Planilha Aletas

Esta é uma pré-visualização de arquivo. Entre para ver o arquivo original

Resultados experimentais
	Prática 2 - Aletas 
	Dimensões das Aletas	Diâmetro (mm)	Comprimento (cm)
	Alumínio	9.8	56.3	Alumínio: k= 237 W/m2
	Aço inox 1	9.6	56.3	Aço Inox: k = 15,1W/m2
	Aço inox 2	10.42	56.3
	Orifício	1	2	3	4	5	6	7	8	9	Extremidade
	Distância (cm)	0	3.5	8.4	13.3	20.7	28.2	35.5	42.9	50.4	56.3
	Regime Transiente	Regime Permanente
	Temperatura na Caldeira (°C)	60	Orifício:1	Orifício	Distância	Temperatura (°C)
	Tempo (min)	Temperatura da Aleta (°C)	Alumínio	Aço Inox 1	Aço Inox 2
	Alumínio	Aço Inox 1	Aço Inox 2	1	0.00	43.90	39.30	41.60
	0	25.20	25.10	25.00	2	3.50	40.80	34.00	35.60
	5	25.90	25.70	25.40	3	8.40	37.20	29.30	30.80
	10	26.90	26.80	26.00	4	13.30	34.90	27.70	28.40
	15	28.10	27.90	27.00	5	20.70	32.30	26.70	26.70
	20	29.10	28.70	27.90	6	28.20	30.30	26.20	26.10
	25	30.50	30.20	29.30	7	35.50	29.00	26.00	26.00
	30	32.30	32.00	30.60	8	42.90	28.30	25.90	25.90
	35	33.90	34.40	33.50	9	50.40	28.30	25.90	25.90
	40	37.80	37.40	36.30	Extremidade	56.30	27.60	25.90	25.90
	45	38.70	38.20	36.10
	50	41.00	40.60	39.10
	55	42.30	41.70	40.60
	60	43.60	42.70	40.60
	65	43.20	39.80	40.90
	70	43.00	42.20	41.10
	75	43.90	39.30	41.60
Cálculo de h
	Dados:
	Tamb(°C)=	25.9
	Alumínio	Alumínio - Caso 1: Convecção na extremidade	Alumínio - Caso 2: Aleta com extremidade adiabática	Alumínio - Caso 3: Aleta com extremidade adiabática	Alumínio - Caso 4: Aleta infinita
	θb (K)=	18.00	h = 	16.3443576888	X(m)	θexp	θcalc	θexp-θcalc	(θexp-θcalc)2	(θexp-θcalc)1/2	h = 	16.3846250603	X(m)	θexp	θcalc	θexp-θcalc	(θexp-θcalc)2	(θexp-θcalc)1/2	h = 	16.0162883587	X(m)	θexp	θcalc	θexp-θcalc	(θexp-θcalc)2	(θexp-θcalc)1/2	h = 	14.9986274323	X(m)	θexp	θcalc	θexp-θcalc	(θexp-θcalc)2	(θexp-θcalc)1/2
	D (m) =	0.01	m = 	5.2521818153	0	18.00	18.00	0.00	0	0	m = 	5.2586476997	0	18.00	18	0.00	0	0	m = 	5.1992028533	0	18.00	18.00	0.00	0	0	m = 	5.0313158444	0	18.00	18	0.00	0	0
	L (m) =	0.563	0.03	14.90	15.39	-0.49	0.2410075783	0.4909252268	0.03	14.90	15.3882475523	-0.49	0.2383856723	0.4882475523	θL (K)=	1.7	0.03	14.90	15.41	-0.51	0.2629800083	0.5128157645	0.03	14.90	15.4781953601	-0.58	0.3343098745	0.5781953601
	AF (m2) = 	0.0177657065	0.081	11.30	11.80	-0.50	0.2542730412	0.5042549367	0.081	11.30	11.7989425932	-0.50	0.2489437113	0.4989425932	0.081	11.30	11.85	-0.55	0.2999875062	0.5477111521	0.081	11.30	11.9751680248	-0.68	0.4558518617	0.6751680248
	k (W/(m K)) =	237	0.131	9.00	9.12	-0.12	0.013544313	0.1163800371	0.131	9.00	9.1101654036	-0.11	0.0121364162	0.1101654036	0.131	9.00	9.17	-0.17	0.0279663385	0.1672313921	0.131	9.00	9.3116786604	-0.31	0.0971435874	0.3116786604
