Onset of double-diffusive convection in a Poiseuille flow with a uniform internal heat source.

This article investigates the linear stability of the onset of double-diffusive convection in a horizontal Poiseuille flow system with a uniform volumetric internal heat source. The study formulates the governing equations incorporating thermal and solutal Rayleigh numbers, Prandtl number, Reynolds number, Lewis number, and an internal heat source parameter, and solves the resulting eigenvalue problem numerically using the Chebyshev–Tau method coupled with the QZ algorithm. Results indicate that a positive solutal Rayleigh number and the internal heat source parameter destabilize the system, while an increase in the Prandtl number and the parameter \( R = Re \cos \phi \) generally stabilize it, with nuanced behavior depending on parameter ranges. The analysis also reveals that the Lewis number influences stability differently below and above a threshold value of approximately 0.4. The findings extend previous studies by incorporating the effect of a uniform internal heat source on double-diffusive convection in Poiseuille flow, providing insights relevant to various industrial and geophysical applications.