Local heat transfer on a finite width surface with laminar boundary layer flow

The effect of a lateral discontinuity in the thermal boundary conditions in two dimensional laminar flow on a flat plate is investigated with numerical and analytical modeling. When the thermal and momentum boundary layers start at the same location, the resulting self-similar two dimensional boundary layer equations were solved numerically. For flow with an unheated starting length, three dimensional numerical simulations were required. For both the two and three dimensional thermal simulations, the Blasius solution for a two dimensional momentum boundary layer was assumed. It is found that all the Nusselt numbers collapse to a single curve when graphed as a function of a spanwise similarity variable. Simple correlations for the local Nusselt number on a rectangular flat plate are presented for a variety of boundary conditions.