Laminar flow inside a circular duct of variable section in the axial direction is modeled, assuming that the working fluid is Newtonian, incompressible, with laminar flow, a permanent state, and constant properties. The results describe the behavior of the stream function, the velocity field, and the pressure field, and graphic results are presented for each of those functions. The method used to solve the problem makes use of regular perturbations around the shape factor ε parameter. This research can be used for the design of new technological devices important to industry, optimizing processes in which fluids are transported, energy is transferred, etc.

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