Lumped vs Unlumped Convective Heat Transfer

23
2.4048 5.5201 0.519153014595 -0.34026345796 1.2484591695 Fo 0.00 1.00E+00 1.00E+00 5.37E-01 0.05 7.49E-01 2.18E-01 9.68E-01 0.10 5.61E-01 4.75E-02 8.48E-01 0.15 4.20E-01 1.04E-02 6.62E-01 0.20 3.15E-01 2.26E-03 5.01E-01 0.25 2.36E-01 4.92E-04 3.77E-01 0.30 1.76E-01 1.07E-04 2.82E-01 0.35 1.32E-01 2.33E-05 2.12E-01 0.40 9.89E-02 5.09E-06 1.58E-01 0.45 7.41E-02 1.11E-06 1.19E-01 0.50 5.55E-02 2.42E-07 8.89E-02 0.55 4.16E-02 5.27E-08 6.66E-02 0.60 3.11E-02 1.15E-08 4.99E-02 0.65 2.33E-02 2.50E-09 3.73E-02 0.70 1.75E-02 5.45E-10 2.80E-02 0.75 1.31E-02 1.19E-10 2.09E-02 0.80 9.79E-03 2.59E-11 1.57E-02 0.85 7.33E-03 5.64E-12 1.17E-02 0.90 5.49E-03 1.23E-12 8.80E-03 0.95 4.11E-03 2.68E-13 6.59E-03 1.00 3.08E-03 5.84E-14 4.93E-03 1.05 2.31E-03 1.27E-14 3.69E-03 1.10 1.73E-03 2.77E-15 2.77E-03 1.15 1.29E-03 6.04E-16 2.07E-03 1.20 9.69E-04 1.32E-16 1.55E-03 1.25 7.25E-04 2.87E-17 1.16E-03 1.30 5.43E-04 6.26E-18 8.70E-04 1.35 4.07E-04 1.36E-18 6.52E-04 1.40 3.05E-04 2.97E-19 4.88E-04 1.45 2.28E-04 6.48E-20 3.66E-04 1.50 1.71E-04 1.41E-20 2.74E-04 1.55 1.28E-04 3.08E-21 2.05E-04 1.60 9.58E-05 6.70E-22 1.54E-04 1.65 7.18E-05 1.46E-22 1.15E-04 1.70 5.37E-05 3.18E-23 8.61E-05 1.75 4.03E-05 6.94E-24 6.45E-05 1.80 3.01E-05 1.51E-24 4.83E-05 1.85 2.26E-05 3.29E-25 3.62E-05 1.90 1.69E-05 7.18E-26 2.71E-05 1.95 1.27E-05 1.56E-26 2.03E-05 2.00 9.48E-06 3.41E-27 1.52E-05 λ1ro λ2ro J11ro) J12ro) λ1roJ11ro) exp(-Fo(λ1ro) 2 ) exp(-Fo(λ2ro) 2 ) θ|r=0i

description

Contains step-by-step process of developing Heisler chart for centerline temperature for an infinitely long cylinder

