64

APÉNDICE A

Apéndice A

65

1. Datos y Resultados del trabajo de Lewandowski.

Lewandowski presenta resultados de investigaciones en

transferencia de calor por convección natural sobre placas

horizontales, rectangulares e isotérmicas. En su trabajo utiliza al

agua como fluido y como longitud característica el ancho de la placa

rectangular [12].

La figura A.1 muestra los resultados obtenidos por

Lewandowski, el factor b es la relación del largo de la placa entre su

ancho. Así, para cada uno de los factores b se tiene una serie de

puntos con valores de Nusselt y Rayleigh.

Beta#

punto Nua Raa h/k gbDT/n a

1 1 24.434 2.299 349.0571 67026239071 2C 23.762 4.39 339.4571 1.2799E+101 3 27.106 5.185 387.2286 1.5117E+101 4 29.39 6.837 419.8571 1.9933E+101 5 32.9 8.453 470.0000 2.4644E+101 6 34.285 11.15 489.7857 3.2507E+101 7C 36.864 15.35 526.6286 4.4752E+101 8 33.24 18.35 474.8571 5.3499E+101 9 36.84 20.7 526.2857 6.035E+101 10 40 31.077 571.4286 9.0603E+101 11 42.084 37.206 601.2000 1.0847E+11

1.81 1 24.745 3.464 353.5000 1.0099E+101.81 2C 27.106 4.338 387.2286 1.2647E+101.81 3 28.513 5.457 407.3286 1.591E+101.81 4 28.15 6.091 402.1429 1.7758E+10

Apéndice A

66

1.81 5 29.09 7.235 415.5714 2.1093E+101.81 6 30 9.498 428.5714 2.7691E+101.81 7C 28.674 11.954 409.6286 3.4851E+101.81 8 29.195 15.35 417.0714 4.4752E+101.81 9 31.576 18.352 451.0857 5.3504E+101.81 10 33.934 22.992 484.7714 6.7032E+101.81 11 35.542 28.35 507.7429 8.2653E+101.81 12 38 33.397 542.8571 9.7367E+10

2.52 1 18.069 0.8317 258.1286 24247813412.52 2 22.691 2.448 324.1571 71370262392.52 3C 26.206 4.427 374.3714 1.2907E+102.52 4 24.83 5.659 354.7143 1.6499E+102.52 5 24.9 7.583 355.7143 2.2108E+102.52 6 27.91 10.215 398.7143 2.9781E+102.52 7 29.459 12.839 420.8429 3.7431E+102.52 8C 29.45 15.46 420.7143 4.5073E+102.52 9 30.41 18.352 434.4286 5.3504E+102.52 10 31.42 22.831 448.8571 6.6563E+102.52 11 37.835 29.153 540.5000 8.4994E+102.52 12 35.125 40.528 501.7857 1.1816E+11

3.66 1 17.412 0.7184 248.7429 20944606413.66 2 19.278 1.4586 275.4000 42524781343.66 3C 25.053 4.0552 357.9000 1.1823E+103.66 4 25.3 4.933 361.4286 1.4382E+103.66 5 27.412 7.482 391.6000 2.1813E+103.66 6 27.91 12.839 398.7143 3.7431E+103.66 7C 28 15.35 400.0000 4.4752E+103.66 8 27.41 20 391.5714 5.8309E+103.66 9 31.42 22.275 448.8571 6.4942E+103.66 10 38.545 49.9 550.6429 1.4548E+113.66 11 37.486 51.825 535.5143 1.5109E+11

4.66 1 15.873 0.5781 226.7571 16854227414.66 2 22.087 2.348 315.5286 68454810504.66 3 28.933 4.769 413.3286 1.3904E+104.66 4 25.738 7.235 367.6857 2.1093E+104.66 5C 28.674 8.127 409.6286 2.3694E+10

Apéndice A

67

4.66 6 27.91 11.371 398.7143 3.3152E+104.66 7 27.412 13.118 391.6000 3.8245E+104.66 8C 28.674 15.46 409.6286 4.5073E+104.66 9 31.129 17.835 444.7000 5.1997E+104.66 10 27.412 21.742 391.6000 6.3388E+104.66 11 36.455 47.024 520.7857 1.371E+114.66 12 37.835 51.076 540.5000 1.4891E+11

A.1.1 Resultados de Lewandowski.

