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A mathematical model of heat and mass transport in non-isothermal partially saturated oil-wax solution was formulated by A. Fasano and M. Primicerio [1]. This paper is devoted to the study of a one-dimensional problem in the framework of that model. The existence of classical solutions in a small time interval is proved, based on the application of a fixed-point theorem to the constructed operator. The technique employed is close to the one of [3] and [4].
This paper is devoted to the numerical solution of stationary laminar Bingham fluids by path-following methods. By using duality theory, a system that characterizes the solution of the original problem is derived. Since this system is ill-posed, a family of regularized problems is obtained and the convergence of the regularized solutions to the original one is proved. For the update of the regularization parameter, a path-following method is investigated. Based on the differentiability properties...
This paper is devoted to the numerical solution of stationary
laminar Bingham fluids by path-following methods. By using duality theory, a
system that characterizes the solution of the original problem is derived.
Since this system is ill-posed, a family of regularized problems is obtained
and the convergence of the regularized solutions to the original one is proved.
For the update of the regularization parameter, a path-following method is
investigated. Based on the differentiability properties...
We study the flow of an incompressible homogeneous fluid whose material coefficients depend on the temperature and the shear-rate. For large class of models we establish the existence of a suitable weak solution for two-dimensional flows of fluid in a bounded domain. The proof relies on the reconstruction of the globally integrable pressure, available due to considered Navier’s slip boundary conditions, and on the so-called -truncation method, used to obtain the strong convergence of the velocity...
We consider the flow of a class of incompressible fluids which are constitutively defined by the symmetric part of the velocity gradient being a function, which can be non-monotone, of the deviator of the stress tensor. These models are generalizations of the stress power-law models introduced and studied by J. Málek, V. Průša, K. R. Rajagopal: Generalizations of the Navier-Stokes fluid from a new perspective. Int. J. Eng. Sci. 48 (2010), 1907–1924. We discuss a potential application of the new...
We present an analytical solution of plane motion for a Bingham fluid initially at rest subjected to a suddenly applied constant pressure gradient. Using the Laplace transform we obtain expressions which allow a direct easy calculation of the velocity, of the plug thickness and of the rate of flow as function of time.
Steady-state system of equations for incompressible, possibly non-Newtonean of the -power type, viscous flow coupled with the heat equation is considered in a smooth bounded domain , or 3, with heat sources allowed to have a natural -structure and even to be measures. The existence of a distributional solution is shown by a fixed-point technique for sufficiently small data if (for ) or if (for ).
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