	P (m) =	0.0314159265	0.204	6.40	6.29	0.11	0.0127726944	0.1130163459	0.204	6.40	6.2813908819	0.12	0.0140681229	0.1186091181	0.204	6.40	6.33	0.07	0.0045266605	0.0672804612	0.204	6.40	6.4493756369	-0.05	0.0024379535	0.0493756369
	Ac (m2)=	0.0000785398	0.28	4.40	4.33	0.07	0.0047793555	0.0691328832	0.28	4.40	4.33	0.07	0.0052552216	0.0724929075	0.28	4.40	4.36	0.04	0.0017448052	0.0417708658	0.28	4.40	4.3999946344	0.00	0	0.0000053656
	AF( Adiabatica) (m2) = 	0.0176871666	0.354	3.10	3.10	-0.00	0.0000000013	0.0000357889	0.354	3.10	3.10	-0.00	0	0.0000049784	0.354	3.10	3.10	-0.00	0	0.0000002266	0.354	3.10	3.03	0.07	0.0045978596	0.0678075189
	0.43	2.40	2.33	0.07	0.0051375337	0.0716765909	0.43	2.40	2.33	0.07	0.0044968781	0.0670587664	0.43	2.40	2.29	0.11	0.0120799767	0.1099089473	0.43	2.40	2.07	0.33	0.109779492	0.331329884
	0.505	2.40	1.94	0.46	0.2156284792	0.4643581367	0.505	2.40	1.95	0.45	0.2056651982	0.4535032505	0.505	2.40	1.85	0.55	0.3065629721	0.5536812911	0.505	2.40	1.42	0.98	0.9634612023	0.9815605953
	0.545	1.70	1.85	-0.15	0.0232735392	0.1525566753	0.545	1.70	1.87	-0.17	0.0281154223	0.1676765406	0.545	1.70	1.73	-0.03	0.0008066164	0.0284009934	0.545	1.70	1.16	0.54	0.2917445607	0.5401338359
	FO=	1.9823366216	FO=	1.9767011105	FO=	2.0288010942	FO=	3.535254882
	Aço Inox 1	Aço Inox 1 - Caso 1: Convecção na extremidade	Aço Inox 1 - Caso 2: Aleta com extremidade adiabática	Aço Inox 1 - Caso 3: Aleta com extremidade adiabática	Aço Inox 1 - Caso 4: Aleta infinita
	θb (K)=	13.40	h = 	10.6288123323	X(m)	θexp	θcalc	θexp-θcalc	(θexp-θcalc)2	(θexp-θcalc)1/2	h = 	10.6288099047	X(m)	θexp	θcalc	θexp-θcalc	(θexp-θcalc)2	(θexp-θcalc)1/2	h = 	10.6288104893	X(m)	θexp	θcalc	θexp-θcalc	(θexp-θcalc)2	(θexp-θcalc)1/2	h = 	10.6288102477	X(m)	θexp	θcalc	θexp-θcalc	(θexp-θcalc)2	(θexp-θcalc)1/2
	D (m) =	0.01	m = 	16.7796883934	0	13.40	13.40	0.00	0	0	m = 	16.7796864771	0	13.40	13.4	0.00	0	0	m = 	16.7796869385	0	13.40	13.40	0.00	0	0	m = 	16.7796867478	0	13.40	13.4	0.00	0	0
	L (m) =	0.563	0.03	8.10	8.10	-0.00	0	0.0000000278	0.03	8.10	8.1000005005	-0.00	0	0.0000005005	θL (K)=	0.00	0.03	8.10	8.10	-0.00	0	0.0000002131	0.03	8.10	8.100000347	-0.00	0	0.000000347
	AF (m2) = 	0.0177657065	0.081	3.40	3.44	-0.04	0.0017777114	0.042162915	0.081	3.40	3.4421634738	-0.04	0.0017777585	0.0421634738	0.081	3.40	3.44	-0.04	0.0017776965	0.042162738	0.081	3.40	3.4421630947	-0.04	0.0017777266	0.0421630947
	k (W/(m K)) =	15.1	0.131	1.80	1.49	0.31	0.0976384675	0.3124715467	0.131	1.80	1.49	0.31	0.0976381968	0.3124711135	0.131	1.80	1.49	0.31	0.0976391813	0.3124726889	0.131	1.80	1.49	0.31	0.0976386939	0.312471909
	P (m) =	0.0314159265	0.204	0.80	0.44	0.36	0.1317608342	0.3629887521	0.204	0.80	0.44	0.36	0.1317605607	0.3629883754	0.204	0.80	0.44	0.36	0.1317643032	0.3629935305	0.204	0.80	0.44	0.36	0.1317624345	0.3629909565
