NONPARALLEL THERMAL-INSTABILITY OF FORCED-CONVECTION FLOW OVER A HEATED, NONISOTHERMAL HORIZONTAL FLAT-PLATE

A linear, non-parallel flow model is employed to study the onset of longitudinal vortex instability in laminar forced convection flow over a heated horizontal flat plate with variable surface temperature, Tw(α)-T∞ = Aαn. In the analysis, the streamise dependence of the disturbance amplitude functions is taken into account. The resulting system of linearized disturbance equations for the amplitude functions constitutes an eigenvalue problem which is solved by a finite difference scheme along with Müller's shooting method. Neutral stability curves as well as the critical values for Grα/Reα3/2 and the corresponding critical wave numbers α* are presented for Prandl numbers 0.7 ≤ Pr ≤ 104 over a range of the exponent -0.5 ≤ n ≤ 1.0. For a given Prandtl number, thermal instability is found to decrease as the value of the exponent n increases. Also, for a given value of the exponent n, fluids with larger Prandtl numbers are found to exhibit less susceptibility to instability than fluids with lower Prandtl numbers. However, this latter trends existsfor Pr ≤ 100. For Pr > 100, thitical values of Grα/Reα3/2 become essentially constant and independent of the Prandtl number. The results from the present non-parallel flow analysis are also compared with available analytical and experimental results from previous studies. The non-parallel flow analysis that accounts for the streamwise dependence of the amplitude functions is found to have a stabilizing effect as compared to the parallel flow analysis in which streamwise dependence of the disturbance is neglected. © 1990.