Calculation

Heat Loss From An Insulated PipeChemSOF.comDate23-Jan-15Tips & Tricks for Chemical EngineersByChemSOFPipeInside Diameter (D1)77.9mmOutside Diameter (D2)88.9mmOperating Temperature180.0CAmbient Temperature28.0CWind Speed3.50m/sInsulationInsulated PipeTypeCalcium SilicateSurface Temperature31.9CSurface Emmisivity0.9Heat Loss73.8W/mThickness50mmBare PipeOutside DiameterD3188.9mmSurface Temperature179.4CHeat Loss1545.2W/mCalculation for Insulated PipeIterations12345Surface Temperaturet_surfaceC2931.8731.8831.8831.88Interface Temperaturet_interfaceC179.0179.97179.97179.97179.97Air PropertiesAverage Film Temperaturet_averageC28.529.9329.9429.9429.94K301.65303.08303.09303.09303.09Thermal ConductivitykW/m.K0.02640.02650.02650.02650.0265ViscosityN/s.m1.86E-051.86E-051.86E-051.86E-051.86E-05Prandtl NumberPr0.7070.7070.7070.7070.707Expansion Coefficient1/K0.00331510030.00329941260.00329934380.00329934360.0032993436Air DensityKg/m1.17161.16601.16601.16601.1660Kinematic Viscositym2/s1.61E-051.62E-051.62E-051.62E-051.62E-05Specific HeatCpkJ/Kg.K1.011.011.011.011.01alpham/s2.27E-052.29E-052.29E-052.29E-052.29E-05Reynold's NumberRe4116140815408144081440814Rayleigh NumberRa6007382272796228000222800282280028Air Film ResistanceRadiationh_radiationW/m.K5.595.635.635.635.63ConvectionForced ConvectionNu_forced189.6188.3188.3188.3188.3h_forcedW/m.K26.4826.4226.4226.4226.42Free ConvectionNu_free12.6018.3418.3618.3618.36h_freeW/m.K1.762.572.582.582.58Combined ConvectionNu_Combined189.6188.3188.3188.3188.3h_convectionW/m.K26.4826.4226.4226.4226.42Overall air side HTCh_airW/m.K32.0732.0532.0532.0532.05Pipe ResistancePipe Thermal conductivityk_pipeW/m.K56.0556.0556.0556.0556.05Pipe wall resistancer_pipem.K/W0.000220.000220.000220.000220.00022Insulation ResistanceAverage Insulation temperatureK377.15379.0704749111379.076763057379.0767852466379.0767853248Insulation Thermal conductivityk_insulationW/m.K0.059640.059790.059790.059790.05979Insulation resistancer_insulationm.K/W1.191.191.191.191.19Overall Resistancer_overallm.K/W1.2251.2221.2221.2221.222Heat FlowQW/m124.07124.38124.38124.38124.38Interface TemperatureT_interfaceC180.0180.0180.0180.0180.0Surface TemeperatureT_surfaceC31.8731.8831.8831.8831.88Heat Loss per Unit LengthW/m73.6373.8173.8173.8173.81Calculation for Bare PipeIterations12345Surface Temperaturet_surfaceC29.0179.4179.4179.4179.4Bare Pipe Emissivity0.80.80.80.80.8Air PropertiesAverage Film Temperaturet_averageC28.5103.71103.71103.71103.71K301.65376.86376.86376.86376.86Thermal ConductivitykW/m.K0.02640.03210.03210.03210.0321ViscosityN/s.m1.86E-052.20E-052.20E-052.20E-052.20E-05Prandtl NumberPr0.7070.6930.6930.6930.693Expansion Coefficient1/K0.00331510030.00265352290.00265349850.00265349850.0026534985Air DensityKg/m31.17160.93780.93780.93780.9378Kinematic Viscositym/s1.61E-052.38E-052.38E-052.38E-052.38E-05Specific HeatCpkJ/Kg.K1.011.011.011.011.01alpham/s2.27E-053.45E-053.45E-053.45E-053.45E-05Reynold's NumberRe1937113088130881308813088Rayleigh NumberRa626173377770337778233777823377782

Air Film ResistanceRadiationh_radiationW/m.K4.977.167.167.167.16ConvectionForced ConvectionNu_forced107.881.281.281.281.2h_forcedW/m.K32.0129.3529.3529.3529.35Free ConvectionNu_free6.8820.5020.5020.5020.50h_freeW/m.K2.047.417.417.417.41Combined ConvectionNu_Combined107.881.381.381.381.3h_convectionW/m.K32.0129.3829.3829.3829.38Overall air side HTCh_airW/m.K36.9836.5436.5436.5436.54Pipe ResistancePipe Thermal conductivityk_pipeW/m.K56.0556.0556.0556.0556.05Pipe wall resistancer_pipem.K/W0.000100.000100.000100.000100.00010Overall Resistancer_overallm.K/W0.0270.0270.0270.0270.027Heat FlowQW/m5599.145532.805532.805532.805532.80Interface TemperatureT_interfaceC179.4179.4179.4179.4179.4Heat Loss per Unit LengthW/m1563.771545.241545.241545.241545.24

