in this paper the optimal control of boundary heat flux in a 2-d solid body with an arbitrary shape is performed in order to achieve the desired temperature distribution at a given time interval. the boundary of the body is subdivided into a number of components. on each component a time-dependent heat flux is applied which is independent of the others. since the thermophysical properties are t...

We consider a model of heat conduction introduced in [6], which consists of a finite nonlinear chain coupled to two heat reservoirs at different temperatures. We study the low temperature asymptotic behavior of the invariant measure. We show that, in this limit, the invariant measure is characterized by a variational principle. The main technical ingredients are some control theoretic arguments...

One and two phase Stefan problems for the linear heat equation have been the subject of many studies in the past [1, 2]. Indeed these problems have a great physical relevance since they provide a mathematical model for the processes of phase changes [3, 4]. The boundary between the two phases is a free boundary: its motion has to be determined as part of the solution. More recently the previous...

numerical solutions obtained by the meshless local petrov–galerkin (mlpg) method are presented for two-dimensional steady-state heat conduction problems. the mlpg method is a truly meshless approach, and neither the nodal connectivity nor the background mesh is required for solving the initial-boundary-value problem. the penalty method is adopted to efficiently enforce the essential boundary co...

We use equations similar to the heat conduction equation to calulate heat transfer, radiation transfer and hydrostatical equilibrium in our stellar evolution programs. We tried various numerical schemes and found that the most convenient scheme for complicated calculations (nonlinear, multidimensional calculations) is a symmetrical semi-implicit (SSI) scheme. The (SSI) scheme is easy to code, v...

Generalized thermoelastic models have been developed with the aim of eliminating the contradiction in the infinite velocity of heat propagation inherent in the classical dynamical coupled thermoelasticity theory. In these generalized models, the basic equations include thermal relaxation times and they are of hyperbolic type. Furthermore, Tzou established the dual-phase-lag heat conduction theo...

0

A flexible solution method for the initial-boundary value problem of the temperature field in a one-dimensional domain of a solid with significantly nonlinear material parameters and radiation boundary conditions is proposed. A transformation of the temperature values allows to isolate the nonlinear material characteristics into a single coefficient of the heat conduction equation. The Galerkin...