O Problema do Reverso de Temperatura com o Modelo McCormack

SCHERER, C. S.

doi:10.5540/tcam.2024.025.e01725

C. S. SCHERER

Escola Politécnica, Universidade do Vale do Rio dos Sinos - UNISINOS, Av. Unisinos, 950, 93022-750, São Leopoldo, RS, Brasil - E-mail: csscherer@unisinos.br

https://orcid.org/0000-0003-2516-555X

Tabelas (2)
Fórmulas (139)

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Tabela 1:
Valores limites de

β_{α}^{T}

e

β_{α}^{Q}

para a mistura Neônio-Argônio.

Thumbnail

Tabela 2:
Valores limites de

β_{α}^{T}

e

β_{α}^{Q}

para a mistura Hélio-Xenônio.

(2.1)

(2.2)

(2.3)

(2.4)

(2.5)

(2.6 a, b)

(2.7 a, b)

(2.8 a, b)

(2.9 a, b)

(2.10 a, b)

(2.11)

(2.12)

(2.13)

(2.14 a)

(2.14 b)

(2.15)

(2.16)

(2.17 a)

(2.17 b)

(2.18)

(2.19)

(2.20)

(2.21 a, b)

(2.22)

(2.23)

(2.24)

(2.25)

(3.1 a)

(3.1 b)

(3.2 a)

(3.2 b)

(3.3)

(3.4 a, b)

(3.5 a, b)

(3.6)

(3.7)

(4.1)

(4.2)

(4.3)

(4.4)

(4.5 a)

(4.5 b)

(4.6)

(4.7)

(4.8)

(4.9)

(4.10)

(4.11 a, b)

(4.12 a, b)

(4.13 a)

(4.13 b)

(4.14)

(4.15)

(4.16 a, b)

(4.17 a)

(4.17 b)

(4.18)

(4.19)

(4.20)

(4.21 a-d)

(4.22 a, b)

(4.23 a, b)

(4.24 a)

(4.24 b)

(4.25 a)

(4.25 b)

(4.25 c)

(4.26 a)

(4.26 b)

(4.26 c)

(4.27 a)

(4.27 b)

(4.28)

(4.29)

(4.30)

(4.31)

(4.32)

(4.33)

(4.34)

(5.1)

(5.2)

(5.3)

(A.1)

(A.2)

(A.3)

(A.4)

(A.5)

(A.6)

(A.7)

(A.8)

(A.9)

(A.10)

(A.11)

(A.12)

(A.13)

(A.14)

(A.15)

(A.16)

(A.17)

(A.18)

(A.19)

(A.20)

(A.21)

(A.22)

(A.23)

(A.24)

(A.25)

(A.26)

(A.27)

(A.28)

(A.29)

(A.30)

(A.31)

(A.32)

(A.33)

(B.1)

(B.2)

(B.3)

(B.4)

(B.5)

(B.6)

(B.7)

(B.8)

(B.9)

(B.10)

(B.11)

(B.12)

(B.13)

(B.14)

(B.15)

(B.16)

(B.17)

(B.18)

(B.19)

(B.20)

(C.1)

(C.2)

(C.3)

(C.4)

	C = 0.3				C = 0.8
a	$β_{1}^{T}$	$β_{2}^{T}$	$β_{1}^{Q}$	$β_{2}^{Q}$	$β_{1}^{T}$	$β_{2}^{T}$	$β_{1}^{Q}$	$β_{2}^{Q}$
0.1	4.25972	3.94438	3.64321	3.61291	4.09996	3.79411	3.63476	3.57029
0.5	5.16536	4.37786	3.81130	3.69401	4.74929	4.04327	3.76934	3.57962
1.0	5.16065	4.33324	3.82879	3.71279	4.70091	4.04985	3.78588	3.61904
1.5	4.94568	4.23991	3.79649	3.73238	4.53992	4.04296	3.77552	3.68680
2.0	4.72926	4.16141	3.75245	3.75612	4.39314	4.03226	3.76180	3.75806
2.5	4.55015	4.10196	3.70844	3.78113	4.27690	4.01855	3.74957	3.82254
5.0	4.10371	3.96903	3.55906	3.87818	3.99995	3.94943	3.71786	4.00528
9.0	3.95080	3.92851	3.48329	3.93266	3.90759	3.90268	3.70755	4.06444
13.0	3.92581	3.92156	3.46768	3.94264	3.89175	3.89114	3.70607	4.06766
15.0	3.92215	3.92021	3.46551	3.94344	3.88920	3.88897	3.70588	4.06655

