The Effect of Heating and Cooling on the Stability of the Boundary-Layer Flow of a Liquid over a Curved Surface

THE STABILITY of the isothermal laminar boundary layer over curved surfaces was first considered by Gortler. He found tha t , for concave curvature, instability occurs with respect to a class of threedimensional disturbances corresponding to vortices with axes parallel to the principal flow direction. He also obtained the impor tant result t ha t this type of instability, in contrast to t ha t for the two-dimensional Tollmien-Schlichting waves, is relatively insensitive to the shape of the basic velocity profile—i.e., to freestream pressure gradient—when the relevant parameters are expressed in terms of boundary-layer momentum thickness. Later work on the same problem by other authors has been concerned mainly with the procedure for solving the eigenvalue problem. In the present investigation the theory is extended to the case of a heated or cooled wall. For simplicity, the results are restricted to liquids, so t h a t viscous dissipation and variations in density can be neglected. Detailed numerical calculations for the boundarylayer flow of water over a curved wall show that , just as for pressure gradient, the influence of heating and cooling is also small, a t least for liquids, in spite