Thermal instability in an inclined fluid layer subjected to Couette-Poiseuille flow

The present work deals with the onset of thermal instability in an inclined fluid layer subjected to Couette-Poiseuille flow. We consider the configuration in which one boundary is maintained at a constant temperature and the other boundary is imposed with a constant heat flux. The collocation method, based on Chebyshev polynomials, is used to discuss the instability of the flow with respect to the thermal Rayleigh number. It is found that there exists a value of the angle of inclination below which the instability sets in as longitudinal rolls, and the critical value of the Rayleigh number remains unaffected by superimposed Couette-Poiseuille flow. However, for angles of inclination greater than this threshold value, the critical mode of instability is transverse mode, and the critical value of the Rayleigh number is significantly affected by the superposition of Couette-Poiseuille flow. Further, the onset of instability also depends upon the Prandtl number of the fluid.