Analytical Thermal Analysis of an Optical Fiber-Based Gamma-Ray Calorimeter With Non-Constant Fluid Temperatures on its Boundary

This paper is an examination of the effect of an axially varying fluid temperature on the measurement of $\Delta {T}({z})$ , the difference in the temperature between the optical fiber within the thermal mass and the optical fiber within the capillary tube that is attached to the outer sheath of an Optical Fiber Based Gamma Calorimeter (OFBGC). Our analysis indicates that for an OFBGC with the general design of the OFBGC that was built and tested in the Ohio State University Research Reactor (OSURR), a sinusoidal variation with spatial frequency ${k}_{B}$ in the bulk fluid temperature ${T}_{B}$ along the length of the OFBGC will create a sinusoidal variation in $\Delta {T}({z})$ , which could be misinterpreted as a sinusoidal variation in the linear energy deposition rate within the OFBGC's thermal mass. However, for the specific design of the OFBGC that was built and tested in the OSURR, for the slowly varying spatial variation of ${T}_{B}({z})$ along the length of the OSURR's Water Irradiation Facility, within which the OFBGC was tested, the perturbation in $\Delta {T}({z})$ is negligibly small.