A.1 Resultados experimentales de transferencia de calor sobre una placa

horizontal, isotérmica y rectangular con diferentes anchos [12].

Apéndice A

68

d[m] Nud Rad

0.017214 6.01 34190.470.029849 10.13 340387.400.034391 13.32 614870.860.043516 18.27 1642605.440.052127 24.50 3490645.520.065978 32.32 9336368.670.086604 45.61 29068575.280.100811 47.87 54810407.480.111697 58.78 84099906.880.157835 90.19 356246975.020.183960110.60 675283748.89

0.024400 8.63 146703.090.029548 11.44 326278.080.035920 14.63 737350.890.039442 15.86 1089595.210.045663 18.98 2008332.930.057562 24.67 5281440.340.070005 28.68 11956621.990.086604 36.12 29068575.280.100820 45.48 54831634.370.122137 59.21 122130830.840.145969 74.11 257066022.100.167807 91.10 460088106.82

0.007247 1.87 922.770.018159 5.89 42736.430.030063 11.25 350690.000.037049 13.14 838991.500.047525 16.91 2373129.830.061240 24.42 6839785.18

0.074392 31.31 15410212.480.087132 36.66 29815447.060.100820 43.80 54831634.370.121409 54.50 119119499.470.149480 80.79 283883822.130.197846 99.28 915049424.14

0.006398 1.59 548.450.011688 3.22 6789.920.027901 9.99 256786.410.032963 11.91 515121.870.046986 18.40 2262728.120.074392 29.66 15410212.480.086604 34.64 29068575.280.108474 42.48 74424452.750.118888 53.36 109129557.500.236159130.041916118330.470.243890130.612191925250.09

0.005318 1.21 253.440.017526 5.53 36850.680.032028 13.24 456816.320.045663 16.79 2008332.930.050411 20.65 3035442.420.067089 26.75 10010625.200.075765 29.67 16633320.520.087132 35.69 29815447.060.098398 43.76 49538185.850.116463 45.61 100132118.630.224526116.931551772434.240.240887130.202081438053.74

A.1.2 Datos de Ecuación adimensional (9.5)

Apéndice A

69

2. Resultados del trabajo de Fujii e Imura

Fujii e Imura hicieron un estudio experimental sobre la

transferencia de calor por convección natural en una placa con

diferentes inclinaciones. El calor se transfiere de un lado de la

superficie de dos placas del mismo largo, pero las placas tienen

diferentes anchos, una tiene 5cm y la otra 10cm. La dimensión

característica usada por Fujii e Imura fue el ancho de la placa.

A.2 Ralación de Nu vs. Ra para una placa horizontal encarada hacia

arriba[3].

Apéndice A

70

[10-7] B[10-7]L [cm] # punto Nusselt Ra h/k (gbDT)/na

5 1 27.478 0.719 549.568 5749.65 2 37.405 1.329 748.100 10635.25 3 40.864 2.245 817.270 17958.45 4 49.471 3.300 989.414 26399.25 5 58.364 4.518 1167.280 36142.45 6 63.905 6.275 1278.100 50196.05 7 70.000 8.291 1400.000 66330.45 8 74.813 10.680 1496.260 85440.05 9 82.206 13.286 1644.120 106288.05 10 86.807 17.005 1736.140 136040.0

30 1 115.280 51.144 384.267 1894.22230 2 139.388 88.337 464.627 3271.74130 3 160.720 132.913 535.733 4922.70430 4 181.829 207.779 606.097 7695.51930 5 224.399 421.576 747.997 15613.92630 6 261.735 771.578 872.450 28576.96330 7 300.0001232.4401000.000 45645.92630 8 339.6101971.7301132.033 73027.03730 9 414.9503360.7001383.167124470.37030 10 463.8904690.0101546.300173704.07430 11 509.3805888.1901697.933218081.111

A.2.1. Resultados de Fujii e Imura

Apéndice A

71

d[m] Nud Rad

0.10718658.9059084 70802712.30.180895135.327778 6295461220.282509 230.88612 40491554180.392114387.963047 1.5916E+100.512273597.965787 4.8587E+100.677467865.870424 1.5607E+110.8587911202.30733 4.2012E+111.0652361593.87023 1.0328E+121.2827252108.95352 2.2433E+121.5824792747.40576 5.3911E+120.04166916.0120387 1370479.940.06634130.8236615 9552546.620.09392050.3158278 40782285.10.13736283.2543821 1994497550.250804187.60020724632759510.419475365.970717 2.1093E+100.624846624.845608 1.1136E+110.9320341055.09331 5.9126E+111.4672082029.39312 3.9313E+121.9483123012.67485 1.2847E+132.3644884014.74289 2.8829E+13

A.2.2. Datos de Ecuación adimensional (9.3).

