# Input Instructions for Thermal Analysis

## Thermal Commands

The following commands are provided to run thermal problems. There is no thermal command. The commands used for thermal analysis take the form of thermal-related keywords on the commands used for standard mechanical analysis. The command model configure thermal must be the first thermal command given before any other commands for thermal analysis are issued. model configure thermal can be specified at any stage of a FLAC3D analysis.

## Thermal FISH Variables

The following scalar variables are available in a FISH function to assist with thermal analysis.

 gp.temp gp.temp.fix gp.temp.source zone.flux zone.thermal.model zone.thermal.prop zone.thermal.ratio zone.thermal.time.total zone.thermal.timestep

## Zone-Based Temperature

A feature that allows you to set zone-based temperature using FISH has been added to FLAC3D. This allows for the rapid import of temperatures from an external source. The stress increment resulting from this zone based temperature change is also incorporated. This feature has been implemented strictly for calculating mechanical changes to a model that result from changes in temperature in a zone. Thermal mode should not to be active in FLAC3D when this zone-based temperature feature is active.

This feature assumes that FLAC3D is configured for thermal calculations (model configure thermal) and that thermal calculations are set to off (zone thermal active off).

Zone-based temperatures are stored in a “thermal-zone” which is enabled by the model configure thermal command. The stress change generated by a change in zone-based temperature is determined by the following equations:

(1)$\begin{split}\begin{matrix} \sigma_{11}^{new} = \sigma_{11}^{old} - 3K \alpha_t \Delta T \\ \\ \sigma_{22}^{new} = \sigma_{22}^{old} - 3K \alpha_t \Delta T \\ \\ \sigma_{33}^{new} = \sigma_{33}^{old} - 3K \alpha_t \Delta T \\ \end{matrix}\end{split}$

where $$K$$ is the bulk modulus of the zone, and $$\alpha_t$$ is the linear thermal expansion coefficient of the zone.

The command to signal the use of zone-based temperature to FLAC3D is zone thermal zone-based-temperature on. When this command is used, then the FISH function zone.temp will allow you to retrieve and assign temperature to a zone. Note that when zone thermal zone-based-temperature on, FLAC3D keeps track of the last two temperatures that were assigned to this zone with the zone.temp function. This allows the computation of a temperature change ($$\Delta T = T^{new} - T^{old}$$). Each time a temperature is assigned to a zone with the zone.temp function the previously stored temperature becomes $$T^{old}$$ and the newly assigned temperature becomes $$T^{new}$$.

If zone thermal zone-based-temperature is initially set to off, FLAC3D will use gridpoint-based temperatures in its calculations (this is FLAC3D’s default mode). If a zone thermal zone-based-temperature on command is encountered, it automatically initializes the zone-based temperature (both $$T^{new}$$ and $$T^{old}$$) with the average gridpoint-based temperatures. This method also establishes the baseline temperatures in the zones. If zone thermal zone-based-temperature was on and a zone thermal zone-based-temperature off command is issued, then the zone-based temperatures are not used to initialize the gridpoint-based temperatures with the zone-based temperatures.

The commands zone gridpoint fix temperature and zone gridpoint initialize temperature do not alter the zone-based temperatures. They only work with gridpoint-related quantities. Plotting “Zone -> Color by Contour -> Value: Temperature” shows only gridpoint-related quantities. Instead, the zone-based temperature can be stored in zone.extra and then can be plotted through “Zone -> Color by Contour -> Extra; Source Zone”.

The following is one modeling sequence demonstrating the use of this feature.

1. Create your model geometry (zones) — remembering model configure thermal.
2. Assign mechanical model and properties to zones.
3. Assign thermal model and linear expansion coefficient to zones.
4. zone thermal active is set to off; zone mechanical active is set to on and zone thermal zone-based-temperature is set to on
5. Assign a baseline temperature to each zone. Use the zone.temp function to do this.
6. Assign updated temperature to each zone. Use the zone.temp function to do this.
7. Solve to mechanical equilibrium.

This is similar to the zone-based pore pressure. The counterparts are summarized below.

Table 3: Zone-Based Pore Pressure and Temperature
Zone-Based Pore Pressure Zone-Based Temperature
Configure model configure fluid model configure thermal
On zone fluid zone-based-pp on zone thermal zone-based-temperature on
Off zone fluid zone-based-pp off zone thermal zone-based-temperature off
FISH zone.pp zone.temp