d5a682d9-8d7c-4278-9af7-4b0fc39c0bcd 9 overlord 4 5 false false 0 0 decimal

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λ.1 20 W m K * / * :

δ.1 20 mm * :

T.c1 10 °C * :

T λ.2 5 0.05 T °C / (* + (W m K * / * :

λ.3 10 W m K * / * :

δ.3 60 mm * :

T.c4 60 °C * :

α.2 18 W m 2^K * / * :

T.x2 150 °C * :

q α.2 T.x2 T.c4 - (* : W m 2^/ 1620

Symbolic integral solving with maple pluginMaxima can also be used A B λ.2_int T λ.2 T A B int maple :

Eq q T.c3 T.c2 - δ.2 1 T.c3 T.c2 - / T.c2 T.c3 λ.2_int * / / ≡ q T.c4 T.c3 - δ.3 λ.3 / / ≡ q T.c2 T.c1 - δ.1 λ.1 / / ≡ 13 mat transpose :

vars Eq Unknowns transpose :

guess vars T.c1 T.c4 δ.1 13 mat ≡ vectorize (:

Eq guess FindRoot 284.77 K * 323.43 K * 0.1563 m * 13 mat

T.c2 284.77 K *

T.c3 323.43 K *

δ.2 0.1563 m *

T.c2 °C 11.62

T.c3 °C 50.28

δ.2 mm 156.2508