3. Resultados del trabajo de Al-Arabi

Al-Arabi desarrolló experimentos en transferencia de calor por

convección natural de placas isotérmicas encaradas hacia arriba y,

utilizando aire como fluido.

Apéndice A

72

A.3 Correlación de resultados de diferentes tipos de placas [14].

En la figura A.3 se muestran los resultados de Al-Arabi en

relación a los números de Nusselt y Rayleigh. Las placas utilizadas

para los experimentos tuvieron diferentes geometrías cuadrada,

rectangular y circular

A.4 Variación del coeficiente de transferencia de calor por

convección con el largo de la placa [14].

Apéndice A

73

La figura A.4 muestra los valores de los coeficientes de

transferencia de calor por convección en realción a diferentes

anchos de la placa.

PLACACUADRADADimensiones #Largo [mm] punto Nusselt Ra h/k (gbDT)/na

50 1 18.197 471162 363.9400 3.769E+0975 2 21.135 1593819 281.8000 3.778E+09100 3 27.227 4211048 272.2700 4.211E+09120 4 33.496 6100506 279.1333 3.53E+09150 5 45.973 12518750 306.4867 3.709E+09250 6 70.796 61694138 283.1840 3.948E+09300 7 63.096 98883072 210.3200 3.662E+09450 8 125.892307471508279.7600 3.374E+09450 9 102.353398107170227.4511 4.369E+09

PLACACIRCULAR

Dimensiones #Diámetro [mm] punto Nusselt Ra h/k (gbDT)/na

100 1 35.481 4404559 354.81004.405E+09150 2 50.119 17534865 334.12675.196E+09250 3 66.834 66740621 267.33604.271E+09300 4 80.353 94538728 267.84333.501E+09400 5 103.514245608788258.78503.838E+09500 6 118.85 473816037237.70003.791E+09500 7 139.637498380424279.27403.987E+09

Apéndice A

74

PLACARECTANGULAR Con mismo

ancho:150

[mm]Dimensiones #Largo [mm] punto Nusselt Ra h/k (gbDT)/na

250 1 40.272 14006882 268.4800 4.15E+09300 2 47.863 14405774 319.0867 4.268E+09350 3 36.099 16208995 240.6600 4.803E+09450 4 276.301806 4.387E+09600 5 240.878498 4.387E+09

A.3.1. Resultados de Al-Arabi

d[m] Nud Rad

0.010547943.838817664423.472410.010568522.97821006 4459.62380.011591053.155895666557.808450.009976292.784713893505.328780.01040481 3.1889353 4178.203170.010973 3.107378935216.75436

0.0102927 2.164760763993.431030.0095994 2.685527972984.691970.011959532.720208337473.168430.01204277 4.272895 7692.74860.013859914.63096396 13832.7790.011732263.136454936897.870470.009906632.653424223404.266370.010710462.771706064715.069990.01059848 2.5192584 4512.63640.011064263.089960735400.305460.011448353.073652666227.249140.011725193.741353036880.546250.012962963.1196658410461.52040.012002513.316313947585.931380.012002512.891145497585.93138

A.3.2 Datos de Ecuación adimensional (9.1)

Apéndice A

75

4. Resultados del trabajo de Lloyd y Moran

Lloyd y Moran investigaron experimentalmente la

transferencia de calor por convección natural sobre placas

circulares, rectangulares, cuadradas y triángulos rectángulos. En sus

experimentos los autores utilizaron el número de Schmidt con valor

de 2200.

A.5.a Resultados para la transferencia de masa laminar [9].

Apéndice A

76

A.5.b Resultados para la transferencia de masa turbulenta [9].

