An additional option to the Internal Combustion Engine model is specification of convective heat loss from the gas to the solid walls during the compression and expansion cycle. The heat loss is calculated at each point in time according to:
 | (8–72) |
where you specify 
and the heat transfer coefficient, 
, is obtained from the following generalized heat transfer correlation [59] based on user-specified constants 
, 
, and 
:
 | (8–73) |
is the Nusselt number for heat transfer, 
is the Reynolds number, and 
is the Prandtl number. These are defined according to:
 | (8–74) |
 | (8–75) |
 | (8–76) |
where 
is the gas conductivity, 
is the mean piston speed ( 
), and 
is the gas viscosity. In calculating the heat transfer coefficient using Equation 8–73 , the gas properties are assumed to be those of air, since, for typical operating conditions, the molar concentrations of fuel and its by-products are relatively dilute. The area available for heat transfer, 
, includes the cylinder walls (time-varying) and end surfaces ( 
). Accordingly, when the IC HCCI Engine heat-transfer correlation is invoked, the user must also specify the engine bore diameter, 
.
A dimensional formulation of the heat transfer coefficient can also be used since engineers working on engine simulations are customary to express the empirical correlation of the heat transfer coefficient as
 | (8–77) |
where the units of the cylinder pressure is [kPa], and the characteristic gas velocity and the bore diameter are in [m/sec] and [m], respectively. The heat transfer coefficient itself is in [W/m 2 K].
Equation 8–77 is equivalent to the dimensionless form given by Equation 8–72 . However, by using all measurable quantities, Equation 8–78 makes the determination of the empirical constants from experimental data much easier.
In addition, the heat transfer coefficient formulation introduced by Hohenberg [59] is available as well:
 | (8–78) |
where 
is the cylinder volume in [m 3 ] and 
is the cylinder pressure in [kPa].
An extension to the heat-transfer correlation described above, is the use of the Woschni Correlation. [59] This option is now provided in the Ansys Chemkin IC HCCI Engine model and the parameters that govern the Woschni correlation are described here.
The Woschni Correlation allows a more accurate estimation of the average cylinder gas speed used in the definition of the Reynold’s number for the heat-transfer correlation. As stated in Equation 8–73 , the convective heat transfer coefficient between the gas and cylinder wall can be obtained from the generalized heat transfer correlation in terms of a Nusselt number (defined in Equation 8–74 ). For the Woschni Correlation option, however, the velocity used in the Reynolds number definition is an estimation of the average cylinder gas velocity, w , instead of the mean piston speed, as stated in Equation 8–79 .
 | (8–79) |
To obtain the average cylinder gas velocity, Woschni proposed a correlation that relates the gas velocity to the mean piston speed and to the pressure rise due to combustion, 
, as given in Equation 8–80 .
 | (8–80) |
Here, 
, 
, and 
are modeling parameters, 
is the swirl velocity, 
is the displacement volume, 
is the motored cylinder pressure, and 
, 
, and 
are the initial temperature, volume and pressure inside the cylinder, respectively.
The motored cylinder pressure is the pressure associated with an isentropic compression, in which the pressure and volume ratios are related by a specific heat ratio 
.
 | (8–81) |
The Huber-Woschni correlation for gas velocity utilizes a different method (than the Woschni correlation) to estimate the gas velocity:
 | (8–82) |
And the actual gas velocity is the larger of 
and 
:
 | (8–83) |
where IMEP is the indicated mean effective pressure in [bar] and is specified as an input parameter.
A turbulent-boundary-layer heat-transfer model for the 0-D engine applications is available. By assuming the existence of a turbulent boundary layer over the cylinder walls during the simulation, the heat flux across the engine cylinder wall 
[ergs/s-cm 2 ] can be computed as [69]
 | (8–84) |
In Equation 8–84 , 
[g/cm 3 ] and 
[ergs/g-K] are the average gas density and the average gas heat capacity inside the cylinder, respectively. 
is dimensionless and, in this case, a model constant to be specified by the user. For Equation 8–84 to be valid, 
must be evaluated at a point that is within the log region of the turbulent boundary layer. The boundary-layer friction velocity 
[cm/s] in Equation 8–84 is given as
 | (8–85) |
[dimensionless] in Equation 8–85 is another model constant that should be provided by the user. 
[cm/s] is a model parameter that is assumed to be a function of crank angle/time and is given as piecewise-linear data points. The kinematic viscosities 
[cm 2 /s] and 
[cm 2 /s] in Equation 8–85 are calculated by Sutherland’s law
 | (8–86) |
For air, the reference viscosity is 
[g/cm-s] and the reference temperature is 
[K]; the Sutherland temperature is 
[K].
The power law can also be used to estimate the gas viscosity
 | (8–87) |
For air, 
and 
in the power law share the same values as in Sutherland’s law, and the exponent n in the power law is equal to 2/3.