Air_Properties4th Order Polynomial FittingThermophysical properties of AirSpecific Heat Curve FittingChemSOF.comDate23-Jan-15C1.T^4C2.T^3C3.T^2C4.TC5Tips & Tricks for Chemical EngineersByChemSOF0-0.00000000110.0000014438-0.00056533881.072238390100.00000000020.00000016870.00004989420.0046703615Literature ValuesCalculated Values0.9990422130.0016371331ERROR:#N/AERROR:#N/AERROR:#N/ATCp.10^7.10^6k.10^3.10^6PrCp.10^7.10^6k.10^3.10^6PrKkJ/Kg.KN.s/m2m2/sw/m.Km2/skJ/Kg.KN.s/m2m2/sw/m.Km2/sViscosity Curve Fitting1001.03271.12.009.342.540.7861.02971.21.959.402.760.784C1.T^4C2.T^3C3.T^2C4.TC51501.012103.44.4313.805.840.7581.016103.24.4513.775.690.759-1.586E-105.115E-07-7.246E-047.978E-01-1.850E+002001.007132.57.5918.1010.300.7371.009132.67.6418.0610.100.73800.00000002330.00001760620.00520698640.48740103892501.006159.611.4422.3015.900.7201.005159.711.4822.2315.760.7210.99999806020.170851955ERROR:#N/AERROR:#N/AERROR:#N/A3001.007184.615.8926.3022.500.7071.005184.815.9126.2622.480.7073501.009208.220.9230.0029.900.7001.008208.220.8930.1330.090.697Kinematic Viscosity Curve Fitting4001.014230.126.4133.8038.300.6901.014230.026.3733.8438.430.690C1.T^4C2.T^3C3.T^2C4.TC54501.021250.732.3937.3047.200.6861.021250.532.3437.3647.370.6850-0.00000008320.00017267320.0106372802-0.76108359135001.030270.138.7940.7056.700.6841.030269.938.7440.7056.810.68300.00000000760.00000573240.00169532640.15869137675501.040288.445.5743.9066.700.6831.041288.445.5543.8766.640.6840.99999838080.0556271526ERROR:#N/AERROR:#N/AERROR:#N/A6001.051305.852.6946.9076.900.6851.052305.952.7446.8576.790.6866501.063322.560.2149.7087.300.6901.063322.860.2949.6787.220.691Thermal Conductivity Curve Fitting7001.075338.868.1052.4098.000.6951.075338.968.1852.3497.880.696C1.T^4C2.T^3C3.T^2C4.TC57501.087354.676.3754.90109.000.7021.087354.576.3954.89108.780.7020-0.0000000590.00000458530.08886788760.52007223948001.099369.884.9357.30120.000.7091.098369.684.9157.32119.920.70800.00000000820.00000621640.00183849070.17209230558501.110384.393.8059.60131.000.7161.110384.193.7359.68131.330.7140.99999107990.06032467ERROR:#N/AERROR:#N/AERROR:#N/A9001.121398.1102.9062.00143.000.7201.121398.1102.8462.00143.060.7209501.131411.3112.2064.30155.000.7231.131411.5112.2464.31155.180.724Alpha Curve Fitting10001.141424.4121.9066.70168.000.7261.141424.3121.9366.67167.780.726C1.T^4C2.T^3C3.T^2C4.TC50.0000000001-0.00000038060.0004464825-0.03593552772.2544891641Source : Fundamentals of Heat and Mass Transfer (2007), Frank P Incropera00.0000000260.00001962640.00580445740.54332743470.99999016060.1904562096ERROR:#N/AERROR:#N/AERROR:#N/APrandtl Number Curve FittingC1.T^4C2.T^3C3.T^2C4.TC5-0-00.0000008006-0.00069460590.845781217800.00000000020.00000014420.0000426330.0039906710.99793029040.0013988767ERROR:#N/AERROR:#N/AERROR:#N/A

Properties

Thermophysical properties of AirChemSOF.comDate23-Jan-15Tips & Tricks for Chemical EngineersByChemSOFThermal Conductivity of Plain Carbon SteelTKK Calculated3rd Order Polynomial Curve FittingKW/m.KW/m.KC1.T^3C2.T^2C3.TC440058.758.702.08E-093.67E-19-5.11E-027960048.848.80000080039.239.2010ERROR:#N/AERROR:#N/A100030.030.00

Thermal Conductivity of Calcium SilicateTKK CalculatedKW/m.KW/m.K4th Order Polynomial Curve Fitting3100.0550.0551C1.T^4C2.T^3C3.T^2C4.TC53650.0590.05870-0.00000000070.0000007366-0.00022488080.07333604044200.0630.063300.00000000190.00000146740.00048355640.05785567915300.0750.07480.99986380050.0004996309ERROR:#N/AERROR:#N/AERROR:#N/A6450.0890.08917500.1040.1040

Source : Fundamentals of Heat and Mass Transfer (2007), Frank P Incropera