# Energy Equation

Energy equation in nanoFluidX is implemented so that it accommodates for conduction and convection heat transfer with initial or Dirichlet boundary conditions.

Where, the indices $i$ and $j$ standing for so called owner and neighboring particles respectively, and the $\mathrm{ij}$ index is a difference between the respective variables of particle $i$ and particle $j$ . The $m$ stands for mass of the particle, the $\nabla W$ is the gradient of the kernel, $r$ is the position vector and $n$ is the unit coordinate vector.

If you want to use the energy transport option, you need to turn the feature on by
setting the `energy_transport` flag in Simulation parameters to
true. Once this step is completed, you can opt for desired output, which can be
either temperature or rate of temperature change (flux). The code will not work if
an output is required and the energy transport flag is turned off.

`temp_0`) in [K], evolve temperature flag (

`evolve_temp`), specific heat capacity of the material (

`heat_cap`) in [J/kg/K] and heat conduction coefficient of the material (

`heat_cond`) in [W/m/K].

`evolve_temp`flag, this parameter is valid only for WALL or MOVINGWALL phases. If the

`evolve_temp`flag is set to false, or if it is not defined (default is false), the set initial temperature will remain constant throughout the simulation. If set to true, the initial temperature will evolve in time and the temperature of the WALL or MOVINGWALL will be influenced by any surrounding phase. For FLUID phases, the temperature always evolves.