Thermal Inertia of Conductivity Cells: Theory

Abstract

The temperature anomaly of a fluid moving through circular and rectangular cylinders induced by the heat stored in the walls of these hollow cylinders is derived under the assumption of quasi-steady heat transfer. These geometries correspond closely to the SBE-4 conductivity cell manufactured by Sea-Bird Electronics (SBE) and the NBIS Mark III cell made by EG&G Ocean Products (NBIS). For a step change of ambient temperature, the initial volume-weighted thermal anomalies are 4.3 and 12%, and the relaxation times are 4.3 and 0.23 s, for the SBE and NBIS cells, respectively, under typical operating conditions. The error in the measured conductivity is significant both in magnitude and longevity. Ale magnitude and the relaxation time of the anomaly can be considerably reduced by increasing the rate of flow through a cell, by forcing the flow to be turbulent, and by appropriate changes in the wall thickness and material. The wall is not a source or sink of salt, consequently no analogous effect is produced by changes in the ambient salinity. The effect of the thermal inertia of the wall has not been previously reported because frequency response calibrations have been made in isothermal salt-stratified tanks. The signal reported by a conductivity cell is governed by: (i) the initial flushing by the free stream in the cell, (ii) the thermal and saline boundary layers on the wall of the cell and (iii) the heat stored in the wall of the cell. The bulk of the response is determined by the flushing of the cell, which has a time scale of order L/u≈0.05 s and should be nearly the same for conductivity changes imposed by either temperature or salinity. The boundary layer is not the same for temperature and salinity because the diffusivities of heat and salt differ by a factor of 100. The time scale of boundary layer diffusion is approximately 0.1 s for heat and 0.4 s for salt. Finally, the heat stored in the wall influences the temperature in the boundary layer. The time scale of this influence is determined by the dimensions and geometry of the cell, the thermal properties of the wall, and the flow through the cell. It is impossible, in principle, to remove transient salinity errors by merely matching the response of a conductivity cell to the response of a thermometer because the temperature and salinity responses of a cell are different.