends on Chandrasekhar's number $Q$ and $P_r$, increases monotonically with$Q$ for a fixed value of $P_r$. The dimensionless number $R_o (Q, P_r)/(R_c QP_r)$ scales with $Q$ as $Q^{-1}$. A stronger magnetic field suppresses chaosand makes the flow two dimensional with roll pattern aligned along itsdirection.

Role of uniform horizontal magnetic field on convective flow