Confined Laminar Jet Mixing of Parallel Streams

Abstract

A new method of studying confined laminar jet mixing is suggested. The governing equation for the velocity field is linearized following an approach proposed by Sparrow, Lin, and Lundgren in their study of laminar flow development in a channel. After linearization the governing equation becomes an integrodifferential equation. The exact solution is found for the case of two uniform streams flowing in a parallel-plate channel. In addition, a variational formulation of the same problem is constructed, completely equivalent to the differential formulation. Approximate variational solutions are sought and obtained. It develops that a simple two-term approximation gives excellent agreement with the exact solution.