Convection in a horizontal fluid layer under an inclined temperature gradient with a negative vertical Rayleigh number

In this paper natural convection is investigated under an inclined temperature gradient with a negative vertical component. This is translated into a negative vertical Rayleigh number R-V. This is important in applications when, for example, R-V < 0 is used to stabilize a liquid layer but a horizontal temperature gradient still persists. Interesting results are found from the numerical analysis of the linear equations. New codimension-two points, where the stationary and oscillatory convection modes compete to be the first unstable one, are found by increasing the magnitude of the negative R-V. Besides, the longitudinal stationary modes intersect again for R-V < 0. Calculations for seven magnitudes of the Prandtl number are presented in detail. (C) 2015 Elsevier Ltd. All rights reserved.