Figure 16.  Piston Heat Transfer
 
    The piston crown conducts heat from the conduction gases to the cooling oil, to the piston rings, and the piston skirt. Frictional heating is also a source of heat.

    Engine Heat Transfer Correlations

    For the overall average heat transfer from the gas to the cylinder coolant, convection type heat transfer equations are used.

    Where:

    Q = overall heat transfer (W/m2)
    A = reference cylinder area (m2)
    Tgas = effective gas temperature, typically 800 C
    Tcool = coolant temperature, typically 80 C
    h= heat transfer coefficient

    The heat transfer coefficient depends on the engine geometric parameters, such as the exposed cylinder area and bore, and piston speed. The coefficient varies with location and piston position. The coefficient is found from a Nusselt - Reynolds number correlation.

    Nusselt # = a (Reynolds #)m

    Where:

    b = cylinder characteristic length (m), usually chosen to be the cylinder bore.
    k = gas thermal conductivity, (W/mK), typical value 0.06
    v = gas thermal diffusivity, (m2/s), typical value 100 x 10-6
    U = characteristic gas velocity (m/s)

    Depending on the correlation used, the characteristic gas velocity U is the mean piston speed

    the average intake velocity
    or a combustion velocity. The coefficient a and exponent m are found from engine experiments. There are three types of heat transfer coefficients used in the computation of engines heat transfer.

    Table III. Types of Heat Transfer Coefficients
     
    Averaging Used for
    h(x,t) averaged over time & space  overall steady state energy balance calculations
    h(x,t) instantaneous, space average heat transfer versus crank angle
    h(x,t) instantaneous, local local calculations of thermal stress
     

    The peak values of the instantaneous and local coefficients can be many times higher than the averaged values.

    A frequently used correlation for an average h is that of Taylor (ref), which uses the mean piston speed for the characteristic velocity.

    For a 1000 rpm engine with a 0.1m stroke, combustion gas temperature of 1000C, and coolant temperature of 80 C

    Where:

    b = 0.1 m
    k = 0.06 W/mK
    v = 100 x 10 -6 m2/s

    the average heat transfer coefficient is

    The average heat transfer per unit area from the cylinder to the coolant is
    For a reference cylinder area of p b2/4, the average heat transfer is
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