Analytical Solution for Different Profiles of Fin with Temperature-Dependent Thermal Conductivity

Table 2

Comparison between exact and DTM results for three profiles at 𝛽=0 and 𝑁=1.

X	Convex profile		Exponential profile (𝑎=1)		Rectangular profile
	Exact	DTM	Exact	DTM	Exact	DTM
0	0.56797321	0.56797323	0.78267175	0.78267175	0.648054274	0.648054274
0.1	0.5799982	0.579997732	0.78633664	0.786336641	0.651297246	0.651297246
0.2	0.60224731	0.602246515	0.796427754	0.796427754	0.66105862	0.66105862
0.3	0.63156711	0.631567222	0.81176631	0.81176631	0.677436092	0.677436091
0.4	0.66704223	0.667041545	0.831369483	0.831369483	0.700593571	0.700593571
0.5	0.70828235	0.708281911	0.85441111	0.854411111	0.730762826	0.730762826
0.6	0.75514423	0.755143954	0.880191752	0.880191753	0.768245801	0.768245801
0.7	0.80762463	0.807623882	0.908115721	0.908115721	0.813417638	0.813417638
0.8	0.86581241	0.865811512	0.937673304	0.937673304	0.866730433	0.866730433
0.9	0.92986609	0.929865636	0.968426886	0.968426886	0.928717757	0.928717757
1	1	1	1	1	1	1