Errors based on location and volume average changes in infinite geometry assumptions in heat and mass transfer processes Original Research Article

The errors associated with assuming a finite geometry as an infinite one during transient heat and mass transfer processes were determined versus Fourier number (Fo) and Biot number (Bi) for slab (circular slab and rectangular slab of 1 × 1, 1 × 2, 1 × 5, and 1 × 10) and rod geometries (cylindrical and square rods). Two types of errors were determined for a given process time: (i) at different locations between the center of symmetry and transfer surface (location error, εL), and (ii) with respect to average temperature or mass change (average error, εa) of a given geometry with respect to a reference. Error curves giving the variation of εL or εa versus Fo were obtained at Bi of 0.01, 0.1, 1, 10, 100, 1000, and 10 000. The errors increased with increasing Fo at a given Bi and the error curves shifted parallel on the Fo-axis with decreasing Fo and increasing Bi. They did not shift significantly after Bi=100. At the same Fo–Bi, εa values were greater than εL values for the same geometry, and the errors in the slab geometries were greater than the corresponding ones for the rod geometries. Rod geometries had the same errors at the same Fo–Bi till Bi=0.1, and after that the circular rod had greater error values than the square rod. The dimension of the geometries had no effect on the errors except for the rectangular slabs. The errors increased with increasing length/width ratio of the rectangular slab geometry at the same Fo–Bi. Error curves of the rectangular slabs got closer with increasing Bi. The errors in the rectangular slab of 1 × 1 were equal to that of the circular slab at all Bi. The errors were modeled using a regression equation as a function of Fo and Bi. This equation exhibited a satisfactory fit with high R2 and small deviation values and random distribution showing the good prediction capability at the applied conditions.