Non-parallel thermal instability of natural convection flow on non-isothermal inclined flat plates

Abstract

The vortex instability characteristics of laminar boundary-layer flow in natural convection on inclined flat plates heated from below, under the variable surface temperature T w ( x) − T ∞ = Ax n , are studied analytically by the linear theory. The analysis is performed by using the non-parallel flow model in which the steady main flow is treated as two-dimensional and account is taken of the streamwise dependence of the disturbance amplitude functions. Neutral stability curves as well as critical Grashof numbers and the corresponding critical wave numbers are presented for fluids having Pr = 0.7 and 7 over the range of inclination angles, 0° ⩽ φ ⩽ 70° from the horizontal, for a range of the exponent values n from − 1 3 to 1. For a given Prandtl number and a given exponent value n, the flow is found to become more stable to the vortex mode of instability as the inclination angle increases from the horizontal. In addition, the local non-similarity non-parallel flow model provides a larger critical Grashof number than that of the local similarity non-parallel flow model. Results from the present non-parallel flow analysis are compared with previous results from the parallel flow analyses and with available experimental data. The streamwise dependence of the disturbances leads to a stabilization of the main flow, which brings the present predictions to a close and qualitative agreement with available experimental data.