Modeling heat transfer from warm water to foot: Analytical solution and experimental validation

• We derive an analytical solution to heat conduction from water to foot.
• We perform footbath experiments in a well-conditioned climate chamber.
• The theoretical model is validated by the experimental results.
• Heat flux through foot may be used to explain subjective thermal sensation.

This paper studies the heat transfer from warm water of constant temperature to human feet analytically and experimentally. This thermal process is represented by a simplified mathematical model: the foot is simplified, on the one hand, as a three-layer structure of skin, fat, and a core zone; Pennes bioheat equation is used, on the other, to describe the thermal process in the fat layer of the foot. An analytical solution is derived for the temperature distribution by applying the method of Laplace transform. A set of experiments were carried out in a climate chamber conditioned by a panel cooling system. Temperature response of feet and subjective thermal sensation were measured and collected. One of the principal findings from the preliminary theoretical and experimental studies is that the heat flux transferred from water to foot can probably serve as an indicator of the explanation of subjective thermal sensation.