# -*- coding: utf-8 -*-
"""
This file is part of FElupe.
FElupe is free software: you can redistribute it and/or modify
it under the terms of the GNU General Public License as published by
the Free Software Foundation, either version 3 of the License, or
(at your option) any later version.
FElupe is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
GNU General Public License for more details.
You should have received a copy of the GNU General Public License
along with FElupe. If not, see <http://www.gnu.org/licenses/>.
"""
import numpy as np
from scipy.sparse import csr_matrix
from ..assembly import IntegralForm
from ..mechanics import Assemble, Results
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class SolidBodyHeatFlux:
r"""A thermal heat flux boundary condition for a thermal solid body.
Parameters
----------
field : felupe.FieldContainer
Field container with the temperature as first field.
coefficient : float
Heat flux per unit area or volume :math:`q` in W/m^2 or W/m^3.
Notes
-----
This class represents a thermal heat flux boundary condition for a thermal solid
body, which is used to model heat flux in or on the surface of a solid material.
The heat flux coefficient is used to calculate the heat flux.
Examples
--------
This class can be used to model a heat flux on a surface of a thermal solid body.
Here, the heat flux is applied on the right end face of a rectangular domain, while
the left end face is kept at a constant temperature.
.. pyvista-plot::
:force_static:
>>> import felupe as fem
>>>
>>> mesh = fem.Rectangle(n=11)
>>> region = fem.RegionQuad(mesh)
>>> temperature = fem.Field(region, dim=1)
>>> field = fem.FieldContainer([temperature])
>>>
>>> region_flux = fem.RegionQuadBoundary(mesh, mask=mesh.x == 1.0)
>>> temperature_flux = fem.Field(region_flux, dim=1)
>>> field_flux = fem.FieldContainer([temperature_flux])
>>>
>>> boundaries = fem.BoundaryDict(
... left=fem.Boundary(temperature, fx=0),
... )
>>>
>>> solid = fem.thermal.SolidBodyThermal(
... field=field,
... mass_density=1.0, # kg/m^3
... specific_heat_capacity=1.0, # J / (kg K)
... time_step=0.01, # s
... thermal_conductivity=1.0, # W / (m K)
... )
>>> heat_flux = fem.thermal.SolidBodyHeatFlux(
... field=field_flux,
... heat_flux=1.0, # W / m^2
... )
>>> time = fem.thermal.TimeStep([solid])
>>> table = fem.math.linsteps([0, 1], num=10)
>>> ramp = {
... time: 0.1 * table,
... heat_flux: 10 * table,
... }
>>> step = fem.Step(
... items=[time, solid, heat_flux], ramp=ramp, boundaries=boundaries
... )
>>> job = fem.Job(steps=[step]).evaluate()
>>>
>>> mesh.view(
... point_data={"Temperature in °C": temperature.values}
... ).plot("Temperature in °C").show()
It is also possible to model a heat flux in the volume of a thermal solid body,
or in other words, a volumetric heat source / heat sink.
.. pyvista-plot::
:force_static:
>>> import felupe as fem
>>>
>>> mesh = fem.Rectangle(n=11)
>>> region = fem.RegionQuad(mesh)
>>> temperature = fem.Field(region, dim=1)
>>> field = fem.FieldContainer([temperature])
>>>
>>> boundaries = fem.BoundaryDict(
... left=fem.Boundary(temperature, fx=0),
... right=fem.Boundary(temperature, fx=1),
... bottom=fem.Boundary(temperature, fy=0),
... top=fem.Boundary(temperature, fy=1),
... )
>>>
>>> solid = fem.thermal.SolidBodyThermal(
... field=field,
... mass_density=1.0, # kg / m^3
... specific_heat_capacity=1.0, # J / (kg K)
... time_step=0.01, # s
... thermal_conductivity=1.0, # W / (m K)
... )
>>> heat_flux = fem.thermal.SolidBodyHeatFlux(
... field=field,
... heat_flux=1.0, # W / m^3
... )
>>> time = fem.thermal.TimeStep([solid])
>>> table = fem.math.linsteps([0, 1], num=10)
>>> ramp = {
... time: 0.1 * table,
... heat_flux: -10 * table, # heat source
... }
>>> step = fem.Step(
... items=[time, solid, heat_flux], ramp=ramp, boundaries=boundaries
... )
>>> job = fem.Job(steps=[step]).evaluate()
>>>
>>> mesh.view(
... point_data={"Temperature in °C": temperature.values}
... ).plot("Temperature in °C").show()
See Also
--------
felupe.thermal.TimeStep : A time step item.
felupe.thermal.SolidBodyThermal : A thermal solid body for heat conduction.
"""
def __init__(self, field, heat_flux=None):
self.field = field
self.time_step = None
self.assemble = Assemble(vector=self._vector, matrix=None, multiplier=-1.0)
self.results = Results()
if heat_flux is not None:
self.results.heat_flux = heat_flux
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def update(self, heat_flux):
self.results.heat_flux = heat_flux
def _vector(self, field=None, **kwargs):
if field is not None:
self.field = field
if self.time_step is not None and self.time_step == 0: # inactive time step
return csr_matrix(([0.0], ([0], [0])), shape=(1, 1))
fun = [-self.results.heat_flux * np.ones((1, 1))]
self.results.force = IntegralForm(
fun=fun, v=self.field, dV=self.field.region.dV, grad_v=[False]
).assemble(**kwargs)
return self.results.force
