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A correlation used to compute the space averaged instantaneous heat
transfer coefficient (Woschni, 1967 , "A universally applicable equation
for the instantaneous heat transfer coefficient in the internal
combustion engine", SAE Paper 670931): is:
Nusselt # = 0.035 (Reynolds #)0.80
 
Where:
- b = cylinder characteristic length (m), usually chosen to be the
cylinder bore.
- k = gas thermal conductivity, (W/mK), typical value 0.06
- n = gas kinematic viscosity, (m2/s),
typical value 100 x 10-6
- U = average gas velocity (m/s)
During intake, compression, and exhaust, the average gas velocity U
is proportional to the mean piston speed, Upiston.
For intake and exhaust, U = 6.18 Upiston
For compression, U = 2.28 Upiston
The instantaneous heat transfer coefficient during combustion depends
on the gas speed and cylinder pressure, which change significantly
during the combustion process. During combustion and expansion, the gas
speed U (m/s) induced by combustion is given by the following equation
(Woschni, 1967) :

Where To, Vo, and Po are reference intake cylinder temperature (K),
volume (m3), and pressure (Pa), V is the instantaneous cylinder volume
(m3), and DPc is the instantaneous
pressure rise due to combustion relative to the unburned gas pressure at
the same crankshaft angle. The unburned gas cylinder pressure is
determined from thermodynamic analysis. An example pressure computation
is given in the Cylinder
Pressure page. For engines with significant swirl, the gas
velocities are higher.
The gas properties in the correlation equation are evaluated at the
instanteous average cylinder temperature determined from the ideal gas
law:

Where:
- P = instantaneous cylinder pressure (kPa)
- r = instantaneous mixture density,
mass/volume (kg/m3)
- M = averaged molecular weight (kg/kmol)
- R = universal gas constant, 8.314 kJ/kmol K
If P= 500 kPa, r = 5 kg/m3, M = 40
kg/kmol,

The thermal conductivity k varies as T^3/4 , and the
viscosity varies as T^0.62 , so that the instantaneous heat
transfer coefficient can be written as

If b=0.1m, P = 500 kPa, T = 1000 K, and U = 10 m/s,
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