	C = 0.3				C = 0.8
a	$β_{1}^{T}$	$β_{2}^{T}$	$β_{1}^{Q}$	$β_{2}^{Q}$	$β_{1}^{T}$	$β_{2}^{T}$	$β_{1}^{Q}$	$β_{2}^{Q}$
0.1	5.23502	3.87788	3.61875	3.54806	4.50875	3.48036	3.60843	3.27077
0.5	8.38807	4.20858	3.78125	3.46330	6.15376	3.19991	3.75215	2.62062
1.0	1.05464(1)	4.10165	3.83102	3.35670	6.94395	2.96023	3.79488	2.25725
1.5	1.16850(1)	3.98969	3.83330	3.30563	7.25373	2.90725	3.79986	2.11909
2.0	1.21901(1)	3.92610	3.81424	3.29815	7.35574	2.96477	3.79146	2.09746
2.5	1.23068(1)	3.90792	3.78277	3.32316	7.36283	3.09138	3.77749	2.14718
5.0	1.10054(1)	4.23072	3.55352	3.73711	7.11468	4.15523	3.69811	2.92426
9.0	9.04903	5.26380	3.22012	4.82324	6.88899	5.72766	3.62225	4.65893
13.0	8.15475	6.22628	3.02862	5.87780	6.82702	6.45015	3.59200	5.85857
15.0	7.92182	6.58502	2.97258	6.28792	6.81603	6.60631	3.58458	6.18857

γ_{1} = \frac{Ψ_{1} Ψ_{2} - ν_{1, 2}^{(4)} ν_{2, 1}^{(4)}}{Ψ_{2} + ν_{1, 2}^{(4)}} e γ_{2} = \frac{Ψ_{1} Ψ_{2} - ν_{1, 2}^{(4)} ν_{2, 1}^{(4)}}{Ψ_{1} + ν_{2, 1}^{(4)}} .

W (\pm, \pm) = [\begin{matrix} W_{11} (\pm, \pm) & W_{12} (\pm, \pm) & W_{13} (\pm, \pm) & W_{14} (\pm, \pm) \\ W_{21} (\pm, \pm) & W_{22} (\pm, \pm) & W_{23} (\pm, \pm) & W_{24} (\pm, \pm) \\ W_{31} (\pm, \pm) & W_{32} (\pm, \pm) & W_{33} (\pm, \pm) & W_{34} (\pm, \pm) \\ W_{41} (\pm, \pm) & W_{42} (\pm, \pm) & W_{43} (\pm, \pm) & W_{44} (\pm, \pm) \end{matrix}],

G_{1} = [\begin{matrix} 1 \\ 0 \\ 0 \\ 0 \end{matrix}], G_{2} = [\begin{matrix} 0 \\ 0 \\ 1 \\ 0 \end{matrix}], G_{3} (ξ) = [\begin{matrix} ξ^{2} - 1 / 2 \\ 1 \\ ξ^{2} - 1 / 2 \\ 1 \end{matrix}], G_{4} (ξ) = [\begin{matrix} r ξ \\ 0 \\ ξ \\ 0 \end{matrix}],

