Artículos (Matemática Aplicada I)https://hdl.handle.net/11441/108942019-09-17T20:47:36Z2019-09-17T20:47:36ZSteel heat treating: Mathematical modelling and numerical simulation of a problem arising in the automotive industryhttps://hdl.handle.net/11441/891432019-09-16T09:55:31Z2017-01-01T00:00:00ZSteel heat treating: Mathematical modelling and numerical simulation of a problem arising in the automotive industry
We describe a mathematical model for the industrial heating and cooling processes of a steel workpiece representing the steering rack of an automobile. The goal of steel heat treating is to provide a hardened surface on critical parts of the workpiece while keeping the rest soft and ductile in order to reduce fatigue. The high hardness is due to the phase transformation of steel accompanying the rapid cooling. This work takes into account both heating-cooling stage and viscoplastic model. Once the general mathematical formulation is derived, we can perform some numerical simulations.
2017-01-01T00:00:00ZThe thermistor problem with degenerate thermal conductivity and metallic conductionhttps://hdl.handle.net/11441/891202019-09-13T10:22:14Z2007-01-01T00:00:00ZThe thermistor problem with degenerate thermal conductivity and metallic conduction
The aim of this work is to establish the existence of a capacity solution
to the thermistor problem supposing that the thermal and the electrical
conductivities are not bounded below by a positive constant value. Furthermore,
the thermal conductivity vanishes at points where the temperature is
null. These assumptions on data include the case of practical interest of the
Wiedemann–Franz law with metallic conduction and lead us to very complex
mathematical situations.
2007-01-01T00:00:00ZRenormalized Solutions to a Nonlinear Parabolic-Elliptic Systemhttps://hdl.handle.net/11441/891182019-09-13T09:23:33Z2005-01-01T00:00:00ZRenormalized Solutions to a Nonlinear Parabolic-Elliptic System
The aim of this paper is to show the existence of renormalized solutions to a parabolicelliptic
system with unbounded diffusion coefficients. This system may be regarded as a modified
version of the well-known thermistor problem; in this case, the unknowns are the temperature in a
conductor and the electrical potential.
2005-01-01T00:00:00ZOn certain doubly non-uniformly and singular non-uniformly elliptic systemshttps://hdl.handle.net/11441/891172019-09-13T09:09:25Z2003-09-01T00:00:00ZOn certain doubly non-uniformly and singular non-uniformly elliptic systems
We consider the steady state of the thermistor problem consisting of a coupled set of nonlinear elliptic equations governing the temperature and the electric potential. We study the existence of weak solutions under two kind of assumptions. The first one considers the case in which the two diffusion coefficients are not bounded below far from zero, arising to a doubly non-uniformly elliptic system. In the second one, we assume in addition that the thermal conductivity blows up for a finite value of the temperature, arising to a singular and non-uniformly coupled system.
2003-09-01T00:00:00Z