The Effect of the Number of Nodes on the Exactness of Heat Loss in the Finite Difference Method

유한차분법에서 열손실 정확도에 미치는 Node 개수의 영향

The effect of the number of nodes on the heat loss from a rectangular fin for a finite difference method is studied. There are two ways for selecting nodes for the upper half fin in this finite difference method. In the first place, all the ${\Delta}x$ are the same and all the ${\Delta}y$ are the same for the entire upper half fin. Incremental length of x (i.e. ${\Delta}x$) is divided by two near the fin tip while all the ${\Delta}y$ are the same for another way. The results show that 1) About 30 nodes are enough to obtain the satisfactory exact analysis (relative error < 5%) on the heat loss for a given range of Biot number in case of short fin (i.e. $L{\leq}2$). 2) Under usual circumstances (Bi<0.1), the relative error of heat loss between using 30 nodes and 90 nodes is within 4% for given range of non-dimensional fin length. 3) The relative error of the calculated heat loss (the number of node=90) as compared to the expected exact heat loss is less then 1.5% for Bi=0.1 and L=10 while that is over 13% for Bi=1.0 and L=10.