  The Graetz problem is a convection-diffusion equation in a pipe invariant
along a direction. The contribution of the present work is to propose a
mathematical analysis of the Neumann, Robin and periodic boundary condition on
the boundary of a semi-infinite pipe. The solution in the 3D space of the
original problem is reduced to eigenproblems in the 2D section of the pipe. The
set of solutions is described, its structure depends on the type of boundary
condition and of the sign of the total flow of the fluid. This analysis is the
cornerstone of numerical methods to solve Graetz problem in finite pipes, semi
infinite pipes and exchangers of arbitrary cross section. Numerical test-cases
illustrate the capabilities of these methods to provide solutions in various
configurations.
