Planilha de Condução Transiente

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Cilindros
	Prática 4 - Condução Transiente
	Aço	T do banho, °C (T∞) 	60
	Cp (J/Kg*K)	442	T incial, °C (Ti)	27
	ρ (Kg/m³)	7836
	Diâmetro (m)	0.0505
	Raio (m)	0.02525
	Comprimento (m)	0.153
	A (m²)	0.02844
	V (m³)	0.00031
	t (s)	T(t) , °C	C	y = ln(C)
	0	27	1	0.00000
	12	29	0.9393939394	-0.06252
	20	31	0.8787878788	-0.12921
	28	33	0.8181818182	-0.20067
	35	35	0.7575757576	-0.27763
	43	37	0.696969697	-0.36101
	51	39	0.6363636364	-0.45199
	59	41	0.5757575758	-0.55207
	69	43	0.5151515152	-0.66329
	81	45	0.4545454545	-0.78846
	93	47	0.3939393939	-0.93156
	107	49	0.3333333333	-1.09861
	127	51	0.2727272727	-1.29928
	148	53	0.2121212121	-1.55060
	179	55	0.1515151515	-1.88707
	224	57	0.0909090909	-2.39790	a	-0.0106
	319	59	0.0303030303	-3.49651	h (w/m².K)	400.17934
	Cobre	T do banho, °C (T∞) 	60
	Cp (J/Kg*K)	385	T inicial, °C (Ti)	29
	ρ (Kg/m³)	8933
	Diâmetro (m)	0.0505
	Raio (m)	0.02525
	Comprimento (m)	0.153
	A (m²)	0.02836
	V (m³)	0.00031
	t (s)	T(t) , °C	C	y = ln(C)
	0	29	1	0.00000
	3	31	0.935483871	-0.06669
	8	33	0.8709677419	-0.13815
	12	35	0.8064516129	-0.21511
	17	37	0.7419354839	-0.29849
	21	39	0.6774193548	-0.38946
	26	41	0.6129032258	-0.48955
	31	43	0.5483870968	-0.60077
	38	45	0.4838709677	-0.72594
	45	47	0.4193548387	-0.86904
	54	49	0.3548387097	-1.03609
	65	51	0.2903225806	-1.23676
	80	53	0.2258064516	-1.48808
	100	55	0.1612903226	-1.82455
	129	57	0.0967741935	-2.33537
	186	59	0.0322580645	-3.43399	a	-0.0185
	h (w/m².K)	695.48098
	Alumínio	T do banho, °C (T∞) 	60
	Cp (J/Kg*K)	903	T inicial, °C (Ti)	25
	ρ (Kg/m³)	2702
	Diâmetro (m)	0.051
	Comprimento (m)	0.152
	Raio (m)	0.0255
	A (m²)	0.02844
	V (m³)	0.00031
	t (s)	T(t) , °C	C	y = ln(C)
	0	27	0.9428571429	-0.05884
	5	29	0.8857142857	-0.12136
	8	31	0.8285714286	-0.18805
	11	33	0.7714285714	-0.25951
	13	35	0.7142857143	-0.33647
	16	37	0.6571428571	-0.41985
	18	39	0.6	-0.51083
	22	41	0.5428571429	-0.61091
	26	43	0.4857142857	-0.72213
	31	45	0.4285714286	-0.84730
	36	47	0.3714285714	-0.99040
	43	49	0.3142857143	-1.15745
	50	51	0.2571428571	-1.35812
	60	53	0.2	-1.60944
	73	55	0.1428571429	-1.94591
	94	57	0.0857142857	-2.45674
	a	-0.0267
	h (w/m².K)	710.09501
	a
	h (w/m².K)
Placas
	Cobre	T do banho, °C (T∞) 	60
	Cp (J/Kg*K)	385	T inicial, °C (Ti)	27
	ρ (Kg/m³)	8933
	Espessura (m)	0.0127
	Comprimento (m)	0.1524
	Largura (m)	0.1009
	A (m²)	0.03687
	V (m³)	0.000187
	t (s)	T(t) , °C	C	y = ln(C)
	0	27	1.00000	0.00000
	3	29	0.93939	-0.06252
	6	31	0.87879	-0.12921
	8	33	0.81818	-0.20067
	10	35	0.75758	-0.27763
	12	37	0.69697	-0.36101
	14	39	0.63636	-0.45199
	17	41	0.57576	-0.55207
	20	43	0.51515	-0.66329
	24	45	0.45455	-0.78846
	30	47	0.39394	-0.93156
	36	49	0.33333	-1.09861
