IM^KLIMINARY CHAPTCR 



FUNDAMEiNTAL PRINCIPLES OF HEAT CONDUCTION 



In llic study of the slatos of l)i()l()i;ical material at low 

 tc'ini)e'ratures the investigators, most of tlie time, "apply" 

 principles "established" l)y the physicists, but often they 

 overlook I he numerous assum])tions on which the physicists 

 built up these princii)les. There results a considerable 

 amount of confusion, ])articularly in the discussions con- 

 ceniinii,' cooliui;-, freezini;' and snbcoolini;' curves, freezing 

 and eutectic points, and even in more common problems 

 such as the inter})retation of the readings of a thermometer. 

 ]\rost of our knowledge on these questions is based on the 

 fundamental principles of heat transmission. We shall 

 here discuss briefly these principles. 



In the last analysis, heat is understood to be the move- 

 ment of the constituent particles of matter. When, in a 

 body, a disturbance at one place causes the particles to 

 move faster than in the surroundings we are accustomed 

 to say that this point is warmer. The faster motion will 

 be transmitted by collisions to the neighbouring particles 

 and this is what we call heat transmission. 



1. The ''Problem of the Wall/' in the Steady State. One 

 of the best-known methods of analysis of heat transmission 

 is that used in the so-called "Problem of the Wall" 

 (Fourier). Let W (Fig. 2) be a wall of homogeneous mate- 



r s 



w 



e s 



Fig. 2 



rial, of thickness d, limited on two sides by two parallel 

 surfaces S and s and unlimited in the other directions. 

 Let T and t be the temperatures, respectively, at S and s, T 

 being higher than t and both temperatures being main- 

 tained constant. Heat will flow through the wall from S to 



l(t4 