	Ac (m2)=	0.0000785398	0.28	0.30	0.12	0.18	0.031651631	0.1779090525	0.28	0.30	0.12	0.18	0.0316513452	0.1779082493	0.28	0.30	0.12	0.18	0.0316578711	0.1779265891	0.28	0.30	0.12	0.18	0.0316546085	0.1779174205
	AF( Adiabatica) (m2) = 	0.0176871666	0.354	0.10	0.04	0.06	0.0041863464	0.0647019818	0.354	0.10	0.04	0.06	0.0041860129	0.0646994039	0.354	0.10	0.04	0.06	0.0041942258	0.0647628429	0.354	0.10	0.04	0.06	0.0041901184	0.0647311239
	0.43	0.00	0.01	-0.01	0.0000991434	0.0099570768	0.43	0.00	0.01	-0.01	0.0000993257	0.0099662269	0.43	0.00	0.01	-0.01	0.0000948512	0.0097391568	0.43	0.00	0.01	-0.01	0.0000970755	0.0098526917
	0.505	0.00	0.00	-0.00	0.0000100266	0.0031664805	0.505	0.00	0.00	-0.00	0.0000102314	0.0031986634	0.505	0.00	0.00	-0.00	0.000005757	0.0023993702	0.505	0.00	0.00	-0.00	0.0000078345	0.0027990167
	0.545	0.00	0.00	-0.00	0.0000046206	0.002149549	0.545	0.00	0.00	-0.00	0.0000048952	0.002212513	0.545	0.00	0.00	-0.00	0.0000004207	0.0006486494	0.545	0.00	0.00	-0.00	0.0000020466	0.0014305811
	FO=	0.9755073822	FO=	0.9756085196	FO=	0.9731057789	FO=	0.9743571412
	Aço Inox 2	Aço Inox 2 - Caso 1: Convecção na extremidade	Aço Inox 2 - Caso 2: Aleta com extremidade adiabática	Aço Inox 2 - Caso 3: Aleta com extremidade adiabática	Aço Inox 2 - Caso 4: Aleta infinita
	θb (K)=	15.70	h = 	11.0779468373	X(m)	θexp	θcalc	θexp-θcalc	(θexp-θcalc)2	(θexp-θcalc)1/2	h = 	11.0779483812	X(m)	θexp	θcalc	θexp-θcalc	(θexp-θcalc)2	(θexp-θcalc)1/2	h = 	11.0779152631	X(m)	θexp	θcalc	θexp-θcalc	(θexp-θcalc)2	(θexp-θcalc)1/2	h = 	11.0779324468	X(m)	θexp	θcalc	θexp-θcalc	(θexp-θcalc)2	(θexp-θcalc)1/2
	D (m) =	0.0142	m = 	14.375633369	0	15.7	15.7	0	0	0	m = 	14.3756343708	0	15.7	15.7	0	0	0	m = 	14.3756128824	0	15.7	15.7	0	0	0	m = 	14.3756240318	0	15.70	15.7	0.00	0	0
	L (m) =	0.563	0.03	9.7	10.2000418852	-0.5000418852	0.250041887	0.5000418852	0.03	9.7	10.2000417053	-0.5000417053	0.250041707	0.5000417053	θL (K)=	0	0.03	9.7	10.2000456735	-0.5000456735	0.2500456756	0.5000456735	0.03	9.70	10.2000435654	-0.50	0.2500435673	0.5000435654
	AF (m2) = 	0.0252741443	0.081	4.9	4.899999928	0.000000072	0	0.000000072	0.081	4.9	4.899999942	0.000000058	0	0.000000058	0.081	4.9	4.8999999941	0.0000000059	0	0.0000000059	0.081	4.90	4.90	0.00	0	0.0000001928
	k (W/(m K)) =	15.1	0.131	2.5	2.3880002488	0.1119997512	0.0125439443	0.1119997512	0.131	2.5	2.3880008495	0.1119991505	0.0125438097	0.1119991505	0.131	2.5	2.387988747	0.112011253	0.0125465208	0.112011253	0.131	2.50	2.39	0.11	0.0125451936	0.1120053285
	P (m) =	0.0446106157	0.204	0.8	0.8361570165	-0.0361570165	0.0013073298
0.0361570165	0.204	0.8	0.8361595104	-0.0361595104	0.0013075102	0.0361595104	0.204	0.8	0.8361082954	-0.0361082954	0.001303809	0.0361082954	0.204	0.80	0.84	-0.04	0.001305654	0.036133834
