Appendix 1 - AC Controls · Appendix 1 Calculation of Convective Heat Transfer Coefficient All calculations are from the following source: Incropera, Frank, & DeWitt, David. (2007)

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).


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


Appendix 2 Thermal Material Properties


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


Figure A-3c. 0.26” thermowell and 1/4" grounded thermocouple

Figure A-3d. 0.385” thermowell and 3/8" exposed thermocouple


Figure A-3e. 0.385” thermowell and 3/8" ungrounded thermocouple

Figure A-3f. 0.385” thermowell and 3/8" grounded thermocouple


Figure A-3g. 0.385” thermowell and 1/4" exposed thermocouple

Figure A-3h. 0.385” thermowell and 1/4" ungrounded thermocouple


Figure A-3i. 0.385” thermowell and 1/4" grounded thermocouple


Appendix 4 FEA Results of Lab Conditions















Appendix 5 Main Results: FEA Results of Steam Conditions














Figure A-5j. Bailey Pyrotron thermowell and 1/2" grounded thermocouple

Documents

Appendix 1 - AC Controls · Appendix 1 Calculation of Convective Heat Transfer Coefficient All calculations are from the following source: Incropera, Frank, & DeWitt, David. (2007)