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"Simple Explicit Expressions for Calculation of the Heisler-Grober Charts"

M. M. Yovanovich, 1996
**Abstract:**
Simple single term approximations for the Heisler cooling charts
and the Grober fractional energy loss are presented for the plate, infinite
circular cylinder and sphere. These solutions are accurate to within 1% of
the series solutions provided the dimensionless time Fo is greater than
some critical value Fo which lies in the range: 0.18 - 0.24. Simple
explicit expressions are provided for the accurate calculation of the first
eigenvalue for all values of the Biot number. Polynomial expressions are
presented for the accurate calculation of the roots of the Bessel functions
of the first kind of orders zero and one. Expressions are developed for the
accurate computation of the Bessel functions of the first kind of orders
zero and one. Simple accurate solutions are proposed for calculating the
dimensionless temperature and the heat loss fraction for finite circular
cylinders, rectangular parallelopipeds and infinite rectangular bars. Maple
V R3 worksheets are given for the accurate calculation of the dimensionless
temperature and dimensionless heat loss for the infinite plate, infinite
circular cylinder and the sphere.

*1996 ASME National Heat Transfer Conference, Aug. 3-6, Houston, Texas, Thermophysics and Thermophysical Properties Session*