Nonparallel thermal instability of mixed convection flow on nonisothermal horizontal and inclined flat plates

A linear theory based on the nonparallel flow model is employed to study the onset of longitudinal vortex instability of laminar mixed convection flow over horizontal and inclined flat plates with variable surface temperature, Tw(x) − T∞ = Axn. In the analysis, the streamwise dependence of the disturbance amplitude functions is taken into account. Neutral stability curves as well as the critical values for the parameter G ∗ = Gr ∗ x /Re x ∗ 3 2 and wave number α ∗ are presented for Prandtl numbers Pr = 0.7, 7, 100, and 1000 over a range of the exponent values −0.5 ⩽ n ⩽ 1.0 and inclination angles 0° ⩽ φ ⩽ 85°. For a given Prandtl number and inclination angle, thermal instability is found to decrease as the value of the exponent n increases. Also, for given values of the exponent n and Prandtl number Pr, the critical value of Gr x ∗ /Re x ∗ 3 2 increases with increasing inclination angle from the horizontal. However, the critical wave number α ∗ appears to be unaffected by the inclination angle. The results from the present nonparallel flow analysis are compared with available analytical and experimental results from previous studies. The nonparallel flow analysis that accounts for the streamwise dependence of the amplitude functions is found to have a stabilizing effect as compared with the parallel flow analysis in which the streamwise dependence of the disturbance is neglected.