Extending the Bejan number to a general form

Abstract

A modified form of the Bejan number (Be), originally proposed by Bhattacharjee and Grosshandler for momentum processes, is obtained by replacing the dynamic viscosity (m) appearing in the original proposition with the equivalent product of the fluid density (r) and the momentum diffusivity of the fluid (n). This modified form is not only more akin to the physics it represents but it also has the advantage of being dependent on only one viscosity coefficient. Moreover, this simple modification allows for a much simpler extension of Be to other diffusion processes, such as a heat or a species transfer process, by simply replacing the diffusivity coefficient. Consequently, a general Be representation for any process involving pressure-drop and diffusion becomes possible. It is shown that this general representation yields analogous results for any process satisfying the Reynolds analogy (i.e., when Pr = Sc = 1), in which case the momentum, energy and species concentration representations of Be turn out to be the same.