Types of Heat Transfer
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1 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 rought on y temperature difference) heat tranfer with phae change (e.g. condening fluid) radiation Faith. Morrion, Michigan ech U. 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, 979 Quantum Mechanic Faith. Morrion, Michigan ech U.
2 Radiation veru Conduction and Convection Continuum view Conduction i caued y macrocopic temperature gradient Convection i caued y macrocopic flow Radiation? NO CONINUUM EXPLNION Molecular view Conduction? Convection? here i, of coure, a molecular explanation of thee effect, ince we know that matter i made of atom and molecule l Radiation i caued y change in electron energy tate in molecule and atom Faith. Morrion, Michigan ech U. Continuum veru Molecular decription of matter Real matter i not a continuum; at mall enough length cale, molecule are dicrete. continuum i infinitely diviile Faith. Morrion, Michigan ech U.
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) Faith. Morrion, Michigan ech U. Kinetic heory J. C. Maxwell, L. Boltzmann, 860 Molecule are in contant motion (Brownian motion) emperature 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 Intermolecula ar potential functio on r - Faith. Morrion, Michigan ech U.
4 Kinetic heory 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. ==> ranport law are due to Brownian motion Heat ranfer y Radiation I due to the releae of energy tored in molecule that i NO related to average kinetic energy (temperature), ut rather to the population of excited tate. ==> Radiation i NO a Brownian effect Faith. Morrion, Michigan ech U. Radiation doe not reuire a medium to tranfer energy (work in a vacuum) travel at the peed of light, c = X 0 0 cm/ travel a a wave; differ from x-ray, light, only y wavelength, radiation i important when temperature are high hot urface example: the un home radiator hot wall in vacuum oven heat exchanger wall when i high and a vapor film ha formed Faith. Morrion, Michigan ech U.
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. he increae in average kinetic energy i reflected in temperature (directly proportional). he increae in numer of electron in excited tate i reflected in increaed radiation flux. Electron enter excited tate in proportion to. Faith. Morrion, Michigan ech U. Electromagnetic Spectrum viile from P.. ipler, Phyic, Worth, 976 Gamma ray X ray Ultraviolet Infrared Short radio wave =nm =mm Wavelength, m =m thermal radiation 0.m 0m 0 0 FM radio, V 0 0 M radio Faith. Morrion, Michigan ech U. 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 reflect emit aorptivity aored aor, increae incident Faith. Morrion, Michigan ech U. aorptivity aored incident orption In general, i a function of wavelength incident reflected aor, increae emitted aored gray ody: a ody for which i contant (doe not depend on ) lack ody: a ody for which =, i.e. aor all incident radiation Faith. Morrion, Michigan ech U. 6
7 emiivity emitted emitted, lack ody Emiion gray ody: a ody for which i contant lack ody: a ody for which = aorptivityty aored emitted incident true for lack and non-lack olid urface Kirchhoff Law: emiivity eual aorptivity at the ame temperature the fraction of energy aored y a material = the relative amount of energy emitted from that material compared to a lack ody Faith. Morrion, Michigan ech U. emiivity emitted emitted, lack ody Black Bodie emitted Stefan-Boltzmann Law: the amount of energy emitted y a lack ody i proportional to emitted, lack ody BU h ft R W m K 8 aolute temperature Faith. Morrion, Michigan ech U. 7
8 Non-Black Bodie emiivity emitted emitted, emitted emitted, nonlack ody emitted, lack ody emitted, lack ody lack ody Stefan-Boltzmann: Energy emitted y a non-lack ody emitted, nonlack ody Faith. Morrion, Michigan ech U. How doe thi relate to chemical engineering? Conider a furnace with an internal lower: here i heat tranfer due to convection: convection h conv here i alo heat tranfer due to radiation: radiation h rad total conv rad Faith. Morrion, Michigan ech U. 8
9 Where do we get h rad? oject in furnace: emitted, nonlack ody aored uing Kirchhoff law energy emitted y wall, which are acting a a lack ody net energy aored: tranfered to ody auming emiivity at Faith. Morrion, Michigan ech U. Finally, calculate h rad net energy aored: euating with expreion for h: h rad tranfered to ody h auming rad Geankopli th ed., en.0-0 p0 Faith. Morrion, Michigan ech U. 9
10 Example: Geankopli.0- horizontal oxidized teel pipe carrying team and having an OD of 0.68m ha a urface temperature of 7.9 K and i expoed to air at 97. K in a large encloure. Calculate the heat lo for 0.05 m of pipe from natural convection plu radiation. For the teel pipe, ue an emiivity of Faith. Morrion, Michigan ech U. Radiation Heat ranfer Between wo Infinite Plate Conider a uantity of radiation energy that i emitted from urface. See: Geankopli, ection.b lo: Bird, Stewart, and Lightfoot, ranport Phenomena 960 Wiley PP6-8 Left plate at emit Right plate at 6 5 reflect aor 7 emit reflect emit aor Faith. Morrion, Michigan ech U. 0
11 Firt round urface Quantity of energy incident at urface : Quantity of energy aored at urface : Quantity of energy reflected from urface : Radiation Heat ranfer Between wo Infinite Plate hi energy goe ack to urface. fraction reflected incident energy Faith. Morrion, Michigan ech U. Second round urface Quantity of energy aored at urface (econd round): Quantity of energy reflected from urface (econd round): Radiation Heat ranfer Between wo Infinite Plate fraction aored incident energy fraction reflected incident energy Faith. Morrion, Michigan ech U.
12 hird round urface Quantity of energy aored at urface (third round): Quantity of energy reflected from urface (third round): Radiation Heat ranfer Between wo Infinite Plate fraction aored incident energy fraction reflected here i a pattern. incident energy Faith. Morrion, Michigan ech U. Now, calculate the radiation energy going from urface to urface : Radiation Heat ranfer Between wo Infinite Plate Later, calculate energy from to ; then utract to otain net energy tranferred. energy aored at urface n n energy from Faith. Morrion, Michigan ech U.
13 Radiation Heat ranfer Between wo Infinite Plate Radiation energy going from urface to urface : 0 n n n How can we calculate? 0 n x nwer: S Faith. Morrion, Michigan ech U. 0 n nwer: x S Radiation Heat ranfer Between wo Infinite Plate Radiation energy going from urface to urface : Faith. Morrion, Michigan ech U. Final Reult
14 Radiation energy going from urface to urface : Radiation Heat ranfer Between wo Infinite Plate Radiation energy going from urface to urface : NE Radiation energy going from urface to urface : Faith. Morrion, Michigan ech U. Radiation Shield Radiation Shield Left plate at Right plate at Purpoe of Heat Shield: o reduce the amount of energy tranfer from (hotter) plate at to econd (cooler) plate at. Note: net, net, Faith. Morrion, Michigan ech U.
15 5 nalyi of Radiation Shield We will aume that the emiivity i the ame for all urface. Radiation Shield, net net Now we eliminate etween thee euation Faith. Morrion, Michigan ech U., net euation. net net,, Note: nalyi of Radiation Shield Radiation Shield Faith. Morrion, Michigan ech U.
16 nalyi of Radiation Shield Radiation Shield Heat Shield With one heat hield preent, fall y half compared to no heat hield. y the ame analyi, N Heat Shield N With N heat hield preent, fall y a factor of /N compared to no heat hield. Faith. Morrion, Michigan ech U. 6
Types of Heat Transfer
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
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CM30 ranport I Part II: Heat ranfer Radiation Heat ranfer Profeor Faith Morrion Department of Chemical Engineering Michigan echnological Univerity CM30 ranport Procee and Unit Operation I Part : Heat ranfer
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