Heat conduction modelling ........................................................................................................................... 1 Case studies ........................................................................................................................................... 2 Analytical solutions.........................................................................

Heat conduction modelling ........................................................................................................................... 1 Case studies ........................................................................................................................................... 2 Analytical solutions.........................................................................

We look at a basic introduction to classical models of heat conduction, with a few examples including both finite and infinite systems, with techniques appropriate to each based on the boundary and initial conditions. Portions of the paper follow chapter 11 of Theoretical Mechanics of Particles and Continua [1], where I have attempted to expand the analysis in an attempt to provide clarity wher...

Heat conduction modelling ........................................................................................................................... 1 Case studies ........................................................................................................................................... 2 Analytical solutions.........................................................................

This paper addresses the distributed control by input–output linearization of a nonlinear diffusion equation that describes a particular but important class of distributed parameter systems. Both manipulated and controlled variables are assumed to be distributed in space. The control law is designed using the concept of characteristic index from geometric control by using directly the PDE model...

Thermal conduction is an important energy transfer and damping mechanism in astrophysical flows. Fourier’s law, in which the heat flux is proportional to the negative temperature gradient, leading to temperature diffusion, is a well-known empirical model of thermal conduction. However, entropy diffusion has emerged as an alternative thermal conduction model, despite not ensuring the monotonicit...

The deterioration of the performance of a cross flow heat exchanger with condensation due to the longitudinal conduction was investigated. For a relatively small change of wall temperature along the flow directions which was shown to be common in many applications, the energy equations were solved numerically. An iterative method was used to solve the resulting equations of the finite differenc...

The interaction of thermal radiation with conduction and laminar natural convection in a vertical circular pin, situated at participating gas, is numerically investigated. An absorbing and emitting gas is considered, and treated to be a gray participating media. Under the idealizing of gray gas, the Rosselan4 approximation is employed to describe the radiative heat flux in the energy equation. ...

In many magnetized, dilute astrophysical plasmas, thermal conduction occurs almost exclusively parallel to magnetic field lines. In this case, the usual stability criterion for convective stability, the Schwarzschild criterion, which depends on entropy gradients, is modified. In the magnetized long mean free path regime, instability occurs for small wavenumbers when (∂P/∂z)(∂ lnT/∂z) > 0, which...

The process of heat conduction in one-dimensional lattice with on-site potential is studied by means of numerical simulation. Using discrete Frenkel-Kontorova, φ–4 and sinh-Gordon we demonstrate that contrary to previously expressed opinions the sole anharmonicity of the on-site potential is insufficient to ensure the normal heat conductivity in these systems. The character of the heat conducti...