Energy equation in nanoFluidX is implemented so that it accommodates
for conduction and convection heat transfer with initial or Dirichlet boundary
conditions.
The rate of temperature change of a specific material is given by:
(1)
With
t being time,
T being the temperature,
k the coefficient of thermal conductivity, ρ
the density and
cp the specific heat
capacity of the material. In SPH form the above analytic expression becomes
(2)
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
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.
Finally, we set up the phase parameters, which are: initial temperature
(
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].
Note: Regarding the
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.