Analytical characterisation of amplitude-dampening and phase-shifting in air/soil heat-exchangers

This article presents the complete analytical solution for the heat diffusion of a cylindrical air/soil heat-exchanger with adiabatic or isothermal boundary condition, submitted to constant airflow with harmonic temperature signal at input. It will be shown that, depending on its thickness, the soil layer will induce either one of two kinds of amplitude-dampening and phase-shifting regimes of the periodic input signal. In particular, for a thin layer submitted to adiabatic boundary condition, it is possible to completely phase-shift the periodic input while barely dampening its amplitude, a phenomenon apparently unexploited up to now, which might give rise to interesting energy handling techniques. Analytical results are validated against a finite-difference numerical simulation model as well as against an experimental setup.