Thermal instability of stagnation point boundary layers
Abstract
An analysis of thermal instability for the twodimensional stagnation flow with respect to the longitudinal cell mode is presented. This mode represents a threedimensional buoyancydrive motion consisting of a row of cells with axes parallel to the direction of the velocity vector near the surface; it is the least stable mode in the presence of shear. The analysis results in an eighthorder eigenvalue problem for the general case, and a sixthorder eigenvalue problem for the limiting case of infinite Prandtl number. The problem was solved by a numerical shooting method for a finite domain and determination of the asymptotic value of the eigenvalue as the limit of the domain approach infinity. It was found that the Grashof number based on the viscous length scale is a more convenient parameter to present the stability results than the Rayleigh number.
 Publication:

American Society of Mechanical Engineers and American Institute of Chemical Engineers, Joint National Heat Transfer Conference
 Pub Date:
 July 1980
 Bibcode:
 1980ceht.confX....C
 Keywords:

 Boundary Layer Stability;
 Convective Heat Transfer;
 Free Convection;
 Stagnation Flow;
 Thermal Instability;
 Two Dimensional Flow;
 Asymptotic Methods;
 Computational Fluid Dynamics;
 Grashof Number;
 Prandtl Number;
 Rayleigh Number;
 Temperature Distribution;
 Thermal Boundary Layer;
 Fluid Mechanics and Heat Transfer