On the implementation of stream-wise periodic boundary conditions

Fully-developed periodic boundary conditions have frequently been employed to perform calculations on the performance of typical elements of heat exchangers. Many such calculations have been achieved by transforming the equations of motion to obtain a new set of state variables which are cyclic in the stream-wise direction. In others, primitive variables, based on substitution schemes are employed. In this paper; a review of existing procedures is provided, and a new method is proposed. The method is based on the use of primitive variables with periodic boundary conditions combined with the use of slip values. Either pressure difference or mass flow rate may be prescribed, and both constant wall temperature and constant heat flux wall conditions may be considered. The example of an offset-fin plate-fin heat exchanger is used to illustrate the application of the procedure. The scope and limitations of the method are discussed in detail, and the mathematical basis by which the method may be extended to the consideration of problems involving mass transfer, with associated continuity, momentum, and species source/sinks is proposed.