On the Rayleigh-Bénard-Poiseuille problem with internal heat generation

► We study the convective instability of Rayleigh-Bénard-Poiseuille flow. ► The instability is due to a uniform internal heat source. ► The linear stability to arbitrary oblique rolls is analyzed. ► The most unstable modes of disturbance are the longitudinal rolls. ► The mass flow rate does not influence the marginal stability condition.