Humans are able to control their heat production rate and heat loss rate to maintain a nearly constant core temperature of under a wide range of environmental conditions. This process is called Thermoregulation. From the perspective of calculating heat transfer between a human body and its surrounding, we focus on a layer of skin and fat, with its outer surface exposed to the environment and its inner surface at a temperature slightly less than the core temperature, . Consider a person with a skin/fat layer of thickness and effective thermal conductivity . The person has a surface area and is dressed in a bathing suit. The emissivity of the skin is .
When the person is in still air at and the convection heat transfer to the air is characterized by a free convection coefficient of ,
a) Express the energy balance at the skin surface in function of the heat transfer three modes
b) Determine an equation for the skin surface temperature
c) By linearizing the radiation term by , evaluate the skin surface temperature for
d) Determine the rate of heat loss to the environment
e) Repeat parts c) and d) without linearization
When the person is in water at , what is the skin surface temperature and heat loss rate? Heat transfer to the water. Note that liquid water is opaque to thermal radiation and heat loss from the skin surface is only by convection with a convection coefficient