Thermal dispersion for water or air flow through a bed of glass beads

The one-temperature model for thermal dispersion in a porous medium is based on the notion of an average ‘enthalpic’ temperature, solution of an energy equation of the convection–diffusion type. It requires the determination of thermal dispersion coefficients. The functional form of the correlations that relate them to dimensionless groups is established as well as the limits of this model. An experimental bench has been built to measure these coefficients for water or air flow through a bed of glass beads. They are estimated through a Bayesian inversion of several local temperature measurements, with uncertainty on their location, and with the use of the analytical solution of a corresponding model. Results are presented in terms of variation of these two coefficients with the Reynolds or Péclet numbers and with the nature of the fluid and corresponding correlations are given.