ThermalSolidProperties

This is the base class for providing thermal solid properties as a function of temperature. This class defines functions to compute the following thermal properties, which are all assumed to be functions of temperature only:

  • cp: isobaric specific heat, cpc_p

  • e: specific internal energy, ee

  • k: thermal conductivity, kk

  • rho: density, ρ\rho

For each of these, the following methods are available, where y should be replaced by the respective property name given in the list above:

Real y_from_T(const Real & T) const

provides the value y(T)y(T) using a Real input value for TT.

void y_from_T(const Real & T, Real & y, Real & dy_dT) const

provides the value y(T)y(T) and its derivative y(T)y'(T) using a Real input value for TT.

ADReal y_from_T(const ADReal & T) const

provides the value y(T)y(T) and its derivative y(T)y'(T) using an ADReal input value for TT.

Thus both AD and non-AD interfaces are available. Derived classes are only responsible for overriding the non-AD interfaces for each property. The AD interfaces are implemented by default by combining the two non-AD interfaces.

Note that the e_from_T interfaces should not be overridden because they have generic implementations, and the non-AD interfaces are not even virtual. Instead, derived classes must override the following:

Real cp_integral(const Real & T) const

which corresponds to the indefinite integral C(T)C(T) of cp(T)c_p(T), minus the constant of integration:

C(T)=cp(T)dT.C(T) = \int c_p(T) dT \,.

Due to the definition of the isobaric specific heat capacity,

cpeTv,c_p \equiv \left.\frac{\partial e}{\partial T}\right|_v \,,

the specific internal energy can be expressed as

e(T)e(T0)=T0Tcp(T)dT=C(T)C(T0),e(T) - e(T_0) = \int\limits_{T_0}^T c_p(T') dT' = C(T) - C(T_0) \,,

where T0T_0 is the temperature at which the specific internal energy is assumed to be zero. This is a convention supplied by the user using the parameter "T_zero_e". By default, this is taken to be at standard temperature, 273.15 K. Note that this is important for comparing specific internal energy values to external sources, which may be based on different reference temperatures.

References

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