Calculation of the minimum mean cooling/heating time of general-geometry solids

This paper establishes a geometric variable with which to linearize the calculation of the minimum mean time (dimensionless) necessary to reach a given mean temperature Y (dimensionless). The variable is defined by the relationshipXΓ=[αy+αz−2/3αyαz].In this way the minimum mean time (minimum Fourier number) is expressed very approximately byFY=P0+P1XΓ.It is also determined that P0 and P1 are, very approximately, linear functions of the log of YP0=A0+B0ln(Y),P1=A1+B1ln(Y).An interpolation method is further proposed for more complex geometries, built up from the “extremes” which limit or shape them.