Types of Heat Transfer
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1 Type of Heat Tranfer Dv Dt x = k dt dx v T S 2 * * ( v GrT * z = + z H vap lat uject in the coure conduction (Fourier Law forced convection (due to flow ource term free convection (fluid motion due to denity variation rought on y temperature difference heat tranfer with phae change (e.g. condening fluid radiation Heat tranfer due to radiation in atom and molecule electron can exit in multiple, dicrete energy tate tranfer etween energy tate are accompanied y an emiion of radiation Energy dicrete energy level Sienko and Plane, Chemitry: Principle and pplication, McGraw Hill, 1979 Quantum Mechanic 1
2 Radiation veru Conduction and Convection Continuum view Conduction i caued y macrocopic temperature gradient Convection i caued y macrocopic flow Radiation? NO CONTINUUM EXPLNTION Molecular view Conduction? There i, of coure, a molecular explanation of thee effect, ince we know that matter i made of atom and molecule Convection? Radiation i caued y change in electron energy tate in molecule and atom Continuum veru Molecular decription of matter Real matter i not a continuum; at mall enough length cale, molecule are dicrete. continuum i infinitely diviile 2
3 Individual molecule carry: chemical identity macrocopic velocity (peed and direction internal energy (Brownian velocity When they undergo Brownian motion within an inhomogeneou mixture, they caue: diffuion (ma tranport exchange of momentum (momentum tranport conduction (energy tranport Kinetic Theory J. C. Maxwell, L. Boltzmann, 1860 Molecule are in contant motion (Brownian motion Temperature i related to E k,av of the molecule Simplet model no particle volume no intermolecular force More realitic model finite particle volume intermolecular force 1 Intermolecular potential function r -1 3
4 Kinetic Theory I aed on Brownian motion (molecule in contant motion proportional to their temperature Predict that propertie that are carried y individual molecule (chemical identity, momentum, average kinetic energy will e tranported DOWN gradient in thee uantitie. ==> Tranport law are due to Brownian motion Heat Tranfer y Radiation I due to the releae of energy tored in molecule that i NOT related to average kinetic energy (temperature, ut rather to the population of excited tate. ==> Radiation i NOT a Brownian effect Radiation doe not reuire a medium to tranfer energy (work in a vacuum travel at the peed of light, c = 3 X cm/ travel a a wave; differ from x-ray, light, only y wavelength, λ radiation i important when temperature are high hot urface example: the un home radiator hot wall in vacuum oven heat exchanger wall when T i high and a vapor film ha formed T
5 Why doe radiation flux cale with temperature, which i related to average kinetic energy? a molecule gain energy, it oth peed up (increae average kinetic energy and increae it population of excited tate. The increae in average kinetic energy i reflected in temperature (directly proportional. The increae in numer of electron in excited tate i reflected in increaed radiation flux. Electron enter excited tate in proportion to T. Electromagnetic Spectrum viile from P.. Tipler, Phyic, Worth, 1976 Gamma ray X ray Ultraviolet Infrared Short radio wave =1nm =1µm =1mm Wavelength λ, m thermal radiation 0.1µ m < λ < 10µm 10 0 FM radio, TV M radio 5
6 What caue energy tranfer y radiation? energy hit urface puhe ome molecule into an excited tate when the molecule/atom relax from the excited tate, they emit radiation incident hot ody emit radiation emit T reflect emit α = aorptivity aored α <1 aor, T increae incident α = aorptivity aored α <1 incident orption In general, α i a function of wavelength α = α( λ incident reflected aor, T increae emitted aored gray ody: a ody for which α i contant (doe not depend on λ lack ody: a ody for which α = 1, i.e. aor all incident radiation 6
7 ε = emiivity emitted ε emitted, lackody < 1 Emiion gray ody: a ody for which α i contant lack ody: a ody for which α = 1 emitted α = aorptivity aored α < 1 incident true for lack and non-lack olid urface Kirchhoff Law: emiivity eual aorptivity at the ame temperature α = ε the fraction of energy aored y a material = the relative amount of energy emitted from that material compared to a lack ody ε = emiivity emitted ε emitted, lackody < 1 Black Bodie emitted Stefan-Boltzmann Law: the amount of energy emitted y a lack ody i proportional to T emitted, lack ody = = = T BTU 2 h ft R W 2 m K 8 aolute temperature 7
8 Non-Black Bodie ε = emiivity emitted ε emitted, lackody emitted emitted, non lackody emitted, lack ody = ε = T emitted, lackody = ε T Stefan-Boltzmann: Energy emitted y a non-lack ody emitted, non lack ody = ε T How doe thi relate to chemical engineering? Conider a furnace with an internal lower: There i heat tranfer due to convection: convection = h conv ( T T There i alo heat tranfer due to radiation: radiation = + total conv rad = h rad ( T T 8
9 Where do we get h rad? T T oject in furnace: emitted, non lack ody T aored = α T = ε T = ε T T T uing Kirchhoff law net energy aored: tranfered to ody energy emitted y wall, which are acting a a lack ody = ε T auming emiivity at T ( T T ε ε T T Finally, calculate h rad net energy aored: euating with expreion for h: h rad ε ( T T ε T = T T tranfered to ody T ( T T = h ( T T = ε T auming ( T T rad Geankopli th ed., en p30 ε ε T T 9
10 Example: Geankopli.10-3 horizontal oxidized teel pipe carrying team and having an OD of m ha a urface temperature of 37.9 K and i expoed to air at K in a large encloure. Calculate the heat lo for m of pipe from natural convection plu radiation. For the teel pipe, ue an emiivity of
Types of Heat Transfer
ype of Heat ranfer * Dvz Dt x k d dx v S * * v Gr z HH vap lat uject in the coure conduction (Fourier Law) forced convection (due to flow) ource term free convection (fluid motion due to denity variation
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