Comparison of Exact Solutions for Heat Transfer in Extended Surfaces of Different Geometries

Table 1

Comparison of the temperature values in fins with rectangular, radial, and spherical profiles. Here 𝑀=4 and 𝑛=1.

𝑟	𝛼=0; (rectangular)	𝛼=1; (radial)	𝛼=2; (spherical)
0	0.125136	0.185069	0.238556
0.1	0.13479	0.192403	0.244902
0.2	0.160849	0.213754	0.363795
0.3	0.199607	0.248095	0.295078
0.4	0.25049	0.295331	0.33908
0.5	0.315255	0.356686	0.396937
0.6	0.397056	0.434579	0.470685
0.7	0.500174	0.532528	0.563297
0.8	0.630101	0.655185	0.678749
0.9	0.793788	0.808503	0.822159
1	1	1	1