Simultaneous measurements of thermal conductivity, thermal diffusivity and specific heat by nuclear magnetic resonance imaging

Abstract

The feasibility of measuring the thermal conductivity ( κ), thermal diffusivity ( α) and specific heat ( c p ) of an aqueous gel noninvasively by nuclear magnetic resonance (NMR) imaging is presented. NMR images acquired with high spatial and temporal resolutions provide the means for a direct evaluation of Fourier's heat conduction relation and the simultaneous measurement of κ, α and c p in a single experiment. An aqueous gel is heated by a diode laser absorbed in a silicon wafer providing a planar constant heat flux boundary condition, and the subsequent spatial and temporal variations of temperature in the gel are measured by changes in the water proton resonance frequency and consequent nuclear spin phase shifts in gradient echo images. The evaluation of the spatial and temporal variations of temperature yields the diffusion length and thermal diffusivity, the ratio of nuclear thermal coefficient to the thermal conductivity; and the temporal variation of the spatially averaged nuclear spin phase shift yields the ratio of heat capacity to the nuclear thermal coefficient. The temporal trajectory of the diffusion length ( λ) is found to be independent of heat flux ( f 0). Furthermore, a direct evaluation of nuclear spin phase shift gradients corresponding to long times and short distances from the heat flux boundary directly yields the ratio of nuclear thermal coefficient to the thermal conductivity per Fourier's heat conduction relation.