2.1.3. Boundary Conditions and the Complete System of Linear Equations

Up to this point, every equation was simply describing some relationship between the node temperatures. For a steady state problem to be completely specified, some temperatures must be known. However, let us first analyze the number of equations available thus far. For a fluid flow system with *n* edges and *m* inflow streams, there are 2*n* unknown temperatures. We can get *n* equations from the heat transfer. The following *n* − *m* equations can be obtained from stream mixing in the nodes. The remaining *m* equations must be provided via boundary conditions, i.e., inlet temperatures must be specified for each of the inflow stream (other arrangements may be possible in selected cases). When there are multiple fluid flow systems connected by heat transfer equations, the number of available equations remains the same.
