Analysis of dimensional ratios of regular geometries for infinite geometry assumptions in conduction heat transfer problems

Assumptions for approximating a finite geometry as an infinite one during unsteady-state conduction heat transfer processes have been widely used in the literature. Comparison of the dimensions has been a unique approach in these assumptions. In this study, the certainty of the infinite body assumption was investigated for regular rod (circular and square rods) and regular slab (circular and rectangular slabs) group geometries. For this objective, at a certain Biot number (Bi), the changes in center temperature and center sterilization values were compared with the ones occurring in the reference infinite geometries versus the ratio of the dimension through which the heat transfer is negligible (VD) and/or the dimension through which the heat transfer is significant (PD). Bi   number was found to be significantly affecting the infinite geometry assumptions. The values of infinite assumption ratio (IAR), the ratio VDPD required to make the infinite assumption ratio, for both rod and slab group geometries exponentially decreased with increasing Bi number until Bi = 10. The VDPD value of four for rod group geometries and eight for slab group geometries for Bi > 10 was enough to make the infinite geometry assumption. To summarize the change of IAR with Bi number, a chart and a regression equation were constructed. The given chart and the equation (IAR vs Bi number) can easily be used to determine the IAR value for rod and slab group geometries with a given Bi number.