Facile prediction of total heat transfer from simple solid bodies to neighboring fluids: A viable alternative to Gröber charts

Abstract

In the analysis of unsteady heat conduction for simple solid bodies (large plate, long cylinder and sphere), the first Heisler chart provides the dimensionless center temperature varying with the dimensionless time and parameterized by the Biot number. The second Heisler chart furnishes the ratio between the dimensionless off-center temperatures and the dimensionless center temperature (taken from the first Heisler chart) varying with the Biot number. A third Gröber chart renders the dimensionless total heat transfer in terms of the dimensionless time and the Biot number. The tandem of Heisler/Gröber charts constitutes integral material in the chapter on unsteady heat conduction in most heat transfer textbooks. The present study addresses a natural interconnection (so far unexplored in the specialized literature) between the dimensionless mean temperature and the dimensionless center temperature (taken from the first Heisler chart) affected by the Biot number. The approach to be proposed in this study is conducive to the construction of a new chart equivalent in format to the second Heisler chart for the three simple solid bodies, but including only a single curve. Alternatively, each new chart is channeled through a compact correlation equation whose evaluation is easy. Thermal design engineers and students enrolled in heat transfer courses will be the beneficiaries of the outcome of this technical paper.