	46	51	0.27273	-1.29928
	61	53	0.21212	-1.55060
	72	55	0.15152	-1.88707
	81	57	0.09091	-2.39790
	107	59	0.03030	-3.49651
	a	-0.0312
	h (w/m².K)	544.2283062653
	Alumínio	T do banho, °C (T∞) 	60
	Cp (J/Kg*K)	903	T inicial, °C (Ti)	25
	ρ (Kg/m³)	2702
	Espessura (m)	0.0122
	Comprimento (m)	0.1521
	Largura (m)	0.1009
	A (m²)	0.03687
	V (m³)	0.000195
	t (s)	T(t) , °C	C	y = ln(C)
	0	25	1.00000	0.00000
	1	27	0.94286	-0.05884
	3	29	0.88571	-0.12136
	5	31	0.82857	-0.18805
	6	33	0.77143	-0.25951
	7	35	0.71429	-0.33647
	9	37	0.65714	-0.41985
	11	39	0.60000	-0.51083
	13	41	0.54286	-0.61091
	15	43	0.48571	-0.72213
	17	45	0.42857	-0.84730
	20	47	0.37143	-0.99040
	23	49	0.31429	-1.15745
	27	51	0.25714	-1.35812
	32	53	0.20000	-1.60944
	41	55	0.14286	-1.94591
	54	57	0.08571	-2.45674
	a	-0.0486
	h (w/m².K)	627.1491500407
Esferas
	Cobre	T do banho, °C (T∞) 	60
	Cp (J/Kg*K)	385	T inicial, °C (Ti)	27
	ρ (Kg/m³)	8933
	Diâmetro (m)	0.0509
	Raio (m)	0.02545
	A (m²)	0.0081392697
	V (m³)	6.90E-05
	t (s)	T(t) , °C	C	y = ln(C)
	0	27	1.00000	0.00000
	2	29	0.93939	-0.06252
	5	31	0.87879	-0.12921
	9	33	0.81818	-0.20067
	12	35	0.75758	-0.27763
	16	37	0.69697	-0.36101
	20	39	0.63636	-0.45199
	23	41	0.57576	-0.55207
	28	43	0.51515	-0.66329
	33	45	0.45455	-0.78846
	39	47	0.39394	-0.93156
	45	49	0.33333	-1.09861
	54	51	0.27273	-1.29928
	65	53	0.21212	-1.55060
	82	55	0.15152	-1.88707
	105	57	0.09091	-2.39790
	150	59	0.03030	-3.49651
	a	-0.0233
	h (w/m².K)	679.7989923083
	Alumínio	T do banho, °C (T∞) 	60
	Cp (J/Kg*K)	903	T inicial, °C (Ti)	27
	ρ (Kg/m³)	2702
	Diâmetro (m)	5.07E-02
	Raio (m)	2.54E-02
	A (m²)	0.0080754325
	V (m³)	6.82E-05
	t (s)	T(t) , °C	C	y = ln(C)
	0	27	1	0
	6	29	0.9393939394	-0.062520357
	9	31	0.8787878788	-0.1292117315
	11	33	0.8181818182	-0.2006706955
	14	35	0.7575757576	-0.2776317366
	17	37	0.696969697	-0.3610133455
	19	39	0.6363636364	-0.4519851237
	22	41	0.5757575758	-0.5520685823
	26	43	0.5151515152	-0.6632942174
	29	45	0.4545454545	-0.7884573604
	33	47	0.3939393939	-0.931558204
	39	49	0.3333333333	-1.0986122887
	44	51	0.2727272727	-1.2992829841
	52	53	0.2121212121	-1.5505974124
	63	55	0.1515151515	-1.887069649
	77	57	0.0909090909	-2.3978952728
	112	59	0.0303030303	-3.4965075615	a	-0.0299
	h (w/m².K)	616.45445043
Resfriamento
	Alumínio	T ambiente, °C (T∞) 	25
	Cp (J/Kg*K)	903	T do banho, °C (Ti)	60
	ρ (Kg/m³)	2702
	Diâmetro (m)	5.07E-02	T inicial (t=0), °C	59
	Raio (m)	2.54E-02
	A (m²)	0.0080754325
	V (m³)	0.0000682374
	CONVECÇÃO FORÇADA
	t (s)	T(t) , °C	C	y = ln(C)
	0	59	1.00000	0.00000
	23	57	0.94118	-0.06062
	42	55	0.88235	-0.12516
	63	53	0.82353	-0.19416
	85	51	0.76471	-0.26826
	110	49	0.70588	-0.34831
	136	47	0.64706	-0.43532
	168	45	0.58824	-0.53063
	200	43	0.52941	-0.63599
	240	41	0.47059	-0.75377
