Mathematical equations for heat conduction in the fins of air-cooled engines

The problem considered in this report is that of reducing actual geometrical area of fin-cooling surface, which is, of course, not uniform in temperature, to equivalent cooling area at one definite temperature, namely, that prevailing on the cylinder wall at the point of attachment of the fin. This makes it possible to treat all the cooling surface as if it were part of the cylinder wall and 100 per cent effective. The quantities involved in the equations are the geometrical dimensions of the fin, thermal conductivity of the material composing it, and the coefficient of surface heat dissipation between the fin and the air streams.