2.4. Heat loss

In order to quantify heat loss to the environment, we assume that its variation is a function of blood temperature, which in the present model will act as a surrogate for the body’s internal temperature. We consider two ways of losing energy to the environment: one by evaporative cooling (via sweating) and the second by convection on the skin [38]. Variation of sweat rate is taken to be as in [39]

where we have neglected the contribution of temperature variation in the skin.

Finally, we model the variation of heat loss by convection on the skin. When the body’s internal temperature increases, it reacts by diverting blood flow to the skin, which leads to vessel dilation through hypothalamic signalling. We account for this effect by varying the heat transfer coefficient h according to the blood temperature T_b, which can be thought of as a surrogate for core temperature. By resorting to the fit for the relative blood flow in the skin, given in [38], which used data from [40], we assume that the heat transfer coefficient varies depending on the blood flow temperature, i.e.

where κ and ν are constants given in table 1.

Variables and parameters of the mathematical model.