Research Article

Steady Thermal Analysis of Two-Dimensional Cylindrical Pin Fin with a Nonconstant Base Temperature

Table 2

Eigenvalues 𝜆 𝑛 for different values of the Biot number with 𝐸 = 2 .

𝐵 𝑖 0.2 0.4 0.6 0.8 1 2

𝜆 1 7.6243 7.5193 7.4141 7.3093 7.2056 6.7249
𝜆 2 14.0098 13.9527 13.8955 13.8384 13.7815 13.5023
𝜆 3 20.3322 20.2928 20.2535 20.2141 20.1748 19.9801
𝜆 4 26.6361 26.6060 26.5760 26.5460 26.5160 26.3667
𝜆 5 32.9322 32.9079 32.8836 32.8593 32.8350 32.7140
𝜆 6 39.2241 39.2037 39.1833 39.1629 39.1425 39.0408
𝜆 7 45.5136 45.4960 45.4784 45.4608 45.4433 45.3556
𝜆 8 51.8016 51.7861 51.7707 51.7552 51.7398 51.6627
𝜆 9 58.0885 58.0747 58.0609 58.0472 58.0334 57.9646
𝜆 1 0 64.3747 64.3623 64.3498 64.3374 64.3250 64.2629