Heat transfer from warm water to a moving foot in a footbath

A model is proposed in this work to investigate the impact of a moving foot on the transfer of heat from a constantly heated warm water into the foot immersed within a footbath. The model is simply based on the well-known Pennes bioheat equation that governs the thermal process of the fat part of the foot in action. Both the steady and transient temperature responses of the foot are analytically evaluated. The visible physical effects of the up and down movement of the foot on the skin layer heat and also on the scaled heat flux in the fat layer are later explored and discussed. It is found that the upward motion heats up the foot whereas the downward motion cools down the foot leading to a better thermal sensation and comfort during the thermal process of the foot in the footbath which is highly desirable during a physiotherapy.