[cm] [m] #Forma de

placa Medidas L=A/P pto Nu Ra h/k (gbDT)/na

circular 0.316 0.000790 1 8.368 27639 10592.4051 5.606E+13circular 0.597 0.001493 2 11.97 179512 8020.1005 5.399E+13circular 1.27 0.003175 3 22.59 2319819 7114.9606 7.248E+13circular 5.08 0.012700 4 80 100000000 6299.2126 4.882E+13circular 10.16 0.025400 5 136.6 848987954 5377.9528 5.181E+13

cuadrada .635x.635 0.001588 1 12.52 216858 7886.6142 5.42E+13cuadrada 1.27x1.27 0.003175 2 19.63 1646233 6182.6772 5.144E+13cuadrada 12.7x12.7 0.031750 3 174.0 1.59E+09 5482.2047 4.969E+13

rectangular .635x1.27 0.002117 1 15.82 500000 7474.0157 5.272E+13rectangular 2.54x1.27 0.004233 2 26.21 3890814 6191.3386 5.129E+13rectangular 3.81x1.27 0.004763 3 28.42 5476627 5967.4541 5.07E+13rectangular 6.35x1.27 0.005292 4 30 7754108 5669.2913 5.233E+13rectangular 12.7x1.27 0.005773 5 35.19 9000000 6095.9055 4.678E+13rectangular 12.7x2.54 0.010583 6 65.53 54933833 6191.8110 4.634E+13rectangular 12.7x5.18 0.018397 7 109.0 285570645 5926.6604 4.587E+13

triángulorecto

1.91x2.54x3.15 0.003179 1 15.96 572919 5020.1921 1.783E+13

triángulorecto

1.27x1.91x2.29 0.002217 2 20 1528290 9020.0767 1.402E+14

triángulorecto

7.62x10.17x12.7 0.012708 3 78.23 9921960 6155.8046 4.834E+12

triángulorecto

15.25x20.3x25.4 0.025396 4 151.5 811788178 5966.7308 4.956E+13

A.5.1 Resultados de Lloyd yMoran

Apéndice A

77

Números de Nusselt y Rayleigh a partir de la ecuación (7.3),

d[m] Nud Rad

37.459854396789.9452.9467E+1836.283064290993.8182.5791E+1846.613775331655.1777.3412E+1833.301663209774.258 1.803E+1835.029159188385.1612.2268E+18

36.402962 287096.12 2.6148E+1834.814292215245.5282.1704E+1833.808672185346.0621.9204E+18

35.555530265742.5922.3699E+1834.727970215012.623 2.148E+1834.390432205223.3232.0622E+1835.329271 200291.93 2.3076E+1832.116834195781.1851.5499E+1831.858184197259.8561.4984E+1831.580578187167.3581.4447E+18

14.13323070951.53035.0336E+1681.719441737115.6257.6511E+194.654950 28654.95964.8761E+14

33.732947201275.4131.9025E+18

A.5.2 Datos de Ecuación adimensional (9.7).

Apéndice A

78

5. Resultados Experimental

Números de Nusselt y Rayleigh a partir de la ecuación (7.3),

(gbDT)/na h/k d[m] Nud Rad

2221098.6172.5241.88334E-050.003249221.4837E-082588029.4347.3602.14503E-050.007450972.5543E-081659778.5444.0601.46985E-050.006527015.2707E-0974762.7 272.0421.05102E-060.00028592 8.68E-14168216.0 290.7212.09553E-060.000609211.5479E-1277994.9 342.6981.08956E-060.000373391.0088E-13

1247540.1231.8011.15282E-050.002672251.9113E-091006475.6146.4539.60308E-06 0.0014064 8.9132E-10475892.7 181.6245.07702E-060.000922116.2278E-11

3551631.4355.8442.80802E-050.009992187.8637E-083897714.2218.4953.03922E-050.006640541.0942E-073242420.7215.431 2.5986E-05 0.005598175.6897E-083296419.9264.3542.63538E-050.006966736.0335E-084138803.0178.8113.19847E-050.005719221.3543E-072644010.0203.3182.18445E-050.00444137 2.756E-084315013.9 74.564 3.31398E-050.002471051.5705E-072614602.4131.1872.16375E-050.002838562.6487E-082421949.3157.0592.02732E-050.003184092.0181E-081229781.1163.6921.13884E-050.001864181.8164E-09

A.6.1 Datos de Ecuación adimensional.

