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In this paper, we use a generic and general variational method to obtainsolutions to the flow of generalized Newtonian fluids through circular pipesand plane slits. The new method is not based on the use of the Euler-Lagrangevariational principle and hence it is totally independent of our previousapproach which is based on this principle. Instead, the method applies a verygeneric and general optimization approach which can be justified by theDirichlet principle although this is not the only possible theoreticaljustification. The results that were obtained from the new method using ninetypes of fluid are in total agreement, within certain restrictions, with theresults obtained from the traditional methods of fluid mechanics as well as theresults obtained from the previous variational approach. In addition to being auseful method in its own for resolving the flow field in circular pipes andplane slits, the new variational method lends more support to the oldvariational method as well as for the use of variational principles in generalto resolve the flow of generalized Newtonian fluids and obtain all thequantities of the flow field which include shear stress, local viscosity, rateof strain, speed profile and volumetric flow rate. The theoretical basis of thenew variational method, which rests on the use of the Dirichlet principle, alsoprovides theoretical support to the former variational method.

Variational approach for resolving the flow of generalized Newtonian fluids in circular pipes and plane slits