#
# Standard thermal parameters
#
import pybamm
from .base_parameters import BaseParameters
[docs]
class ThermalParameters(BaseParameters):
"""
Standard thermal parameters
"""
def __init__(self):
# Get geometric parameters
self.geo = pybamm.geometric_parameters
self.n = DomainThermalParameters("negative", self)
self.s = DomainThermalParameters("separator", self)
self.p = DomainThermalParameters("positive", self)
self.domain_params = {
"negative": self.n,
"separator": self.s,
"positive": self.p,
}
# Set parameters
self._set_parameters()
def _set_parameters(self):
"""Defines the dimensional parameters"""
for domain in self.domain_params.values():
domain._set_parameters()
# Reference temperature
self.T_ref = pybamm.Parameter("Reference temperature [K]")
# Cooling coefficient
self.h_total = pybamm.Parameter("Total heat transfer coefficient [W.m-2.K-1]")
# Initial temperature
self.T_init = pybamm.Parameter("Initial temperature [K]")
def T_amb(self, y, z, t):
"""Ambient temperature [K]"""
return pybamm.FunctionParameter(
"Ambient temperature [K]",
{
"Distance across electrode width [m]": y,
"Distance across electrode height [m]": z,
"Time [s]": t,
},
)
def T_amb_av(self, t):
"""YZ-averaged ambient temperature [K]"""
y = pybamm.standard_spatial_vars.y
z = pybamm.standard_spatial_vars.z
return pybamm.yz_average(self.T_amb(y, z, t))
def h_edge(self, y, z):
"""Cell edge heat transfer coefficient [W.m-2.K-1]"""
inputs = {
"Distance along electrode width [m]": y,
"Distance along electrode height [m]": z,
}
return pybamm.FunctionParameter(
"Edge heat transfer coefficient [W.m-2.K-1]",
inputs,
)
def rho_c_p_eff(self, T):
"""Effective volumetric heat capacity [J.m-3.K-1]"""
return (
self.n.rho_c_p_cc(T) * self.geo.n.L_cc
+ self.n.rho_c_p(T) * self.geo.n.L
+ self.s.rho_c_p(T) * self.geo.s.L
+ self.p.rho_c_p(T) * self.geo.p.L
+ self.p.rho_c_p_cc(T) * self.geo.p.L_cc
) / self.geo.L
def lambda_eff(self, T):
"""Effective thermal conductivity [W.m-1.K-1]"""
return (
self.n.lambda_cc(T) * self.geo.n.L_cc
+ self.n.lambda_(T) * self.geo.n.L
+ self.s.lambda_(T) * self.geo.s.L
+ self.p.lambda_(T) * self.geo.p.L
+ self.p.lambda_cc(T) * self.geo.p.L_cc
) / self.geo.L
class DomainThermalParameters(BaseParameters):
def __init__(self, domain, main_param):
self.domain = domain
self.main_param = main_param
def _set_parameters(self):
Domain = self.domain.capitalize()
self.h_tab = pybamm.Parameter(
f"{Domain} tab heat transfer coefficient [W.m-2.K-1]"
)
def h_cc(self, y, z):
"""Current collector surface heat transfer coefficient [W.m-2.K-1]"""
inputs = {
"Distance across electrode width [m]": y,
"Distance across electrode height [m]": z,
}
Domain = self.domain.capitalize()
return pybamm.FunctionParameter(
f"{Domain} current collector surface heat transfer coefficient "
"[W.m-2.K-1]",
inputs,
)
def c_p(self, T):
"""Electrode specific heat capacity [J.kg-1.K-1]"""
inputs = {"Temperature [K]": T}
if self.domain == "separator":
name = "Separator specific heat capacity [J.kg-1.K-1]"
else:
Domain = self.domain.capitalize()
name = f"{Domain} electrode specific heat capacity [J.kg-1.K-1]"
return pybamm.FunctionParameter(name, inputs)
def c_p_cc(self, T):
"""Current collector specific heat capacity [J.kg-1.K-1]"""
inputs = {"Temperature [K]": T}
Domain = self.domain.capitalize()
return pybamm.FunctionParameter(
f"{Domain} current collector specific heat capacity [J.kg-1.K-1]",
inputs,
)
def lambda_(self, T):
"""Electrode thermal conductivity [W.m-1.K-1]"""
inputs = {"Temperature [K]": T}
if self.domain == "separator":
name = "Separator thermal conductivity [W.m-1.K-1]"
else:
Domain = self.domain.capitalize()
name = f"{Domain} electrode thermal conductivity [W.m-1.K-1]"
return pybamm.FunctionParameter(name, inputs)
def lambda_cc(self, T):
"""Current collector thermal conductivity [W.m-1.K-1]"""
inputs = {"Temperature [K]": T}
Domain = self.domain.capitalize()
return pybamm.FunctionParameter(
f"{Domain} current collector thermal conductivity [W.m-1.K-1]", inputs
)
def rho(self, T):
"""Electrode density [kg.m-3]"""
inputs = {"Temperature [K]": T}
if self.domain == "separator":
name = "Separator density [kg.m-3]"
else:
Domain = self.domain.capitalize()
name = f"{Domain} electrode density [kg.m-3]"
return pybamm.FunctionParameter(name, inputs)
def rho_cc(self, T):
"""Current collector density [kg.m-3]"""
inputs = {"Temperature [K]": T}
Domain = self.domain.capitalize()
return pybamm.FunctionParameter(
f"{Domain} current collector density [kg.m-3]", inputs
)
def rho_c_p(self, T):
return self.rho(T) * self.c_p(T)
def rho_c_p_cc(self, T):
return self.rho_cc(T) * self.c_p_cc(T)
thermal_parameters = ThermalParameters()
