Finite elements numerical solution of a coupled profile–velocity–temperature shallow ice sheet approximation model

AbstractThis work deals with the numerical solution of a complex mathematical model arising in theoretical glaciology. The global moving boundary problem governs thermomechanical processes jointly with ice sheet hydrodynamics. One major novelty is the inclusion of the ice velocity field computation in the framework of the shallow ice model so that it can be coupled with profile and temperature equations. Moreover, the proposed basal velocity and shear stress laws allow the integration of basal sliding effects in the global model. Both features were not taking into account in a previous paper (Math. Model. Methods Appl. Sci. 12 (2) (2002) 229) and provide more realistic convective terms and more complete Signorini boundary conditions for the thermal problem. In the proposed numerical algorithm, one- and two-dimensional piecewise linear Lagrange finite elements in space and a semi-implicit upwinding scheme in time are combined with duality and Newton's methods for nonlinearities. A simulation example involving real data issued from Antarctic shows the temperature, profile and velocity qualitative behaviour as well as the free boundaries and basal effects

A coupled problem of heat and mass transfer applied to porous textile media surrounding the human foot

There have been many attempts in the literature to model human thermoregulation systems in order to predict central temperature and other heat stress indicators (see [3, 9], among many others). These models depend on a wide range of variables, including individual characteristics, surrounding textile and environmental factors. The main objective of this work is to formulate a stable, realistic and versatile 2-D mathematical model describing the heat transfer of the human foot (bare foot and foot surrounded by textile materials). The novelty, but also the difficulty , lies on the theoretical multiphysics that models the textile as a porous media, involving energy transport but also mass transport of liquid water, water vapour and gas, including evaporation phenomena. The numerical solution to the global problem involves a segregated algorithm and fixed point techniques for the nonlinearities jointly with finite elements spatial discretizations. Implementation has been performed through commercial software COMSOL TM Multiphysics

Some aspects of lubrication in heavy regimes: thermal effects, stability and turbulence

In this work, a combination of numerical methods applied to thermohydrodynamic lubrication problems with cavitation is presented. It should be emphasized the difficulty of the nonlinear mathematical coupled model involving a free boundary problem, but also the simplicity of the algorithms employed to solve it. So, finite element discretizations for the hydrodynamic and thermal equations combined with upwind techniques for the convection terms and duality methods for nonlinear features are proposed. Additionally, a model describing the movement of the shaft is provided. Considering the shaft as a rigid body this model will consist of an ODE system relating acceleration of the center of gravity and external and pressure loads. The numerical experiments of mechanical stability try to clarify the position of the neutral stability curve. Finally, a rotating machine for ship propulsion involving both axial and radial bearings operating with nonconventional lubricants (seawater to avoid environmental pollution) is analyzed by using laminar and turbulent inertial flows

Phosphoglycerate mutase, 2,3-bisphosphoglycerate phosphatase, creatine kinase and enolase activity and isoenzymes in breast carcinoma

We have compared the levels of phosphoglycerate mutase (EC 5.4.2.1), 2,3-bisphosphoglycerate phosphatase (EC 3.1.3.13), creatine kinase (EC 2.7.3.2) and enolase (EC 4.2.1.11) activities and the distribution of their isoenzymes in normal breast tissue and in breast carcinoma. Tumour tissue had higher phosphoglycerate mutase and enolase activity than normal tissue. Creatine kinase activity was higher in seven out of 12 tumours. In contrast 2,3-bisphosphoglycerate phosphatase activity was lower. Phosphoglycerate mutase, enolase and 2,3-bisphosphoglycerate phosphatase presented greater changes in the oestrogen receptor-negative/progesterone receptor-negative breast carcinomas than in the steroid receptor-positive tumours. Determined by electrophoresis, type BB phosphoglycerate mutase, type BB creatine kinase and αα-enolase were the major isoenzymes detected in normal breast tissue. Types αγ and γγ enolase, types MB and MM phosphoglycerate mutase were detected in much lower proportions. In tumours a decrease of phosphoglycerate mutase isoenzymes possessing M-type subunit and some increase of enolase isoenzymes possessing γ-type subunit was observed. No detectable change was observed in the creatine kinase phenotype. © 2000 Cancer Research Campaig