Transcript of Lumped vs Unlumped Convective Heat Transfer

Const T1ro2roJ1(1ro)J1(2ro)1roJ1(1ro)2roJ1(2ro)2.40485.52010.5191530146-0.3402634581.2484591695-1.8782883143Foexp(-Fo(1ro)2)exp(-Fo(2ro)2)|r=0/i0.001.00E+001.00E+005.37E-010.057.49E-012.18E-019.68E-010.105.61E-014.75E-028.48E-010.154.20E-011.04E-026.62E-010.203.15E-012.26E-035.01E-010.252.36E-014.92E-043.77E-010.301.76E-011.07E-042.82E-010.351.32E-012.33E-052.12E-010.409.89E-025.09E-061.58E-010.457.41E-021.11E-061.19E-010.505.55E-022.42E-078.89E-020.554.16E-025.27E-086.66E-020.603.11E-021.15E-084.99E-020.652.33E-022.50E-093.73E-020.701.75E-025.45E-102.80E-020.751.31E-021.19E-102.09E-020.809.79E-032.59E-111.57E-020.857.33E-035.64E-121.17E-020.905.49E-031.23E-128.80E-030.954.11E-032.68E-136.59E-031.003.08E-035.84E-144.93E-031.052.31E-031.27E-143.69E-031.101.73E-032.77E-152.77E-031.151.29E-036.04E-162.07E-031.209.69E-041.32E-161.55E-031.257.25E-042.87E-171.16E-031.305.43E-046.26E-188.70E-041.354.07E-041.36E-186.52E-041.403.05E-042.97E-194.88E-041.452.28E-046.48E-203.66E-041.501.71E-041.41E-202.74E-041.551.28E-043.08E-212.05E-041.609.58E-056.70E-221.54E-041.657.18E-051.46E-221.15E-041.705.37E-053.18E-238.61E-051.754.03E-056.94E-246.45E-051.803.01E-051.51E-244.83E-051.852.26E-053.29E-253.62E-051.901.69E-057.18E-262.71E-051.951.27E-051.56E-262.03E-052.009.48E-063.41E-271.52E-052.057.10E-067.43E-281.14E-052.105.32E-061.62E-288.52E-062.153.98E-063.53E-296.38E-062.202.98E-067.69E-304.78E-062.252.23E-061.68E-303.58E-062.301.67E-063.65E-312.68E-062.351.25E-067.96E-322.01E-062.409.38E-071.74E-321.50E-062.457.03E-073.78E-331.13E-062.505.26E-078.24E-348.43E-072.553.94E-071.80E-346.31E-072.602.95E-073.91E-354.73E-072.652.21E-078.53E-363.54E-072.701.66E-071.86E-362.65E-072.751.24E-074.05E-371.99E-072.809.28E-088.83E-381.49E-072.856.95E-081.92E-381.11E-072.905.21E-084.19E-398.34E-082.953.90E-089.14E-406.25E-083.002.92E-081.99E-404.68E-083.052.19E-084.34E-413.50E-083.101.64E-089.46E-422.62E-083.151.23E-082.06E-421.96E-083.209.18E-094.49E-431.47E-083.256.88E-099.79E-441.10E-083.305.15E-092.13E-448.25E-093.353.86E-094.65E-456.18E-093.402.89E-091.01E-454.63E-093.452.16E-092.21E-463.47E-093.501.62E-094.81E-472.60E-093.551.21E-091.05E-471.94E-093.609.09E-102.29E-481.46E-093.656.81E-104.98E-491.09E-093.705.10E-101.09E-498.16E-103.753.82E-102.37E-506.11E-103.802.86E-105.16E-514.58E-103.852.14E-101.12E-513.43E-103.901.60E-102.45E-522.57E-103.951.20E-105.34E-531.92E-104.008.99E-111.16E-531.44E-10

