# Energy Equation

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

_{p}the specific heat capacity of the material. In SPH form the above analytic expression becomes

Where, the indices i and j standing for so called ‘owner’ and ‘neighboring’ particles respectively, and the 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 nis the unit coordinate vector.

If one would like to use the energy transport option, he needs to turn the feature ON
by setting the `energy_transport` flag in Simulation parameters to
true. Once this step is completed, the user can opt for desired output, which can be
either temperature or rate of temperature change (flux). Keep in mind that 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.