On temperature factor and the effect of viscosity on blood temperature in the arteries

A mathematical theory which could be used to explain a clinical observation in some sickle-cell anemia patients is proposed. It is shown that if the energy stored in the elastic walls of the artery of such a patient is accompanied by thermal effects, then the existence of a local hot spot on the body of a sickle-cell anemia patient could be due to shock formation even when the viscosity of the blood is zero. On the other hand, if the energy stored is not accompanied by thermal effects, then a jump in the temperature can only occur if the viscosity is not zero. We give the location of such a jump in the temperature and the time of its occurrence in both cases.