(Bi)^-1=1Bi-1Bi1ro2roJ0(1ro)J0(2ro)111.25584.07950.6429404871-0.3907101378Foexp(-Fo(1ro)2)exp(-Fo(2ro)2)|r=0/i0.001.00E+001.00E+009.17E-010.059.24E-014.35E-019.89E-010.108.54E-011.89E-019.76E-010.157.89E-018.24E-029.29E-010.207.29E-013.58E-028.70E-010.256.74E-011.56E-028.09E-010.306.23E-016.79E-037.50E-010.355.76E-012.95E-036.94E-010.405.32E-011.29E-036.42E-010.454.92E-015.59E-045.93E-010.504.55E-012.43E-045.49E-010.554.20E-011.06E-045.07E-010.603.88E-014.61E-054.69E-010.653.59E-012.00E-054.33E-010.703.32E-018.72E-064.00E-010.753.06E-013.80E-063.70E-010.802.83E-011.65E-063.42E-010.852.62E-017.19E-073.16E-010.902.42E-013.13E-072.92E-010.952.24E-011.36E-072.70E-011.002.07E-015.92E-082.49E-011.051.91E-012.58E-082.30E-011.101.76E-011.12E-082.13E-011.151.63E-014.88E-091.97E-011.201.51E-012.12E-091.82E-011.251.39E-019.23E-101.68E-011.301.29E-014.02E-101.55E-011.351.19E-011.75E-101.44E-011.401.10E-017.61E-111.33E-011.451.02E-013.31E-111.23E-011.509.39E-021.44E-111.13E-011.558.68E-026.27E-121.05E-011.608.02E-022.73E-129.68E-021.657.41E-021.19E-128.95E-021.706.85E-025.16E-138.27E-021.756.33E-022.25E-137.64E-021.805.85E-029.78E-147.06E-021.855.41E-024.25E-146.53E-021.905.00E-021.85E-146.03E-021.954.62E-028.05E-155.57E-022.004.27E-023.50E-155.15E-022.053.94E-021.53E-154.76E-022.103.65E-026.64E-164.40E-022.153.37E-022.89E-164.07E-022.203.11E-021.26E-163.76E-022.252.88E-025.47E-173.47E-022.302.66E-022.38E-173.21E-022.352.46E-021.04E-172.97E-022.402.27E-024.50E-182.74E-022.452.10E-021.96E-182.53E-022.501.94E-028.53E-192.34E-022.551.79E-023.71E-192.16E-022.601.66E-021.61E-192.00E-022.651.53E-027.03E-201.85E-022.701.42E-023.06E-201.71E-022.751.31E-021.33E-201.58E-022.801.21E-025.79E-211.46E-022.851.12E-022.52E-211.35E-022.901.03E-021.10E-211.25E-022.959.54E-034.77E-221.15E-023.008.82E-032.07E-221.06E-023.058.15E-039.03E-239.84E-033.107.53E-033.93E-239.09E-033.156.96E-031.71E-238.40E-033.206.43E-037.44E-247.76E-033.255.94E-033.24E-247.18E-033.305.49E-031.41E-246.63E-033.355.08E-036.13E-256.13E-033.404.69E-032.67E-255.66E-033.454.34E-031.16E-255.23E-033.504.01E-035.05E-264.84E-033.553.70E-032.20E-264.47E-033.603.42E-039.56E-274.13E-033.653.16E-034.16E-273.82E-033.702.92E-031.81E-273.53E-033.752.70E-037.87E-283.26E-033.802.50E-033.43E-283.01E-033.852.31E-031.49E-282.79E-033.902.13E-036.49E-292.57E-033.951.97E-032.82E-292.38E-034.001.82E-031.23E-292.20E-036.007.77E-054.31E-449.38E-058.003.32E-061.51E-584.00E-0610.001.42E-075.29E-731.71E-0712.006.04E-091.85E-877.29E-0914.002.58E-106.50E-1023.11E-1016.001.10E-112.28E-1161.33E-1118.004.70E-137.98E-1315.67E-1320.002.00E-142.80E-1452.42E-1422.008.56E-169.80E-1601.03E-1524.003.65E-173.44E-1744.41E-1726.001.56E-181.20E-1881.88E-1828.006.65E-204.22E-2038.03E-2030.002.84E-211.48E-2173.43E-21

(Bi)^-1=10Bi-1Bi1ro2roJ0(1ro)J0(2ro)100.10.44173.85770.9518168082-0.4026236371Foexp(-Fo(1ro)2)exp(-Fo(2ro)2)|r=0/i0.001.00E+001.00E+009.91E-011.008.23E-013.44E-078.43E-012.006.77E-011.19E-136.94E-013.005.57E-014.08E-205.71E-014.004.58E-011.40E-264.69E-015.003.77E-014.84E-333.86E-016.003.10E-011.66E-393.18E-017.002.55E-015.73E-462.61E-018.002.10E-011.97E-522.15E-019.001.73E-016.79E-591.77E-0110.001.42E-012.34E-651.46E-0111.001.17E-018.05E-721.20E-0112.009.62E-022.77E-789.86E-0213.007.92E-029.54E-858.11E-0214.006.51E-023.28E-916.67E-0215.005.36E-021.13E-975.49E-0216.004.41E-023.89E-1044.52E-0217.003.63E-021.34E-1103.72E-0218.002.98E-024.61E-1173.06E-0219.002.46E-021.59E-1232.52E-0220.002.02E-025.47E-1302.07E-0221.001.66E-021.88E-1361.70E-0222.001.37E-026.48E-1431.40E-0223.001.13E-022.23E-1491.15E-0224.009.26E-037.68E-1569.48E-0325.007.62E-032.64E-1627.80E-0326.006.27E-039.10E-1696.42E-0327.005.16E-033.13E-1755.28E-0328.004.24E-031.08E-1814.35E-0329.003.49E-033.71E-1883.58E-0330.002.87E-031.28E-1942.94E-03

Heisler Chart (Image)

