Principles of naval engineering - Historic Naval Ships Association

1PRINCIPLES OF NAVAL ENGINEERINGconductivity (k) represents the quantity of heat•which will flow through unit cross section andunit length of a material in unit time when thereis unit temperature difference between the hotterand the colder faces of the material .Thermal conductivity is determined experimentallyfor various materials. We may perhapsvisualize the process of conduction more clearlyand understand its quantitative aspects morefully by examining an apparatus for the determinationof thermal conductivity and by settingup a problem.Figure 8-1 shows a device that could be usedfor determining thermal conductivity. Assumethat we have a bar of uniform diameter, madeof an unknown metal. (If we knew the kind ofmetal, we could look up the thermal conductivityin a table; since we do not know the metal,we shall find k experimentally.) One end of thebar is inserted into a steam chest in which aconstant temperature is maintained; the otherend of the bar is inserted into a water chest.The quantity of water flowing through the waterchest and the entrance and exit temperature ofthe water are measured. Also, the temperatureof the bar itself is measured at two points bymeans of thermometers inserted into holes inthe bar; we may choose any two points along thebar, provided they are reasonably far apart andprovided they are some distance away from thesteam chest and the water chest.We will assume that the entire apparatus isperfectly insulated so that the temperature differencebetween t. and t„ is an accurate reflectionof the heat conducted along the bar and sothat the amount of heat absorbed by the circulatingwater in the water chest is a true indicationof the heat conducted from the hotter end of thebar to the colder end. We will assume that thefollowing data are known at the outset or learnedby measurement or determined in the course ofthe experiment:Specific heat of water =1.00Temperature of water entering water chest20° CTemperature of water leaving water chest =30" CMass of water passing through water chest =1300 gramst- (temperature at hotter end of bar) = SO^Ct„ (temperature at cooler end of bar) 60° CA (cross-sectional area of bar) • 20 squarecentimetersL (distance between points of temperaturemeasurement on bar) = 10 centimetersT (time of heat flow) = 6 minutes = 360 secondsTo determine the thermal conductivity, k, ofour unknown metal, we will use two equations.tit2WATER INSTEAM INSTEAMCHESTBARr< ^IWATERCHEST a 1 1 11 1 1 1 1 ftSTEAMOUTWATEROUTFigure 8-1.— Device for measuring thermal conductivity.147.60164