H_{1} (ξ) = [\begin{matrix} - 1 + c_{1} (ξ^{2} - 1 / 2) \\ c_{1} \\ c_{1} (ξ^{2} - 1 / 2) \\ c_{1} \end{matrix}], H_{2} (ξ) = [\begin{matrix} c_{2} (ξ^{2} - 1 / 2) \\ c_{2} \\ - 1 + c_{2} (ξ^{2} - 1 / 2) \\ c_{2} \end{matrix}],

A_{1}^{l} G_{1} + A_{2}^{l} G_{2} + A_{3}^{l} G_{3} (ξ_{i}) + B_{1}^{l} G_{4} (ξ_{i}) + B_{2}^{l} G_{5} (- a, ξ_{i}) + B_{3}^{l} G_{6} (- a, ξ_{i}) + \sum_{j = 4}^{4 N} [A_{j}^{l} Φ (ν_{j}, ξ_{i}) + B_{j}^{l} Φ (ν_{j}, - ξ_{i}) e^{- 2 a / ν_{j}}] = G^{l} (- a, ξ_{i})

A_{1}^{l} G_{1} + A_{2}^{l} G_{2} + A_{3}^{l} G_{3} (ξ_{i}) + B_{1}^{l} G_{4} (- ξ_{i}) + B_{2}^{l} G_{5} (a, - ξ_{i}) + B_{3}^{l} G_{6} (a, - ξ_{i}) + \sum_{j = 4}^{4 N} [A_{j}^{l} Φ (ν_{j}, - ξ_{i}) e^{- 2 a / ν_{j}} + B_{j}^{l} Φ (ν_{j}, ξ_{i})] = G^{l} (a, - ξ_{i}),

A = [\begin{matrix} 1 - η_{1, 2}^{(1)} & - (1 / 2) η_{1, 2}^{(2)} & r η_{1, 2}^{(1)} & (r^{3} / 2) η_{1, 2}^{(2)} \\ - (1 / 2) η_{1, 2}^{(2)} & (2 / 5) Δ_{1} & (r / 2) η_{1, 2}^{(2)} & (2 / 5) η_{1, 2}^{(6)} \\ s η_{2, 1}^{(1)} & (s^{3} / 2) η_{2, 1}^{(2)} & 1 - η_{2, 1}^{(1)} & - (1 / 2) η_{2, 1}^{(2)} \\ (s / 2) η_{2, 1}^{(2)} & (2 / 5) η_{2, 1}^{(6)} & - (1 / 2) η_{2, 1}^{(2)} & (2 / 5) Δ_{2} \end{matrix}],

B = [\begin{matrix} - (1 / 2) η_{1, 2}^{(2)} & (2 / 5) Δ_{1} & (r / 2) η_{1, 2}^{(2)} & (2 / 5) η_{1, 2}^{(6)} \\ 0 & 0 & 0 & 0 \\ (s / 2) η_{2, 1}^{(2)} & (2 / 5) η_{2, 1}^{(6)} & - (1 / 2) η_{2, 1}^{(2)} & (2 / 5) Δ_{2} \\ 0 & 0 & 0 & 0 \end{matrix}],

C = [\begin{matrix} - (3 / 4) η_{1, 2}^{(2)} & 0 & (3 r^{3} / 4) η_{1, 2}^{(2)} & 0 \\ (3 / 5) Δ_{1} & 0 & (3 / 5) η_{1, 2}^{(6)} & 0 \\ (3 s^{3} / 4) η_{2, 1}^{(2)} & 0 & - (3 / 4) η_{2, 1}^{(2)} & 0 \\ (3 / 5) η_{2, 1}^{(6)} & 0 & (3 / 5) Δ_{2} & 0 \end{matrix}]

D = [\begin{matrix} (3 / 5) Δ_{1} & 0 & (3 / 5) η_{1, 2}^{(6)} & 0 \\ 0 & 0 & 0 & 0 \\ (3 / 5) η_{2, 1}^{(6)} & 0 & (3 / 5) Δ_{2} & 0 \\ 0 & 0 & 0 & 0 \end{matrix}] .

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O Problema do Reverso de Temperatura com o Modelo McCormack

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