	287	39	0.41176	-0.88730
	a	-0.0031
	CONVECÇÃO NATURAL	h (w/m².K)	63.91333767
	Alumínio	T ambiente, °C (T∞) 	25
	Cp (J/Kg*K)	903	T do banho, °C (Ti)	60
	ρ (Kg/m³)	2702
	Diâmetro (m)	5.09E-02	T inicial (t=0), °C	59
	Raio (m)	0.02545
	A (m²)	0.0080754325
	V (m³)	0.0000682374
	t (s)	T(t) , °C	C	y = ln(C)
	0	59	1.00000	0.00000
	54	57	0.94118	-0.06062
	118	55	0.88235	-0.12516
	198	53	0.82353	-0.19416
	300	51	0.76471	-0.26826
	426	49	0.70588	-0.34831
	566	47	0.64706	-0.43532
	682	45	0.58824	-0.53063
	853	43	0.52941	-0.63599
	1050	41	0.47059	-0.75377
	1277	39	0.41176	-0.88730
	a	-0.0007
	h (w/m².K)	14.43204399
Biot
	Corpo de Prova	Convecção	Lc = V/A (m)	h (W/m2∙K)	Bi
	Aquecimento	Cilindro	Alumínio	―	0.01092	710.0950056962	0.0327183015
	Aço	―	0.01081	400.1793400844	0.0884650034
	Cobre	―	0.01084	695.4809828984	0.0188005333
	Placa	Alumínio	―	0.00507	627.1491500407	0.0134162287	Corpo de Prova	A (m2)	V (m3)	Lc = V/A (m)
	Cobre	―	0.00522	544.2283062653	0.0070844682	Cilindro	Alumínio	0.02844	3,105 ∙ 10-4	0.01092
	Esfera	Alumínio	―	0.00845	616.45445043	0.0219790722	Aço	0.02836	3,065 ∙ 10-4	0.01081
	Cobre	―	0.00848	679.7989923083	0.0143757991	Cobre	0.02828	3,065 ∙ 10-4 	0.01084
	Resfriamento	Esfera	Alumínio	Natural	0.00845	14.43204399	0.0005145602	Placa	Alumínio	0.03687	1,87 ∙ 10-4	0.00507
	Forçada	0.00845	63.91333767	0.0022787667	Cobre	0.03729	1,95 ∙ 10-4	0.00522
	Esfera	Alumínio	8,075 ∙ 10-3	6,824 ∙ 10-5	0.00845
	Cobre	8,139 ∙ 10-3	6,905 ∙ 10-5	0.00848
	Material	ρ (kg/m³)	CP (J/kg.K)	k (W/m.K)	α (m2/s)
	Alumínio	903	2702	237	97,1 ∙ 10-6
	Aço	443	7836	48.9	14,1 ∙ 10-6
	Cobre	385	8933	401	11,7 ∙ 10-5
Tcal - Cilindros
	Dados - Aço	T do banho, °C (T∞) 	60	Dados - Cobre	T do banho, °C (T∞) 	60	Dados - Alumínio	T do banho, °C (T∞) 	60
	Cp (J/Kg*K)	442	T incial, °C (Ti)	27	Cp (J/Kg*K)	385	T inicial, °C (Ti)	29	Cp (J/Kg*K)	903	T inicial, °C (Ti)	27
	ρ (Kg/m³)	7836	ρ (Kg/m³)	8933	ρ (Kg/m³)	2702
	Diâmetro (m)	0.0505	hexp(w/m².K) =	400.1793400844	Diâmetro (m)	0.0505	hexp(w/m².K) =	695.4809828984	Diâmetro (m)	0.051	hexp(w/m².K) =	710.0950056962
	Raio (m)	0.02525	a =	-0.0106	Raio (m)	0.02525	a	-0.0185	Comprimento (m)	0.152	a	-0.0267
	Comprimento (m)	0.153	Comprimento (m)	0.153	Raio (m)	0.0255
	A (m²)	0.02844	hcal(w/m².K)
367.4870092706	A (m²)	0.02836	hcal(w/m².K)	707.840919075	A (m²)	0.02844	hcal(w/m².K)	678.4339245907
	V (m³)	0.00031	V (m³)	0.00031	V (m³)	0.00031
	t (s)	TExp(t) , °C	TCal(t) , °C	((TExp - Tcal)2)1/2	t (s)	TExp(t) , °C	TCal(t) , °C	((TExp - Tcal)2)1/2	t (s)	TExp(t) , °C	TCal(t) , °C	((TExp - Tcal)2)1/2
	0	27	27	0.00000	0	29	29	0.00000	0	27	27	0.00000
	12	29	30.63806629	1.63807	3	31	30.7025386008	0.29746	5	29	30.9517006306	1.95170
	20	31	32.8377882969	1.83779	8	33	33.3348630283	0.33486	8	31	33.0917920787	2.09179
