Study of the Influence of Thermal Convection on Temperature Measurement in Thermal Control Boreholes during Artificial Ground Freezing

Abstract

This paper considers the problem of thermal convection of a calcium chloride solution in a vertical borehole. A non-uniform temperature distribution with a given vertical gradient is set at the walls of the borehole. The non-stationary temperature distribution along the borehole axis was analyzed, and its deviations from the temperature at the walls were investigated. From a practical point of view, this problem is important for estimating the error in distributed temperature measurements over the depth of thermal control boreholes during artificial ground freezing. In this study, an area near the bottom of the borehole was identified where the fluid temperature at the borehole axis deviates significantly from the temperature at the wall. The maximum deviations of the fluid temperature from the temperature at the walls, as well as the length of the temperature deviation sections, were determined.

Exact Solutions of the Oberbeck–Boussinesq Equations for the Description of Shear Thermal Diffusion of Newtonian Fluid Flows

“…It should be noted that the thermal and concentration mechanisms of convection generation are fundamentally different physically. Mathematically speaking, the Oberbeck-Boussinesq equations for thermal convection and concentration convection differ only in dissipative coefficients in the heat conduction equation and in the diffusion equation, respectively [14,[18][19][20][21][22][23][24]. These coefficients differ from each other by several orders of magnitude; therefore, one should expect differences in the structure and evolution of thermal and thermal solution flows.…”