modelFixed

Fixed properties
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Extends from Solid (Base model for an inert, stationary solid).

Information

Assumptions:

  1. The thermal independity and thermal resistivity are fixed (e.g., independent of thermodynamic state).
  2. The specific heat capacity is independent of temperature.
  3. Mobility is zero.

The default isobaric specific heat capacity (via bc = [935*U.J*Data.m/(U.kg*U.K)]) and thermal resistivity (θ = U.m*U.K/(11.1*U.W)) are for graphite fiber epoxy (25% vol) composite (with heat flow parallel to the fibers) at 300 K [Incropera2002, p. 909]. The integration offset for specific entropy is set such that the specific entropy is 154.663 J/(mol·K) at 25 °C and po (1 atm). This is the value from Table B in [McBride2002]. Additional thermal data is listed in Table 1.

Table 1: Properties of forms of C [Incropera2002, p. 909].
T
/U.K		 Diamond (type IIa) Amorphous
carbon		 Graphite (pyrolytic) Graphite fiber epoxy (25% vol)
composite
cp*U.kg
*U.K
/(U.J
*Data.m)		 θ
*U.W
/(U.m
*U.K)		 θ
*U.W
/(U.m
*U.K)		 cp*U.kg
*U.W
/(U.J
*Data.m)		 θ*U.W/(U.m*U.K) cp*U.kg
*U.K
/(U.J
*Data.m)		 θ*U.W/(U.m*U.K)
Parallel
to layers		 Perpendicular
to layers		 Parallel
to layers		 Perpendicular
to layers
100211/100001/0.671361/49701/16.83371/5.71/0.46
2001941/40001/1.184111/32301/9.236421/8.71/0.68
3005091/23001/1.897091/19501/5.709351/11.11/0.87
4008531/15401/2.199921/13901/4.0912161/13.01/1.1
600--1/2.3714061/8921/2.68---
800--1/2.5316501/6671/2.01---
1000--1/2.8417931/5341/1.60---
1200--1/3.4818901/4481/1.34---
1500---19741/3571/1.08---
2000---20431/2621/0.81---

For more information, please see the Species model.

Parameters

TypeNameDefaultDescription
Integern_intra (from Species)0Number of exchange connections within the phase
Integern_inter (from Species)0Number of exchange connections with other phases
Geometry
Q.NumberAbsoluteepsilon (from Solid)0.25Volumetric fill fraction
Q.Length[:]kL (from Solid)L[cartTrans]Effective transport length
Assumptions
Integern_trans (from Species)1Number of transport axes
Initialization
Q.AmountN_IC (from Species)Initial amount of material
Q.Densityrho_IC (from Species)Initial density
Q.VolumeV_IC (from Species)Initial volume
Q.PressureAbsolutep_IC (from Species)Initial pressure
Q.TemperatureAbsoluteT_IC (from Species)Initial temperature
Q.Potentialh_IC (from Species)Initial specific enthalpy
Q.Potentialg_IC (from Species)Initial Gibbs potential
Independence factors
Q.NumberAbsolute[n_intra,n_trans]k_intra_Phi (from Species)ones(n_intra, n_trans)For translational exchange among species within the phase
Q.NumberAbsolute[n_intra]k_intra_Q (from Species)ones(n_intra)For thermal exchange among species within the phase
Assumptions › Formulation of the conservation equations
ConsThermoconsEnergy (from Solid)ConsThermo.dynamicEnergy

Connectors

TypeNameDefaultDescription
Connectors.Intra[n_intra]intra (from Species)Connectors to exchange translational momentum and energy within the phase
Connectors.Inter[n_inter]inter (from Species)Connectors to exchange translational momentum and energy with all other species
Connectors.Daltondalton (from Species)Connector for additivity of pressure
Connectors.ThermalDiffusive[n_trans,Side]boundaries (from Solid)Connectors for transport

Components

TypeNameDefaultDescription
Q.Mobilitymu (from Species)Data.mu(T, v)Mobility
Q.TimeAbsolutenu (from Species)Data.nu(T, v)Thermal independity
Q.AmountN (from Species)Amount of material
Q.TemperatureAbsoluteT (from Species)Temperature
Q.Velocity[n_trans]phi (from Species)Velocity
Q.PressureAbsolutep (from Species)Pressure
Q.Potentialg (from Species)Specific Gibbs energy
Q.MassM (from Species)Mass
Q.VolumeSpecificv (from Species)Specific volume
Q.Potentialh (from Species)Specific enthalpy
Q.NumberAbsolutes (from Species)Specific entropy
Q.Densityrho (from Species)1/vDensity
Q.MassVolumicmrho (from Species)Data.m*rhoVolumic mass
Q.AmountS (from Species)N*sEntropy
Q.CapacityThermalSpecificc_p (from Species)Data.c_p(T, p)Isobaric specific heat capacity
Q.CapacityThermalSpecificc_v (from Species)Data.c_v(T, p)Isochoric specific heat capacity
Q.PressureReciprocalbeta (from Species)Data.beta(T, p)Isothermal compressibility
Q.TimeAbsolute[n_intra,n_trans]tau_PhiE_intra (from Species){Data.m*mu*k_intra_Phi[i, :] for i in 1:n_intra}Time constants for translational intra-phase exchange
Q.TimeAbsolute[n_inter,n_trans]tau_PhiE_inter (from Species){Data.m*mu*k_inter_Phi[i, :] for i in 1:n_inter}Time constants for translational inter-phase exchange
Q.TimeAbsolute[n_intra]tau_QE_intra (from Species)c_p*nu*k_intra_QTime constants for thermal intra-phase exchange
Q.TimeAbsolute[n_inter]tau_QE_inter (from Species)c_p*nu*k_inter_QTime constants for thermal inter-phase exchange
Q.Force[n_trans]f_DE (from Species)sum(intra[i].mPhidot for i in 1:n_intra) + sum(inter[i].mPhidot for i in 1:n_inter)Friction from other configurations (diffusive exchange)
Q.PowerEdot_DE (from Species)sum(intra[i].phi*intra[i].mPhidot for i in 1:n_intra) + sum(inter[i].phi*inter[i].mPhidot for i in 1:n_inter) + sum(intra.Qdot) + sum(inter.Qdot)Rate of diffusion of energy from other configurations
Q.ResistivityThermaltheta (from Solid)Data.theta(T, v)Thermal resistivity
Q.TimeAbsolute[n_trans]tau_QT (from Solid)N*c_v*theta*kL./(2*Aprime)Time constants for thermal transport (through the whole subregion)
Q.Temperature[n_trans]DeltaT (from Solid)Delta(boundaries.T)Differences in temperatures across the boundaries