A simple model of thermal conduction in human skin: temperature perception and thermal effusivity

In this work we address the well-known fact that upon touching different materials, even if at the same environment temperature, one perceives warmer or cooler sensations depending on properties other than temperature itself. A simple, one-dimensional, non-stationary model for thermal behavior of the human skin layer is devised mainly with educational purposes and the associated Fourier heat equation is solved and discussed. In particular, we emphasize the fact that thermal conductivity alone is not adequate to properly characterize different thermal sensations and the so-called effusivity is instead needed to support a quantitative description. We also obtain some information, within the framework of this model, about the specific response of the skin thermal receptors. We furthermore suggest a possible, direct experimental estimate of thermal effusivity based on the use of infrared imaging in a demonstrative and educational perspective.