All-101 



97 



In this section wg shall discuss the application of 

 the boundary layer technique to the solution of the problem 

 defined by the equation 



eAAoj) - ^))^ = (i+a sinT) sin nsy (1) 



and the boundary conditions 



^ = ^^ = on X = 0,r (2) 



^ - ^|Jyy ^ on y = 0,1. 



The nature of the boundary layer problem is characterized 

 by throe features; (1) the problem is non-dimonsionalizod so 

 that the size of the domain has lengths of order unity 5 (2) 

 the coefficient of the most highly differentiated term is 

 sm.all compared to unity; (3) the remaining terras have coeffi- 

 cif^nts of order unity. The problem to be considered here has 

 already been put into a suitable non-dimensional form. 



If \|j were everywhere a smooth** function of its arguments 

 and of order unity, then it should be possible to determine a 

 good approximation to the solution by neglecting the term with 

 coefficient e(e<<l) and by considering the remaining equation 



* For an interesting account of boundary layer technique, in- 

 cluding the treatment of non-linear problems, the reader is 

 referred to [8] . 



By" smooth" v/e mean that ij) has no lar^;e derivatives, i.e., 

 ^|i , iIj^, ib,.^^^., etc. are all of the same order of magnitude. 



