226 SPEEDS OF SOME PROCESSES IN BIOLOGICAL SYSTEMS 



The important effective-thickness term which determines dT/d.v, depends 

 upon the nature of the contact, whether skin-air, skin-water, skin-metal, etc., 

 and also depends critically on the heat capacity and heat conductivity of the 

 materials of the contact. Thus the rate of heat loss into cold water is greater 

 than into cold air at the same temperature because of the higher heat capac- 

 ity of the water; while the rate of heat loss to steel at the same temperature 

 is greater because of the rate at which steel can conduct heat away. 



Clothing increases the effective thickness and hence decreases the- tem- 

 perature gradient: so do hair, thickness of skin, and subcutaneous fat. One 

 of the best insulators in the body is the dermis-epidermis combination, 

 whose effective thickness changes with the ambient temperature by virtue of 

 involuntary, lateral muscle movements which govern the depth of blood 

 capillaries carrying the heat energy to be thrown away: in the cold these 

 capillaries retract, thus increasing the effective thickness of the insulation. 



Aides to Conduction 



Conduction is aided — often exceeded — by convection, radiation and 

 vaporization. A very brief account of these allied processes is now given, 

 and then a comparison drawn among the relative methods of heat loss for 

 man in different aspects. 



For convection the rate is given by: 



v 2 = K 2 dT/dx /(») Cal/hr 



where f(v) is related to "wind chill" and increases with the velocity, v, of 

 the air flowing over the surface. Convection losses are those of air circula- 

 tion, and act primarily by removing the layers of semiwarmed air from above 

 the surface of the skin, thus reducing the effective thickness of insulation. 



The form of/ is beyond the scope of this book, for it involves complex 

 principles of eddy currents in the subject of aerodynamics. We shall con- 

 tent ourselves with the general observation that the stronger the breeze pass- 

 ing over the body, the greater the rate of cooling. In extreme cases this could 

 be several hundred Cal/hr. 



For radiation the rate, v 3 , is given by 



v 



3 



aA'(T b 4 - T 4 ) (the Stefan-Boltzmann law) 



where T h is skin temperature, T a is ambient temperature, A' is the body's 

 effective radiating surface area (70 to 85 per cent of real area (~20 ft 2 ), de- 

 pending upon posture and position, and correspondingly less if the area is 

 clothed), and a is the Stefan-Boltzmann constant. For the so-called black- 

 body, which the human body approximates in the sense that it absorbs and 

 emits all wave lengths in the infrared (that is, those important at 37°C), the 

 value of a is about 0.045 Cal ft" 2 deg~ 4 hr" 1 . Thus if the surroundings are 



