Luisa Consiglieri

Theoretical analysis of the heat convection coefficient in large vessels and the significance for thermal ablative therapies.

Ablative therapies such as radio-frequency (RF) ablation are increasingly used for treatment of tumours in liver and other organs. Often large vessels limit the extent of the thermal lesion, and cancer cells close to the vessel survive resulting in local tumour recurrence. Accurate estimates of the heat convection coefficient h for large vessels will help improve ablation techniques, and are required for estimation of thermal lesion dimensions in simulations. Previous estimates of h did not consider that only part of the vessel is heated, and assumed uniform temperature distribution at the vessel wall. An analytical relationship between the heat convection coefficient, blood velocity and temperature is formulated. The heat convection coefficient evaluated will assist both simulations and design of proper protocols for in vivo measurements. The mathematical model developed in this work describes the exchange of heat between a solid surface and a moving fluid and it is based on energy and motion equations for Navier-Stokes fluids. A particular case of a laminar blood flow in the portal vein is studied when a portion of its surface is heated. The results show that heating a larger portion of the vessels reduces convective heat loss, which may result in more effective ablation strategies.

Weak Solutions for a Class of Non-Newtonian Fluids with Energy Transfer

Abstract. In the present paper, we shall consider a nonlinear thermoconvection problem consisting of a coupled system of nonlinear partial differential equations due to temperature dependent coefficients. We prove that weak solutions exist in appropriate Sobolev spaces under mild hypothesis on the regularity of the data. This result is established through a fixed point theorem for multivalued functions, which requires a detailed analysis of the continuous dependence of auxiliary problems, including the associated Lagrange multipliers of the generalized Navier—Stokes system.

Stationary weak solutions for a class of non-Newtonian fluids with energy transfer

Abstract We prove the existence of weak solutions to the coupled system of stationary equations for a class of general non-Newtonian fluids with energy transfer. In particular, we may include Bingham flows that lead to classical free boundary problems of fluid dynamics. Using convex analysis and L1-theory for elliptic mixed boundary value problems, we consider separately two auxiliary problems, obtained by prescribing the essential non-linearities in the equations for the velocity and for the energy. We use then a general fixed point theorem, due to Glicksberg, for the multivalued mapping in a product of Banach spaces endowed with the weak topologies.

Regularity of Stationary Weak Solutions in the Theory of Generalized Newtonian Fluids with Energy Transfer

In this paper, we prove regularity results for weak solutions to some stationary problems arising in the theory of generalized Newtonian fluids with energy transfer. Namely, we prove that these solutions are strong. In the two-dimensional case, we prove the Hölder continuity of the first gradient of a solution. Bibliography: 30 titles.

An analytical model for the ergometer rowing: inverse multibody dynamics analysis

A model for the ergometer rowing exercise is presented in this paper. From the quantitative observations of a particular trajectory (motion), the model is used to determine the moment of the forces produced by the muscles about each joint. These forces are evaluated according to the continuous system of equations of motion. An inverse dynamics analysis is performed in order to predict the joint torques developed by the muscles during the execution of the task. An elementary multibody mechanical system is used as an example to discuss the assumptions and procedures adopted.

Explicit Estimates for Solutions of Mixed Elliptic Problems

We deal with the existence of quantitative estimates for solutions of mixed problems to an elliptic second-order equation in divergence form with discontinuous coefficients. Our concern is to estimate the solutions with explicit constants, for domains in () of class . The existence of and estimates is assured for and any (depending on the data), whenever the coefficient is only measurable and bounded. The proof method of the quantitative estimates is based on the De Giorgi technique developed by Stampacchia. By using the potential theory, we derive estimates for different ranges of the exponent depending on the fact that the coefficient is either Dini-continuous or only measurable and bounded. In this process, we establish new existences of Green functions on such domains. The last but not least concern is to unify (whenever possible) the proofs of the estimates to the extreme Dirichlet and Neumann cases of the mixed problem.

A limit model for thermoelectric equations

We analyze the asymptotic behavior corresponding to the arbitrary high conductivity of the heat in the thermoelectric devices. This work deals with a steady-state multidimensional thermistor problem, considering the Joule effect and both spatial and temperature dependent transport coefficients under some real boundary conditions in accordance with the Seebeck–Peltier–Thomson cross-effects. Our first purpose is that the existence of a weak solution holds true under minimal assumptions on the data, as in particular nonsmooth domains. Two existence results are studied under different assumptions on the electrical conductivity. Their proofs are based on a fixed point argument, compactness methods, and existence and regularity theory for elliptic scalar equations. The second purpose is to show the existence of a limit model illustrating the asymptotic situation.

PARTIAL REGULARITY FOR THE NAVIER-STOKES-FOURIER SYSTEM

This paper addresses a nonstationary flow of heat-conductive incompressible Newtonian fluid with temperature-dependent viscosity coupled with linear heat transfer with advection and a viscous heat source term, under Navier/Dirichlet boundary conditions. The partial regularity for the velocity of the fluid is proved for each proper weak solution, that is, for such weak solutions which satisfy some local energy estimates in a similar way to the suitable weak solutions of the Navier-Stokes system. Finally, we study the nature of the set of points in space and time upon which proper weak solutions could be singular.

Radiative effects for some bidimensional thermoelectric problems

Abstract There are two main objectives in this paper. One is to find sufficient conditions to ensure the existence of weak solutions for some bidimensional thermoelectric problems. At the steady-state, these problems consist of a coupled system of elliptic equations of the divergence form, commonly accomplished with nonlinear radiation-type conditions on at least a nonempty part of the boundary of a C 1

Explicit estimates for solutions of nonlinear radiation-type problems

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