# temperatureRelaxation¶

Computes the relaxation of temperature between separate fluid species due to collisions. The term $$Q_{i}$$ below is computed in this source and stored for each input species

The relaxation term is typically added to the energy equation below

$\begin{equation} \frac{\partial e_{i}}{\partial t}+\nabla\cdot\left[U_{i}\cdot\left(e_{i}+P_{i}\right)\right]=Q_{i} \end{equation}$

and has the form

$\begin{equation} Q_{i}=-\sum_{j}3\,k\,n_{i}\left(\frac{\mu_{i\,j}}{m_{i}+m_{j}}\right)\tau_{i\,j}^{-1}\left(T_{i}-T_{j}\right) \end{equation}$

Descriptions of this model can be found in

Zhdanov, Viktor Mikhailovich. “Transport processes in multicomponent plasma.” Plasma Physics and Controlled Fusion 44.10 (2002): 2283.

## Parameters¶

speciesMass (vector float)
The particle mass of each fluid species
isNumberDensity (boolean)
True if the densities being passed in are number densities, false if they are mass densities

## Parent Updater Data¶

in (string vector, required)

1st Variable

1. $$\rho$$ mass density or number density of the first species

2nd Variable

1. $$\rho$$ mass density or number density of the second species

Nth Variable

1. $$\rho$$ mass density or number density of the nth species

(N+1)th Variable

1. $$T$$ temperature of the first species

(N+2)th Variable

1. $$T$$ temperature of the second species

(N+N)th Variable

1. $$T$$ temperature of the Nth species

(2N+1)th Variable

This variable is the collision frequency matrix that can be computed by the source collisionFrequency. The order of species should be the same as provided to collisionFrequency.
out (string vector, required)
There are N outputs each of length 1 corresponding to the energy exchange source term for the 1st through Nth inputs.

## Example¶

<Equation thisGas>
kind = temperatureRelaxation
speciesMass = [ELECTRON_MASS, ION_MASS, ION_MASS]
</Equation>