Competition between stationary and oscillatory thermocapillary convection of a Cattaneo–Christov fluid over a thick wall with finite thermal conductivity

In this paper, the linear thermocapillary stability of a liquid layer coating a thick wall with finite thermal conductivity is studied under the assumption that the heat flux in the liquid obeys the Cattaneo–Christov constitutive equation. The interplay between stationary and oscillatory instability modes is examined through plots of codimension-two points. It is demonstrated that the damping of heat flux, induced by the thermal relaxation time in the Cattaneo–Christov model, plays a crucial role in destabilizing the system. Additionally, the wall’s thickness, thermal conductivity, and specific heat capacity are identified as key factors influencing the system’s stability in the monotonic mode. These properties also significantly affect the critical wavenumbers and frequencies associated with oscillatory convection. • Thermocapillary instability of a Cattaneo–Christov fluid. • Marangoni instability for a non-Fourier liquid. • Oscillatory thermocapillary convection is preferred. • Codimension-two points for a non-Fourier liquid. • The wall’s thermal and geometric parameters have great influence on instability.