Abstract
In this article we challenge the claim that the previously proposed variational method to obtain flow solutions for generalized Newtonian fluids in circular tubes and plane slits is exact only for power law fluids. We also defend the theoretical foundation and formalism of the method which is based on minimizing the total stress through the application of the Euler-Lagrange principle.
Highlights
∂r dr where r is the tube radius, μ is the generalized Newtonian viscosity and γ is the rate of strain
The failure of a particular formulation does not mean a failure of the variational principle on which it is based because the failure of the former may be caused by mathematical technicalities and not necessarily by the failure of the working principle
We believe that it can be established independently by a physical argument based on the linearity of the stress function in the investigated 1D flow systems, i.e. circular pipes and plane slits
Summary
∂r dr where r is the tube radius, μ is the generalized Newtonian viscosity and γ is the rate of strain. In [2] the Dirichlet-based variational approach was formulated in a more general way to provide exact solutions, considering its numerical nature, even for viscoplastic fluids.
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