Human thermoregulation (modified from example 1.7 of textbook) humans are able to control their heat production rate and heat loss rate to maintain a nearly constant core temperature of t, = 310 k 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 surroundings, 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, t, = 308 k. consider a person with a skin/fat layer of thickness l = 3 mm and effective thermal conductivity k = 0.3 w/mk. the person has a surface area a =1.8 m² and is dressed in a bathing suit. the emissivity of the skin is € = 0.95. 1. when the person is in still air in the middle of a summer day at t = 303 k, what is the skin surface temperature? convection heat transfer to the air is characterized by a free convection coefficient of hfree = 2 w/m²k. 2. given the hot summer temperatures, the person starts using a fan and notices that her skin surface temperature drops by 1 k. what is the new convection coefficient, hun, imposed by the fan? 3. at what temperature would the environment need to be for the person to experience the same skin surface temperature as in question 2 without the fan (i. e., only free convection)?