Onset of Viscous Dissipation Instability in Plane Couette Flow with Temperature-Dependent Viscosity

The conditions for the onset of dissipation thermal instability with temperature-dependent viscosity in plane Couette flow a Newtonian fluid are analyzed. studied system consists horizontal layer confined between an adiabatic (fixed) lower wall and isothermal (moving) upper wall. Both exponential linear fluidity models considered order to account thermodependency fluid’s viscosity. stability analysis base solution respect arbitrarily oriented normal modes is carried out numerically by employing shooting method. most unstable disturbances proven be stationary longitudinal rolls, their governed three dimensionless parameters: viscous Rayleigh number, Prandtl number parameter that represents variability temperature. It shown effect variation promote flow. As expected, two models’ results diverge as increases, model found more stable than one. By considering thermophysical properties real fluids, it precedes hydrodynamic instability. An energy budget proposed better understand both stabilization differences