  Several deterministic and stochastic multi-variable global optimization
algorithms (Conjugate Gradient, Nelder-Mead, Quasi-Newton, and Global) are
investigated in conjunction with energy minimization principle to resolve the
pressure and volumetric flow rate fields in single ducts and networks of
interconnected ducts. The algorithms are tested with seven types of fluid:
Newtonian, power law, Bingham, Herschel-Bulkley, Ellis, Ree-Eyring and Casson.
The results obtained from all those algorithms for all these types of fluid
agree very well with the analytically derived solutions as obtained from the
traditional methods which are based on the conservation principles and fluid
constitutive relations. The results confirm and generalize the findings of our
previous investigations that the energy minimization principle is at the heart
of the flow dynamics systems. The investigation also enriches the methods of
Computational Fluid Dynamics for solving the flow fields in tubes and networks
for various types of Newtonian and non-Newtonian fluids.
