Principles of naval engineering - Historic Naval Ships Association

Chapter 8-INTRODUCTION TO THERMODYNAMICSAlthough three modes of heat transferconduction,radiation, and convection— are commonlyrecognized, we will find it easier tounderstand heat transfer if we make a distinctionbetween conduction and radiation, on the onehand, and convection, on the other. Conductionand radiation may be regarded as the primarymodes of heat flow. Convection may best bethought of as a related but basically differentand special kind of process which involves themovement of a mass of fluid from one place toanother.CONDUCTION.— Conduction is the mode bywhich heat flows from a hotter to a colder regionwhen there is physical contact between thetwo regions. For example, consider a metal barwhich is held so that one end of it is in boilingwater. In a very short time the end of the barwhich is not in the boiling water will have becometoo hot to hold. We say that heat has beenconducted from molecule to molecule along theentire length of the bar. The molecules in thelayer nearest the source of heat become increasinglyactive as they receive thermalenergy. Since each layer of molecules is boundto the adjacent layers by cohesive forces, themotion is passed on to the next layer which, inturn, sets up increased activity in the next layer.The process of conduction continues as long asthere is a temperature difference between thetwo ends of the bar.The total quantity of heat conducted dependsupon a number of factors. Let us consider a barof homogeneous material which is uniform incross-sectional area throughout its length. Oneend of the bar is kept at a uniformly high temperature,the other end. is kept at a uniformlylow temperature. After a steady and uniformflow of heat has been established, the total quantityof heat that will be conducted through thisbar depends upon the following relationships:1. The total quantity of heat passing throughthe conductor in a given length of time is directlyproportional to the cross-sectional areaof the conductor. The cross-sectional area ismeasured normal to (that is, at right angles to)the direction of heat flow.2. The total quantity of heat passing throughthe conductor in a given length of time is proportionalto the thermal gradient— that is, to thedifference in temperature between the two endsof the bar, divided by the length of the bar.3. The quantity of heat is directly proportionalto the time of heat flow.4. The quantity of heat depends upon thethermal conductivity of the material of whichthe bar is made. Thermal conductivity (k) isdifferent for each material.These relationships may be expressed bythe equationwhereQ =kTA ^1-^2Q = quantity of heat, in Btu or caloriesk =coefficient of thermal conductivity(characteristic of each material)T = time during which heat flowsA =cross-sectional area, normal to the pathof heatt. = temperature at the hot end of the bart„ = temperature at the cold end of the barL =distance between the two ends of the barThis equation, which is sometimes called thegeneral conduction equation , applies whether weare using a metric system or a British system.Consistency in the use of units is, of course,vital.t. - t„The quantity ^5^ =- is called the thermalgradient or the temperature gradient. In themetric CGS system, the temperature gradient isexpressed in degrees Celsius per centimeter oflength; the cross-sectional area is expressed insquare centimeters; and the time is expressedin seconds. In British units, the temperaturegradient is expressed in Btu per inch (or sometimesper foot) of length; the cross-sectionalarea is expressed in square feet; and the time isexpressed in seconds or in hours. (As may benoted, some caution is required in using theBritish units; we must know whether the temperaturegradient indicates Btu per inch or Btuper foot, and we must know whether the time isexpressed in seconds or in hours.)From the general conduction equation, wemay infer that the coefficient of thermal163