Unlumped (Small Bi^-1 =0.25)Bi-1Bi1ro2roJ0(1ro)J0(2ro)0.2541.90814.60180.2771120147-0.2956756334Foexp(-Fo(1ro)2)exp(-Fo(2ro)2)|r=0/i0.001.00E+001.00E+007.42E-011.002.62E-026.36E-103.86E-022.006.88E-044.04E-191.01E-033.001.80E-052.57E-282.65E-054.004.73E-071.63E-376.96E-075.001.24E-081.04E-461.83E-086.003.26E-106.59E-564.79E-107.008.54E-124.19E-651.26E-118.002.24E-132.66E-743.29E-139.005.88E-151.69E-838.64E-1510.001.54E-161.07E-922.27E-1611.004.04E-186.83E-1025.94E-1812.001.06E-194.34E-1111.56E-1913.002.78E-212.76E-1204.09E-2114.007.30E-231.75E-1291.07E-2215.001.91E-241.11E-1382.81E-2416.005.02E-267.08E-1487.38E-2617.001.32E-274.50E-1571.94E-2718.003.45E-292.86E-1665.08E-2919.009.06E-311.82E-1751.33E-3020.002.38E-321.16E-1843.49E-3221.006.23E-347.34E-1949.16E-3422.001.64E-354.67E-2032.40E-3523.004.29E-372.97E-2126.31E-3724.001.13E-381.88E-2211.65E-3825.002.95E-401.20E-2304.34E-4026.007.74E-427.61E-2401.14E-4127.002.03E-434.84E-2492.98E-4328.005.33E-453.07E-2587.83E-4529.001.40E-461.95E-2672.05E-4630.003.66E-481.24E-2765.39E-48

Unlumped(Small Bi^-1)vs LumpedBi-1Bi0.254Fo|r=0/i0.001.00E+001.003.35E-042.001.13E-073.003.78E-114.001.27E-145.004.25E-186.001.43E-217.004.78E-258.001.60E-289.005.38E-3210.001.80E-3511.006.05E-3912.002.03E-4213.006.81E-4614.002.29E-4915.007.67E-5316.002.57E-5617.008.63E-6018.002.89E-6319.009.71E-6720.003.26E-7021.001.09E-7322.003.67E-7723.001.23E-8024.004.13E-8425.001.38E-8726.004.64E-9127.001.56E-9428.005.22E-9829.001.75E-10130.005.88E-105

Unlumped (Large Bi^-1=50)Bi-1Bi1ro2roJ0(1ro)J0(2ro)500.020.19953.83690.9900746634-0.4027539633Foexp(-Fo(1ro)2)exp(-Fo(2ro)2)|r=0/i0.001.00E+001.00E+009.98E-011.009.61E-014.04E-079.66E-012.009.23E-011.63E-139.28E-013.008.87E-016.59E-208.92E-014.008.53E-012.66E-268.57E-015.008.20E-011.08E-328.24E-016.007.88E-014.35E-397.92E-017.007.57E-011.76E-457.61E-018.007.27E-017.10E-527.31E-019.006.99E-012.87E-587.02E-0110.006.72E-011.16E-646.75E-0111.006.45E-014.68E-716.49E-0112.006.20E-011.89E-776.23E-0113.005.96E-017.64E-845.99E-0114.005.73E-013.09E-905.76E-0115.005.50E-011.25E-965.53E-0116.005.29E-015.04E-1035.32E-0117.005.08E-012.04E-1095.11E-0118.004.89E-018.23E-1164.91E-0119.004.69E-013.32E-1224.72E-0120.004.51E-011.34E-1284.53E-0121.004.34E-015.43E-1354.36E-0122.004.17E-012.19E-1414.19E-0123.004.00E-018.86E-1484.02E-0124.003.85E-013.58E-1543.87E-0125.003.70E-011.45E-1603.72E-0126.003.55E-015.84E-1673.57E-0127.003.41E-012.36E-1733.43E-0128.003.28E-019.53E-1803.30E-0129.003.15E-013.85E-1863.17E-0130.003.03E-011.56E-1923.05E-01

Unlumped(Large Bi^-1)vs LumpedBi-1Bi500.02Fo|r=0/i0.001.00E+001.009.61E-012.009.23E-013.008.87E-014.008.52E-015.008.19E-016.007.87E-017.007.56E-018.007.26E-019.006.98E-0110.006.70E-0111.006.44E-0112.006.19E-0113.005.95E-0114.005.71E-0115.005.49E-0116.005.27E-0117.005.07E-0118.004.87E-0119.004.68E-0120.004.49E-0121.004.32E-0122.004.15E-0123.003.99E-0124.003.83E-0125.003.68E-0126.003.53E-0127.003.40E-0128.003.26E-0129.003.13E-0130.003.01E-01