Appendix 1 - AC Controls · Appendix 1 Calculation of Convective Heat Transfer Coefficient All calculations are from the following source: Incropera, Frank, & DeWitt, David. (2007).
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The Effect of Robust Thermowells on Thermocouple Response Time - 19
Appendix 1 Calculation of Convective Heat Transfer Coefficient
All calculations are from the following source: Incropera, Frank, & DeWitt, David. (2007). Fundamentals of heat and mass transfer. Wiley.
Given a number of fluid properties, the series of equations used to calculate the convective heat transfer coefficient of flow around a sphere are as follows,
Where,
ReD is the Reynolds Number, dimensionless, is the density of the fluid, lbm/in3,
V is the velocity of the fluid, in/s, D is the diameter of the sphere, in,
is the dynamic viscosity of the fluid, lbm/(in*s).
Where, Pr is the Prandtl Number, dimensionless, cp is the specific heat of the fluid Btu/(lb*°F), kfluid is the thermal conductivity of the fluid, Btu/(in*s*°F).
When,
Where, NuD is the Nusselt Number, dimensionless,
is the viscosity ratio, dimensionless.
Where, h is the convective heat transfer coefficient, Btu/(in2*s*°F).
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The conditions, intermediate values, and the convective heat transfer coefficients for each thermowell are provided in the table below.
Thermowell Type WIKA Thermowell WIKA Thermowell Bailey Pyrotron
Fluid Steam Molten Salt Steam
Sphere diameter (in) 0.80 0.80 1.4375
Density (lbm/in^3) 1.466E-03 7.031E-02 1.466E-03
Velocity (in/s) 1262 4.3 1262
Dynamic Viscosity (lbm/in*s) 1.730E-06 4.083E-04 1.730E-06
Reynolds Number 8.560E+05 5.931E+02 1.540E+06
Specific Heat (Btu/lb*°F) 0.164 0.373 0.164
Thermal Conductivity (Btu/in*s*°F) 1.114E-06 8.102E-06 1.114E-06
Prandtl Number 0.995 18.8 0.995
Viscosity Ratio 1 1 1
Nusselt Number 9.115E+02 4.719E+01 1.295E+03
Convective Heat Transfer Coefficient (Btu/in^2*s*°F)
1.27E-03 4.79E-04 1.00E-03
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Appendix 2 Thermal Material Properties
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Appendix 3 Results of Lab Testing
Figure A-3a. 0.26” thermowell and 1/4" exposed thermocouple
Figure A-3b. 0.26” thermowell and 1/4" ungrounded thermocouple
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Figure A-3c. 0.26” thermowell and 1/4" grounded thermocouple
Figure A-3d. 0.385” thermowell and 3/8" exposed thermocouple
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Figure A-3e. 0.385” thermowell and 3/8" ungrounded thermocouple
Figure A-3f. 0.385” thermowell and 3/8" grounded thermocouple
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Figure A-3g. 0.385” thermowell and 1/4" exposed thermocouple
Figure A-3h. 0.385” thermowell and 1/4" ungrounded thermocouple
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Figure A-3i. 0.385” thermowell and 1/4" grounded thermocouple
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Appendix 4 FEA Results of Lab Conditions
Figure A-4a. 0.26” thermowell and 1/4" exposed thermocouple
Figure A-4b. 0.26” thermowell and 1/4" ungrounded thermocouple
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Figure A-4c. 0.26” thermowell and 1/4" grounded thermocouple
Figure A-4d. 0.385” thermowell and 3/8" exposed thermocouple
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Figure A-4e. 0.385” thermowell and 3/8" ungrounded thermocouple
Figure A-4f. 0.385” thermowell and 3/8" grounded thermocouple
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Figure A-4g. 0.385” thermowell and 1/4" exposed thermocouple
Figure A-4h. 0.385” thermowell and 1/4" ungrounded thermocouple
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Figure A-4i. 0.385” thermowell and 1/4" grounded thermocouple
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Appendix 5 Main Results: FEA Results of Steam Conditions
Figure A-5a. 0.26” thermowell and 1/4" exposed thermocouple
Figure A-5b. 0.26” thermowell and 1/4" ungrounded thermocouple
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Figure A-5c. 0.26” thermowell and 1/4" grounded thermocouple
Figure A-5d. 0.385” thermowell and 3/8" exposed thermocouple
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Figure A-5e. 0.385” thermowell and 3/8" ungrounded thermocouple
Figure A-5f. 0.385” thermowell and 3/8" grounded thermocouple
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Figure A-5g. 0.385” thermowell and 1/4" exposed thermocouple
Figure A-5h. 0.385” thermowell and 1/4" ungrounded thermocouple
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Figure A-5i. 0.385” thermowell and 1/4" grounded thermocouple
Figure A-5j. Bailey Pyrotron thermowell and 1/2" grounded thermocouple
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