thermal

Description

This is the basic thermal behavior. The conductivity is determined using a CONDUCTIVITY object. Transient thermal problems require that a coefficient capacity be defined as well (global behavior coefficient, see capacity).

The behavior calculates the heat flux from the gradient in temperature:

(320)\[\vect{q} = \bf k \nabla T\]

The enthalpy term is

(321)\[dH = \int_{T0}^T C_p(\tau) d\tau\]

where the integration will be carried out numerically if the heat capacity depends on the temperature.

Syntax

***behavior thermal \(~\,\) **conductivity CONDUCTIVITY \(~\,\) **coefficient \(~\,~\,~\,~\,\) capacity val

Note that capacity and the coefficients in the conductivity object can be a variable coefficients (e.g. tables, functions, etc) of the temperature variable. This gives the model the possibility of including considerable non-linear effects.

Stored Variables

The grad variable is the gradient of temperature, and the flux is the heat flux.

prefix	size	description	default
dT	V	gradient of temperature	yes
q	V	heat flux	yes
temperature	S	the temperature at the Gauss point	yes

Example

Two examples of thermal behavior follow:

***behavior thermal
 **conductivity isotropic
   k  48.822
 **coefficient
   capacity 4.8168e6
***return

***behavior thermal
**conductivity isotropic
k temperature
0.1   0.0
0.6    500.0
***return