	Ac (m2)=	0.0001583677	0.28	0.2	0.2804800893	-0.0804800893	0.0064770448	0.0804800893	0.28	0.2	0.2804879764	-0.0804879764	0.0064783143	0.0804879764	0.28	0.2	0.2803256052	-0.0803256052	0.0064522029	0.0803256052	0.28	0.20	0.28	-0.08	0.006465247	0.0804067598
	AF( Adiabatica) (m2) = 	0.0251157766	0.354	0.1	0.0969947828	0.0030052172	0.0000090313	0.0030052172	0.354	0.1	0.0970178347	0.0029821653	0.0000088933	0.0029821653	0.354	0.1	0.0965431032	0.0034568968	0.0000119501	0.0034568968	0.354	0.10	0.10	0.00	0.0000103655	0.0032195429
	0.43	0	0.0330963353	-0.0330963353	0.0010953674	0.0330963353	0.43	0	0.0331651637	-0.0331651637	0.0010999281	0.0331651637	0.43	0	0.0317476374	-0.0317476374	0.0010079125	0.0317476374	0.43	0.00	0.03	-0.03	0.0010534179	0.0324564002
	0.505	0	0.0129235184	-0.0129235184	0.0001670173	0.0129235184	0.505	0	0.0131258623	-0.0131258623	0.0001722883	0.0131258623	0.505	0	0.0089585485	-0.0089585485	0.0000802556	0.0089585485	0.505	0.00	0.01	-0.01	0.0001219306	0.0110422172
	0.545	0	0.0095568189	-0.0095568189	0.0000913328	0.0095568189	0.545	0	0.0099164262	-0.0099164262	0.0000983355	0.0099164262	0.545	0	0.0025102382	-0.0025102382	0.0000063013	0.0025102382	0.545	0.00	0.01	-0.01	0.0000386058	0.0062133543
	FO=	0.787260704	FO=	0.7878780181	FO=	0.775164154	FO=	0.7815211951
	Encontrar h por solver:
	Xm = distância dos orificios
	teta exp = diferença entre T e T amb
	Estimar h e calcular m pela equação
	com m e h, calcular teta cal, pelas equações para cada caso
	calcular as diferenças e raiz
	da raiz, obteve-se a FO e pelo solver foi minimizada
	obteve-se h
Comparando os tipos de aletas
	Caso 1: Covecção na extremidade
	Caso 2: Aleta com extremidade adiabática
	Caso 3: Aleta com temperatura conhecida
	Caso 4: Aleta infinita
	Alumínio	Aço Inox 1	Aço Inox 2
	x (cm)	T exp	T calc	x (cm)	T exp	T calc	x (cm)	T exp	T calc
	Caso 1	Caso 2	Caso 3	Caso 4	Caso 1	Caso 2	Caso 3	Caso 4	Caso 1	Caso 2	Caso 3	Caso 4
	0.000	43.90	43.90	43.90	43.90	43.90	0.000	39.30	39.30	39.30	39.30	39.30	0.000	41.60	41.60	41.60	41.60	41.60
	3.500	40.80	41.29	41.29	41.31	41.38	3.500	34.00	34.00	34.00	34.00	34.00	3.500	35.60	36.10	36.10	36.10	36.10
	8.400	37.20	37.70	37.70	37.75	37.88	8.400	29.30	29.34	29.34	29.34	29.34	8.400	30.80	30.80	30.80	30.80	30.80
	13.300	34.90	35.02	35.01	35.07	35.21	13.300	27.70	27.39	27.39	27.39	27.39	13.300	28.40	28.29	28.29	28.29	28.29
	20.700	32.30	32.19	32.18	32.23	32.35	20.700	26.70	26.34	26.34	26.34	26.34	20.700	26.70	26.74	26.74	26.74	26.74
	28.200	30.30	30.23	30.23	30.26	30.30	28.200	26.20	26.02	26.02	26.02	26.02	28.200	26.10	26.18	26.18	26.18	26.18
	35.500	29.00	29.00	29.00	29.00	28.93	35.500	26.00	25.94	25.94	25.94	25.94	35.500	26.00	26.00	26.00	26.00	26.00
