Influence of thermal flux on Marangoni convection in weakly viscoelastic thin films on uniformly heated substrate

This study examines the hydrodynamic stability of weakly viscoelastic thin film of Walters liquid B '' type on a uniformly heated rigid inclined plane. The current model incorporates a heat flux (HF) boundary condition, which is a realistic representation. This approach accounts for heat flux and heat loss at the wall-liquid and wall-air interfaces, allowing for an examination of the effects of a nonvanishing temperature gradient at the top of the rigid wall. This consideration is essential, as maintaining a constant temperature throughout the wall in laboratory settings poses significant challenges. A Benney-type evolution equation is derived using the long-wave expansion of the flow variables, describing the film thickness as a function of x, t. A linear stability analysis in normal mode is conducted to determine the onset of instability to the critical Reynolds number. The linear study indicates the dual role of the wall film Biot number (Bw). For small values of (Bw), a destabilizing effect is observed; however, upon reaching a critical value, a stabilizing effect is produced. The linear study confirms that the presence of Bw consistently results in a destabilizing effect on the viscoelastic parameter. The nonlinear free surface equation is numerically simulated using the Fourier Spectral method. The temporal evolution of hmax and hmin in the presence of (Bw) proves the viscoelastic parameter's destabilizing effect.