	28	33	34.8727126798	1.87271	12	35	35.2693869994	0.26939	11	33	35.0742153842	2.07422
	35	35	36.5278148509	1.52781	17	37	37.4913882787	0.49139	13	35	36.3140097214	1.31401
	43	37	38.2862917527	1.28629	21	39	39.1243612868	0.12436	16	37	38.0590408019	1.05904
	51	39	39.9130280008	0.91303	26	41	41.0000000315	0.00000	18	39	39.1503716221	0.15037
	59	41	41.4178932727	0.41789	31	43	42.7071159948	0.29288	22	41	41.1728867056	0.17289
	69	43	43.1414373153	0.14144	38	45	44.8425275409	0.15747	26	43	42.9992080159	0.00079
	81	45	45.0000000002	0.00000	45	47	46.7142478213	0.28575	31	45	45.0350274221	0.03503
	93	47	46.6536664956	0.34633	54	49	48.7852127843	0.21479	36	47	46.8270605001	0.17294
	107	49	48.3539726431	0.64603	65	51	50.8832203148	0.11678	43	49	48.9812538521	0.01875
	127	51	50.4141860434	0.58581	80	53	53.1264207502	0.12642	50	51	50.7831682767	0.21683
	148	53	52.1863717431	0.81363	100	55	55.2832999723	0.28330	60	53	52.8584052563	0.14159
	179	55	54.2216733407	0.77833	129	57	57.2678882429	0.26789	73	55	54.8740683736	0.12593
	224	57	56.2712156516	0.72878	186	59	59.0658941302	0.06589	94	57	57.0000000276	0.00000
	319	59	58.5210264093	0.47897	FO	3.32864	FO	9.52588
	FO	14.01292
	710.09501
Tcal - Placas
	Dados- Cobre	T do banho, °C (T∞) 	60	Dados - Alumínio	T do banho, °C (T∞) 	60
	Cp (J/Kg*K)	385	T inicial, °C (Ti)	27	Cp (J/Kg*K)	903	T inicial, °C (Ti)	25
	ρ (Kg/m³)	8933	ρ (Kg/m³)	2702
	Espessura (m)	0.0126	hexp(w/m².K) =	544.2283062653	Espessura (m)	0.0122	hexp(w/m².K) =	627.1491500407
	Comprimento (m)	0.1524	a =	-0.0312	Comprimento (m)	0.1521	a	-0.0486
	Largura (m)	0.1009	Largura (m)	0.1009
	A (m²)	0.03687	hcal(w/m².K) =	532.3145060007	A (m²)	0.03687	hcal(w/m².K) =	621.2426261546
	V (m³)	0.000187	V (m³)	0.000195
	t (s)	TExp(t) , °C	TCal(t) , °C	((TExp - Tcal)2)1/2	t (s)	TExp(t) , °C	TCal(t) , °C	((TExp - Tcal)2)1/2
	0	27	27.00000	0.00000	0	25	25.00000	0.00000
	3	29	29.88701	0.88701	1	27	26.64506	0.35494
	6	31	32.52145	1.52145	3	29	29.70686	0.70686
	8	33	34.14842	1.14842	5	31	32.48760	1.48760
	10	35	35.67906	0.67906	6	33	33.78074	0.78074
	12	37	37.11907	0.11907	7	35	35.01309	0.01309
	14	39	38.47383	0.52617	9	37	37.30675	0.30675
	17	41	40.35705	0.64295	11	39	39.38986	0.38986
	20	43	42.07551	0.92449	13	41	41.28176	0.28176
	24	45	44.13525	0.86475	15	43	42.99999	0.00001
	30	47	46.78969	0.21031	17	45	44.56050	0.43950
	36	49	48.99999	0.00001	20	47	46.63683	0.36317
	46	51	51.89302	0.89302	23	49	48.43393	0.56607
	61	53	54.87069	1.87069	27	51	50.45988	0.54012
	72	55	56.33333	1.33333	32	53	52.50081	0.49919
	81	57	57.21393	0.21393	41	55	55.13769	0.13769
	107	59	58.73990	0.26010	54	57	57.39960	0.39960
	FO	12.09477	FO	7.26695
Tcal - Esferas
	Dados- Cobre	T do banho, °C (T∞) 	60	Ddos - Alumínio	T do banho, °C (T∞) 	60