6. Resultados del trabajo de Restrepo y Glicksman

Restrepo y Glicksman estudiaron los efectos en las condiciones

de frontera en la convección natural de placas horizontales.

La tabla A.7.1 muestra los resultados obtenidos por los autores,

Apéndice A

79

Lados fríos Lados calientes Extensiones aisladas

d[in] Ra d[in] Ra d[in] Ra

0.83 1.66E6 0.81 2.02E6 0.94 2.42E6

0.82 2.12E6 0.75 2.44E6 0.81 2.92E6

0.80 2.58E6 0.68 2.70E6

0.76 2.93E6 0.58 2.86E6

0.68 3.19E6 0.55 2.81E6

A.7.1. Datos según Restrepo (1974).

7. COMPARACIÓN VARIOS AUTORES.

Al-ArabilogNud logRad

0.58419748 3.645763320.47395533 3.649298220.49912264 3.816758730.44478058 3.544728760.50364571 3.620989550.49239422 3.717400390.33540991 3.601346190.42902968 3.474899520.43460217 3.873504770.63072222 3.886081540.6656714 4.14090944

0.49643905 3.838715040.42380669 3.532023530.44274717 3.67348814

Apéndice A

80

0.40127271 3.654430340.48995296 3.732418330.48765479 3.794296240.57302869 3.837622920.49410808 4.019594810.52065564 3.880008910.46106995 3.88000891

Fujii e ImuralogNud logRad

1.775886 7.852.131695 8.792.363783 9.602.588036 10.202.776634 10.682.937491 11.193.080019 11.623.202456 12.013.324061 12.353.43828 12.731.204443 6.131.488883 6.981.701702 7.611.92071 8.292.273331 9.392.563634 10.322.795772 11.043.023287 11.773.307318 12.593.478956 13.103.603657 13.44

Experimental

Apéndice A

81

logNud logRad-2.48822059-7.82864252-2.12778734-7.59273269-2.1852858 -8.27813287

-3.54375182-13.0614804-3.21523009-11.8102513-3.42783629-12.9961759-2.57312321-8.71866268-2.85189203-9.04996447-3.03521833-10.2056652-2.00033992 -7.1043714-2.17779656-6.96090242-2.25195391-7.24491437-2.15697077-7.21942963-2.24266283-6.86829989-2.35248299-7.55971346-2.60711903-6.80396802-2.54690258-7.57697093-2.49701491-7.69506765-2.72951104-8.74078493

Lloyd MoranlogNud logRad

5.59856066 18.46933935.46388376 18.41146235.52068678 18.86576585.32175219 18.25598665.27504669 18.34768955.45802732 18.41744445.33293414 18.33653285.26798336 18.2833855.42446117 18.37473415.33246396 18.33203135.31222672 18.31432115.30166345 18.36315845.29177095 18.19029765.29503871 18.17563555.27223011 18.1597659

Apéndice A

82

4.85096177 16.70187995.86753562 19.88372264.4571998 14.6880769

5.30379073 18.279319

Lewandowski et allogNud logRad

0.778783294.533905131.005719315.531973471.124410485.788783911.261755486.215533261.389160866.542905751.5094052 6.970177991.659040917.46342375

1.68007 7.738863031.769261347.924795511.955164028.551751192.04374145 8.82948630.935774595.166439271.05849822 5.51358791.165283 5.86767421

1.200337266.037265191.278209456.302835711.392161336.722752381.45752003 7.07760851.557746947.463423751.657806387.739031191.772384588.086825311.869905738.410044681.959494788.662841010.271976342.965093370.769849264.630798281.051338695.544923391.118649345.923757561.22802616 6.37532151.387694536.83504246

1.495643817.187808631.564162587.474441331.641465687.739031191.736358828.075982861.907379548.453140641.996846138.961444550.2017715 2.739134840.507704843.831864810.999379665.409572031.076053485.711909991.264812286.354632371.472185657.187808631.539596497.463423751.628137597.871715651.727247748.037942392.114075319.282422332.115964589.340825740.081285372.403882040.742719214.566445531.121831565.659741611.225040526.302835711.31491886 6.4822221.42731402 7.00046121.472311177.220978961.552565567.474441331.64105416 7.69494011.659032038.000573412.067926599.190828032.114609289.31836349