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

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

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