	Cp (J/Kg*K)	385	T inicial, °C (Ti)	27	Cp (J/Kg*K)	903	T inicial, °C (Ti)	27
	ρ (Kg/m³)	8933	ρ (Kg/m³)	2702
	Diâmetro (m)	0.0509	hexp(w/m².K) =	679.7989923083	Diâmetro (m)	5.07E-02	hexp(w/m².K) =	616.45445043
	Raio (m)	0.02545	a =	-0.0233	Raio (m)	2.54E-02	a =	-0.0299
	A (m²)	0.0081392697	A (m²)	0.0080754325
	V (m³)	6.90E-05	hcal(w/m².K) =	696.0016884646	V (m³)	6.82E-05	hcal(w/m².K) =	560.5443948774
	t (s)	TExp(t) , °C	TCal(t) , °C	((TExp - Tcal)2)1/2	t (s)	TExp(t) , °C	TCal(t) , °C	((TExp - Tcal)2)1/2
	0	27	27.00000	0.00000	0	27	27	0
	2	29	28.53748	0.46252	6	29	31.9671102781	2.9671102781
	5	31	30.71045	0.28955	9	31	34.1628365339	3.1628365339
	9	33	33.37610	0.37610	11	33	35.5302531845	2.5302531845
	12	35	35.21488	0.21488	14	35	37.4468898955	2.4468898955
	16	37	37.47058	0.47058	17	37	39.213402606	2.213402606
	20	39	39.52099	0.52099	19	39	40.3135210236	1.3135210236
	23	41	40.93537	0.06463	22	41	41.8554997208	0.8554997208
	28	43	43.07896	0.07896	26	43	43.7252510675	0.7252510675
	33	45	44.98152	0.01848	29	45	44.9999999033	0.0000000967
	39	47	46.98439	0.01561	33	47	46.5457173356	0.4542826644
	45	49	48.72016	0.27984	39	49	48.5708356904	0.4291643096
	54	51	50.89959	0.10041	44	51	50.0235487763	0.9764512237
	65	53	53.00000	0.00000	52	53	51.973713551	1.026286449
	82	55	55.33369	0.33369	63	55	54.0484485674	0.9515514326
	105	57	57.30420	0.30420	77	57	55.9325456136	1.0674543864
	150	59	59.07854	0.07854	112	59	58.429442135	0.570557865
	FO	3.60894	FO	21.6905127372
	a
	h (w/m².K)	616.45445043
Tcal - Resfriamento
	Dados - Alumínio	T ambiente, °C (T∞) 	25	Dados - Alumínio	T ambiente, °C (T∞) 	25
	Cp (J/Kg*K)	903	T do banho, °C 	60	Cp (J/Kg*K)	903	T do banho, °C 	60
	ρ (Kg/m³)	2702	T inicial (t=0), °C (Ti)	59	ρ (Kg/m³)	2702	T inicial (t=0), °C (Ti)	59
	Diâmetro (m)	5.07E-02	hexp(w/m².K) =	63.91333767	Diâmetro (m)	5.09E-02	hexp(w/m².K) =	14.43204399
	Raio (m)	2.54E-02	a =	-0.0031	Raio (m)	0.02545	a =	-0.0007
	A (m²)	0.0080754325	A (m²)	0.0080754325
	V (m³)	0.0000682374	hcal(w/m².K) =	66.1464374099	V (m³)	0.0000682374	hcal(w/m².K) =	15.8569649581
	t (s)	TExp(t) , °C	TCal(t) , °C	((TExp - Tcal)2)1/2	t (s)	TExp(t) , °C	TCal(t) , °C	((TExp - Tcal)2)1/2
	0	59	59.00000	0.00000	0	59	59.00000	0.00000
	23	57	56.58143	0.41857	54	57	57.61683	0.61683
	42	55	54.71379	0.28621	118	55	56.05020	1.05020
	63	53	52.77779	0.22221	198	53	54.19730	1.19730
	85	51	50.88475	0.11525	300	51	51.99432	0.99432
	110	49	48.88967	0.11033	426	49	49.50111	0.50111
	136	47	46.97774	0.02226	566	47	47.00000	0.00000
	168	45	44.83333	0.16667	682	45	45.12223	0.12223
	200	43	42.89816	0.10184	853	43	42.64243	0.35757
	240	41	40.74252	0.25748	1050	41	40.16199	0.83801
	287	39	38.53901	0.46099	1277	39	37.73308	1.26692
	FO	2.16180	FO	6.94449