Thermodynamics

Chapter 2 | 93In solids, heat conduction is due to two effects: the lattice vibrational wavesinduced by the vibrational motions of the molecules positioned at relativelyfixed position in a periodic manner called a lattice, and the energy transportedvia the free flow of electrons in the solid. The thermal conductivity of a solidis obtained by adding the lattice and the electronic components. The thermalconductivity of pure metals is primarily due to the electronic component,whereas the thermal conductivity of nonmetals is primarily due to the latticecomponent. The lattice component of thermal conductivity strongly dependson the way the molecules are arranged. For example, the thermal conductivityof diamond, which is a highly ordered crystalline solid, is much higher thanthe thermal conductivities of pure metals, as can be seen from Table 2–3.Convection is the mode of energy transfer between a solid surface and theadjacent liquid or gas that is in motion, and it involves the combined effectsof conduction and fluid motion. The faster the fluid motion, the greater theconvection heat transfer. In the absence of any bulk fluid motion, heat transferbetween a solid surface and the adjacent fluid is by pure conduction. Thepresence of bulk motion of the fluid enhances the heat transfer between thesolid surface and the fluid, but it also complicates the determination of heattransfer rates.Consider the cooling of a hot block by blowing of cool air over its top surface(Fig. 2–70). Energy is first transferred to the air layer adjacent to thesurface of the block by conduction. This energy is then carried away fromthe surface by convection; that is, by the combined effects of conductionwithin the air, which is due to random motion of air molecules, and the bulkor macroscopic motion of the air, which removes the heated air near the surfaceand replaces it by the cooler air.Convection is called forced convection if the fluid is forced to flow in atube or over a surface by external means such as a fan, pump, or the wind. Incontrast, convection is called free (or natural) convection if the fluid motionis caused by buoyancy forces induced by density differences due to the variationof temperature in the fluid (Fig. 2–71). For example, in the absence ofa fan, heat transfer from the surface of the hot block in Fig. 2–70 will be bynatural convection since any motion in the air in this case will be due to therise of the warmer (and thus lighter) air near the surface and the fall of thecooler (and thus heavier) air to fill its place. Heat transfer between the blockand surrounding air will be by conduction if the temperature differencebetween the air and the block is not large enough to overcome the resistanceof air to move and thus to initiate natural convection currents.Heat transfer processes that involve change of phase of a fluid are alsoconsidered to be convection because of the fluid motion induced during theprocess such as the rise of the vapor bubbles during boiling or the fall of theliquid droplets during condensation.The rate of heat transfer by convection Q # conv is determined from Newton’slaw of cooling, expressed asQ # conv hA 1T s T f 21W2(2–53)where h is the convection heat transfer coefficient, A is the surface areathrough which heat transfer takes place, T s is the surface temperature, and T fis bulk fluid temperature away from the surface. (At the surface, the fluidtemperature equals the surface temperature of the solid.)TABLE 2–3Thermal conductivities of somematerials at room conditionsThermalconductivity,MaterialW/m · KDiamond 2300Silver 429Copper 401Gold 317Aluminium 237Iron 80.2Mercury () 8.54Glass 1.4Brick 0.72Water () 0.613Human skin 0.37Wood (oak) 0.17Helium (g) 0.152Soft rubber 0.13Glass fiber 0.043Air (g) 0.026Urethane, 0.026rigid foamVelocityvariationof airAVAIRFLOWQ convHOT BLOCKTTemperaturevariationof airFIGURE 2–70Heat transfer from a hot surface to airby convection.T fT s