Theory

The specific heat capacity of air rises from 1005 J/(kg K) at room temperature to about 1136 J/(kg K) at 700 °C; that of exhaust gas rises more (water vapour and CO₂). With a hot gas and heat transfer, a constant $c_p$ therefore misstates the enthalpy carried by the flow and the ratio $\gamma$ that sets the speed of sound.

With "temperature":

The molar heat capacity of the gas is the 7-coefficient polynomial of equation (1), with one set of coefficients below and one above the common temperature 1000 K.
The mixture coefficients are the mole-fraction-weighted sums of the species coefficients of N₂, O₂, Ar, CO₂ and H₂O (exact for an ideal-gas mixture of fixed composition). The program writes them into the solver's thermophysicalProperties together with the mixture molar mass.
The molar mass and $c_p$ boxes show the mixture's values and are locked.
Enthalpy differences (heat balance) are integrals of the same polynomial, equation (2).

With "constant", Specific heat capacity cp and Molar mass are used as typed, for any fluid.

The model also serves incompressible and acoustics-only cases: the density uses the molar mass, and the acoustics the ratio $\gamma(T)$ .

Equations

\frac{c_p(T)\,M}{\mathcal{R}} = a_1 + a_2 T + a_3 T^2 + a_4 T^3 + a_5 T^4

(1)

h_s(T) = \frac{\mathcal{R}}{M}\left(a_1 T + \frac{a_2}{2}T^2 + \frac{a_3}{3}T^3 + \frac{a_4}{4}T^4 + \frac{a_5}{5}T^5 + a_6\right) - h(298.15\,\mathrm{K})

(2)

\gamma(T) = \frac{c_p(T)}{c_p(T) - \mathcal{R}/M}

(3)

where	meaning	unit
$c_p$	Specific heat capacity at constant pressure	J/(kg K)
$M$	Molar mass of the mixture	kg/kmol
$\mathcal{R}$	Universal gas constant, 8314.47	J/(kmol K)
$a_1 \ldots a_6$	Mixture polynomial coefficients (low or high set)	-
$h_s$	Sensible enthalpy relative to 298.15 K	J/kg
$\gamma$	Ratio of heat capacities	-

Default and rule

Default

temperature (cp(T) of the selected gas)

Rule

Temperature. A saved case without this setting is read as "constant" when its molar mass or $c_p$ differ from the defaults (28.9644 kg/kmol, 1006 J/(kg K)), so typed values are kept; otherwise as "temperature".

Source

The species data are the NASA Glenn 9-term polynomials (McBride et al., 2002). The program fits the 7-term form of equation (1) to them once per species:

least squares on $c_p$ over 200-1000 K and 1000-3000 K;
$c_p$ continuous at 1000 K and exact at 298.15 K;
enthalpy and entropy constants matched at 298.15 K.

The fit stays within 0.11 % of the NASA $c_p$ from 250 to 1500 K (0.34 % worst over 200-3000 K). The resulting $c_p$ of air agrees with standard heat-transfer textbook tables within ±0.5 %. The coefficients are written to the solver's constant/thermophysicalProperties with janaf thermodynamics.

Valid range temperature | constant

Verified

Checked on real runs (2026-11-11): the solver selects the janaf package; a heat-transfer muffler run with it closed its energy balance to 0.7 %, with cp 1034 J/(kg K) at 523 K.

Data not readable

When the program's species data cannot be read, the gas falls back to the constant $c_p$ and molar mass with a warning; the program never substitutes estimated values.

Validity

The fitted polynomials are valid from 200 to 3000 K. The composition is frozen (no dissociation or reaction).

References 1

McBride, B. J., Zehe, M. J. and Gordon, S. (2002). NASA Glenn coefficients for calculating thermodynamic properties of individual species. NASA/TP-2002-211556, NASA Glenn Research Center. Web page

Theory

Equations

Default and rule

Valid range temperature | constant

Related 5

References 1