Channel flow of a viscous fluid in the boundary layer
where f3, called the Nahme-GrifRth number, is assumed to be large. For some positive constant a (< 2/?1/2), let fl = (0, a) x (0,T), and dfl be the parabolic boundary ([0, a] x {0}) U ({0, a} x (0, T)) of tt, where T < oo. Ockendon found that as x —> oc, u ~ t/x and tp ~ x2/2. Since (3 is very large, «-»0as2i-> 2 (31^2. Thus, the model of the channel flow of a fluid with temperature-dependent viscosity in the boundary layer is simplified to the following degenerate parabolic problem (cf. Lacey [4], Stuart and Floater [6], and Floater [3]), uxx xut — —eu in u = 0 on dfl, (1.1)