Error associated with assuming a finite regular geometry as an infinite one for modeling of transient heat and mass transfer processes

摘要

Error (ε) due to assuming a finite regular geometry as an infinite one was determined for transient heat and mass transfer processes. Dimensionless numbers Fourier (Fo) and Biot (Bi), and geometrical properties (type, shape, and size) were the possible effective parameters on ε. Types of geometries used were slab (circle, square, and rectangle) and rod (cylinder and square). The error decreased with decreasing Fo, with the ε-curves shifting in parallel to the Fo-axis in the decreasing direction with increasing Bi. And Bi≥100 was found to be infinite for all geometries. The error for circle and square slab geometries was same at all Bi. The size of the dimension through which the transfer occurs did not affect the error in all geometries. However, the size of the dimensions, through which the transfer occurs was neglected, affected the error in squared slabs. It increased with decreasing ratio of width over length, e.g. In the order of square slab and rectangular slab of 1 x 2, 1x5, and 1x10. The error was same for the cylindrical and square rods for Bi = 0.01 and 0.1. For Bi≥1, square rod had greater ε values than cylindrical rod at the same Fo-Bi. An error chart was constructed as a function of Fo, Bi, and geometrical properties that can be used to determine the error due to assuming a finite slab and rod geometry as an infinite one during transient heat or mass transfer processes.