	42.900	28.30	28.23	28.23	28.19	27.97	42.900	25.90	25.91	25.91	25.91	25.91	42.900	25.90	25.93	25.93	25.93	25.93
	50.400	28.30	27.84	27.85	27.75	27.32	50.400	25.90	25.90	25.90	25.90	25.90	50.400	25.90	25.91	25.91	25.91	25.91
	56.300	27.60	27.75	27.77	27.63	27.06	56.300	25.90	25.90	25.90	25.90	25.90	56.300	25.90	25.91	25.91	25.90	25.91
Cálculo das taxas e eficiências
	Dados:
	Tamb(°C)=	25.9
	Alumínio	Caso 1: Covecção na extremidade	Caso 2: Aleta com extremidade adiabática	Caso 3: Aleta com temperatura conhecida	Caso 4: Aleta infinita
	θb (K)=	18.00
	D (m) =	0.01	h =	16.3443576888	Qf =	1.7505109345	h =	16.3846250603	Qf =	1.7524892077	h=	16.0162883587	Qf =	1.734345809	h=	14.9986274323	Qf =	1.685746683
	L (m) =	0.563	m =	5.2521818153	ηf =	0.3364079087	m =	5.2586476997	ηf =	0.3359603863	m =	5.1992028533	ηf =	0.3401285152	m =	5.0313158444	ηf =	0.3530287084
	AF (m2) = 	0.0177657065	θL =	1.7
	k (W/(m K)) =	237
	P (m) =	0.0314159265
	Ac (m2)=	0.0000785398
	AF( Adiabatica) (m2) = 	0.0176871666
	Aço inox 1	Caso 1: Covecção na extremidade	Caso 2: Aleta com extremidade adiabática	Caso 3: Aleta com temperatura conhecida	Caso 4: Aleta infinita
	θb (K)=	13.40
	D (m) =	0.01	h =	10.6288123323	Qf =	0.2666585502	h =	10.6288099047	Qf =	0.2666585195	h=	10.6288104893	Qf =	0.2666585335	h=	10.6288102477	Qf =	0.2666585271
	L (m) =	0.563	m =	16.7796883934	ηf =	0.105854106	m =	16.7796864771	ηf =	0.105854118	m =	16.7796869385	ηf =	0.1058541177	m =	16.7796867478	ηf =	0.1058541176
	AF (m2) = 	0.0177657065	θL =	0.00
	k (W/(m K)) =	15.1
	P (m) =	0.0314159265
	Ac (m2)=	0.0000785398
	AF( Adiabatica) (m2) = 	0.0176871666
	Aço inox 2	Caso 1: Covecção na extremidade	Caso 2: Aleta com extremidade adiabática	Caso 3: Aleta com temperatura conhecida	Caso 4: Aleta infinita
	θb (K)=	15.70
	D (m) =	0.0142	h =	11.0779468373	Qf =	0.539721955	h=	11.0779483812	Qf =	0.5397219828	h=	11.0779152631	Qf =	0.5397213775	h=	11.0779324468	Qf =	0.5397216954
	L (m) =	0.563	m =	14.375633369	ηf =	0.1235562002	m =	14.3756343708	ηf =	0.1235561894	m =	14.3756128824	ηf =	0.1235564202	m =	14.3756240318	ηf =	0.1235563013
	AF (m2) = 	0.0252741443	θL =	0.00
	k (W/(m K)) =	15.1
	P (m) =	0.0446106157
	Ac (m2)=	0.0001583677
	AF( Adiabatica) (m2) = 	0.0251157766
	eficiencia: Qf / Qmax
	Qmax = h . A. teta exp
	Eficiência (ηf)	Taxa de transferência de calor da aleta (Qf (W))
	Caso 1	Caso 2	Caso 3	Caso 4	Caso 1	Caso 2	Caso 3	Caso 4
	Alumínio	0.336408	0.3359603863	0.340129	0.353029	Alumínio	1.7505	1.7525	1.7343	1.6857
	Aço inox 1	0.105854	0.105854	0.105854	0.105854	Aço inox 1	0.2667	0.2667	0.2667	0.2667
	Aço inox 2	0.123556	0.123556	0.123556	0.123556	Aço inox 2	0.5397	0.5397	0.5397	0.5397