Conventional and multiple deck boundary layer approach to second and third grade fluids

Abstract

A general analysis of boundary layers of second and third grade fluids are made in which the conventional as well as the multiple deck structures are investigated. It is shown that for second grade fluids only conventional two deck structure exists and a multiple deck boundary layer is impossible. For the third grade fluids, three conventional boundary layers are formulated. In the first one, we retain all the terms whereas in the second one the viscous, and in the third one, second grade terms come out to be negligible compared to other terms. A similarity solution is presented for the third case. Under some restricted conditions, it is shown that quadruple decks exist for the third grade fluids. For the lower deck equations to be matched with the middle deck equations, a decaying solution should exist, and this further requires that 2α 1 + α 2 = 0 where α 1 and α 2 are the material moduli for third grade fluids.