PRINCIPLES OF NAVAL ENGINEERING 



conductivity (k) represents the quantity of heat 

 •which will flow through unit cross section and 

 unit length of a material in unit time when there 

 is unit temperature difference between the hotter 

 and the colder faces of the material . 



Thermal conductivity is determined experi- 

 mentally for various materials. We may perhaps 

 visualize the process of conduction more clearly 

 and understand its quantitative aspects more 

 fully by examining an apparatus for the deter- 

 mination of thermal conductivity and by setting 

 up a problem. 



Figure 8-1 shows a device that could be used 

 for determining thermal conductivity. Assume 

 that we have a bar of uniform diameter, made 

 of an unknown metal. (If we knew the kind of 

 metal, we could look up the thermal conduc- 

 tivity in a table; since we do not know the metal, 

 we shall find k experimentally.) One end of the 

 bar is inserted into a steam chest in which a 

 constant temperature is maintained; the other 

 end of the bar is inserted into a water chest. 

 The quantity of water flowing through the water 

 chest and the entrance and exit temperature of 

 the water are measured. Also, the temperature 

 of the bar itself is measured at two points by 

 means of thermometers inserted into holes in 

 the bar; we may choose any two points along the 

 bar, provided they are reasonably far apart and 

 provided they are some distance away from the 

 steam chest and the water chest. 



We will assume that the entire apparatus is 

 perfectly insulated so that the temperature dif- 

 ference between t. and t„ is an accurate reflec- 

 tion of the heat conducted along the bar and so 



that the amount of heat absorbed by the circulat- 

 ing water in the water chest is a true indication 

 of the heat conducted from the hotter end of the 

 bar to the colder end. We will assume that the 

 following data are known at the outset or learned 

 by measurement or determined in the course of 

 the experiment: 



Specific heat of water =1.00 



Temperature of water entering water chest ■ 

 20° C 



Temperature of water leaving water chest = 

 30" C 



Mass of water passing through water chest = 

 1300 grams 



t- (temperature at hotter end of bar) = SO^C 



t„ (temperature at cooler end of bar) ■ 60° C 



A (cross-sectional area of bar) • 20 square 

 centimeters 



L (distance between points of temperature 

 measurement on bar) = 10 centimeters 



T (time of heat flow) = 6 minutes = 360 sec- 

 onds 



To determine the thermal conductivity, k, of 

 our unknown metal, we will use two equations. 



ti 



STEAM IN 



STEAM 

 CHEST 



t2 



WATER IN 



BAR 



I 



WATER 

 CHEST a 1 1 1 1 1 1 1 1 1 ft 



r< ^ 



STEAM 

 OUT 



WATER 

 OUT 



147.60 



Figure 8-1.— Device for measuring thermal conductivity. 



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