Thermodynamics

94 | ThermodynamicsForcedconvectionAIRhot eggNaturalconvectionAIRhot eggFIGURE 2–71The cooling of a boiled egg by forcedand natural convection.Person30°CAir5°CRadiationFire900°CFIGURE 2–72Unlike conduction and convection,heat transfer by radiation can occurbetween two bodies, even when theyare separated by a medium colder thanboth of them.The convection heat transfer coefficient h is not a property of the fluid. Itis an experimentally determined parameter whose value depends on all thevariables that influence convection such as the surface geometry, the natureof fluid motion, the properties of the fluid, and the bulk fluid velocity. Typicalvalues of h, in W/m 2 · K, are in the range of 2–25 for the free convectionof gases, 50–1000 for the free convection of liquids, 25–250 for the forcedconvection of gases, 50–20,000 for the forced convection of liquids, and2500–100,000 for convection in boiling and condensation processes.Radiation is the energy emitted by matter in the form of electromagneticwaves (or photons) as a result of the changes in the electronic configurationsof the atoms or molecules. Unlike conduction and convection, the transfer ofenergy by radiation does not require the presence of an intervening medium(Fig. 2–72). In fact, energy transfer by radiation is fastest (at the speed oflight) and it suffers no attenuation in a vacuum. This is exactly how theenergy of the sun reaches the earth.In heat transfer studies, we are interested in thermal radiation, which is theform of radiation emitted by bodies because of their temperature. It differsfrom other forms of electromagnetic radiation such as X-rays, gamma rays,microwaves, radio waves, and television waves that are not related to temperature.All bodies at a temperature above absolute zero emit thermal radiation.Radiation is a volumetric phenomenon, and all solids, liquids, and gasesemit, absorb, or transmit radiation of varying degrees. However, radiation isusually considered to be a surface phenomenon for solids that are opaque tothermal radiation such as metals, wood, and rocks since the radiation emittedby the interior regions of such material can never reach the surface, and theradiation incident on such bodies is usually absorbed within a few micronsfrom the surface.The maximum rate of radiation that can be emitted from a surface at anabsolute temperature T s is given by the Stefan–Boltzmann law asQ # emit,max sAT 4s1W2(2–54)where A is the surface area and s 5.67 10 8 W/m 2 · K 4 is theStefan–Boltzmann constant. The idealized surface that emits radiation atthis maximum rate is called a blackbody, and the radiation emitted by ablackbody is called blackbody radiation. The radiation emitted by all realsurfaces is less than the radiation emitted by a blackbody at the same temperaturesand is expressed asQ # emit esAT 4s1W2(2–55)where e is the emissivity of the surface. The property emissivity, whosevalue is in the range 0 e 1, is a measure of how closely a surfaceapproximates a blackbody for which e 1. The emissivities of some surfacesare given in Table 2–4.Another important radiation property of a surface is its absorptivity, a,which is the fraction of the radiation energy incident on a surface that isabsorbed by the surface. Like emissivity, its value is in the range 0 a 1.A blackbody absorbs the entire radiation incident on it. That is, a blackbodyis a perfect absorber (a 1) as well as a perfect emitter.