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 Summary Within homogeneou phae: Microcopic Energy Balance Steady olution rectangular: conduction cylindrical: ln emperature and Newton law of cooling boundary condition (if i upplied) Unteady olution (from literature) Carlaw and Jeager Heiler chart
CM30 ranport Procee and Unit Operation I Part : Heat ranfer Summary cro phae boundarie: Microcopic Energy, Momentum, and Ma Balance Micro momentum: Micro energy: Simultaneou effect (complex) Solution are difficult to obtain (and often not really neceary) ue to obtain Data correlation for: forced convection natural convection radiation 3 Radiation veru Conduction and Convection Continuum view Conduction i caued by macrocopic temperature gradient Convection i caued by 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 Radiation i caued by change in electron energy tate in molecule and atom
Heat tranfer due to radiation in atom and molecule electron can exit in multiple, dicrete energy tate tranfer between energy tate are accompanied by an emiion of radiation Sienko and Plane, Chemitry: Principle and pplication, McGraw Hill, 979 dicrete energy level Energy Quantum Mechanic 5 Continuum veru Molecular decription of matter Real matter i not a continuum; at mall enough length cale, molecule are dicrete. continuum i infinitely diviible 6 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) 7 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 Intermolecular potential function 0.5 0 0 3-0.5 r - 8
Kinetic heory I baed on Brownian motion (molecule in contant motion proportional to their temperature) Predict that propertie that are carried by individual molecule (chemical identity, momentum, average kinetic energy) will be tranported DOWN gradient in thee uantitie. => ranport law are due to Brownian motion Heat ranfer by Radiation I due to the releae of energy tored in molecule that i NO related to average kinetic energy (temperature), but rather to the population of excited tate. ==> Radiation i NO a Brownian effect 9 Radiation doe not reuire a medium to tranfer energy (work in a vacuum) travel at the peed of light, c = 3 X 0 0 cm/ travel a a wave; differ from x-ray, light, only by wavelength, l radiation i important when temperature are high hot urface example: the un home radiator hot wall in vacuum oven heat exchanger wall when D i high and a vapor film ha formed Note: abolute temperature unit 0 5
Why doe radiation flux cale with temperature, which i related to average kinetic energy? a molecule gain energy, it both 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 number of electron in excited tate i reflected in increaed radiation flux. Electron enter excited tate in proportion to abolute. Electromagnetic Spectrum viible from P.. ipler, Phyic, Worth, 976 Gamma ray X ray Ultraviolet Infrared Short radio wave 0-0 -3 0-0 - 0-0 0-9 0-8 0-7 0-6 0-5 0-0 -3 0-0 - 0 0 0 =nm =mm =mm Wavelength l, m thermal radiation 0.m 0m FM radio, V 0 M radio 6
What caue energy tranfer by 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 body reflect aborb, increae emit radiation emit emit aborptivity aborbed incident 3 aborptivity aborbed incident borption In general, a i a function of wavelength incident reflected aborb, increae emitted aborbed gray body: a body for which a i contant (doe not depend on ) black body: a body for which =, i.e. aborb all incident radiation 7
emiivity emitted emitted, black body Emiion gray body: a body for which a i contant black body: a body for which = emitted aborptivity aborbed incident true for black and non-black olid urface Kirchhoff Law: emiivity eual aborptivity at the ame temperature the fraction of energy aborbed by a material = the relative amount of energy emitted from that material compared to a black body 5 emiivity emitted emitted, black body Black Bodie Stefan-Boltzmann Law: the amount of energy emitted by a black body i proportional to emitted emitted, black body 0.70 5.6760 8 BU h ft R W m K 8 abolute temperature 6 8
Non-Black Bodie emiivity emitted emitted, black body emitted emitted, nonblack body emitted, black body emitted, black body Stefan-Boltzmann: Energy emitted by a non-black body emitted, nonblack body 7 How doe thi relate to chemical engineering? Conider a furnace with an internal blower: here i heat tranfer due to convection: convection h conv here i alo heat tranfer due to radiation: radiation h rad urface temp b b Bulk temp total conv rad 8 9
Where do we get h rad? b object in furnace: emitted, nonblack body b b uing Kirchhoff law energy emitted by wall, which are acting a a black body net energy aborbed: tranfered to body auming emiivity at b b 9 Finally, calculate h rad net energy aborbed: euating with expreion for : h rad tranfered to body b h b b auming rad b Geankopli th ed., en.0-0 p30 b b 0 0
Example: Geankopli.0-3 horizontal oxidized teel pipe carrying team and having an OD of 0.683m ha a urface temperature of 37.9 K and i expoed to air at 97. K in a large encloure. Calculate the heat lo for 0.305 m of pipe from natural convection plu radiation. For the teel pipe, ue an emiivity of 0.79. Example: Geankopli.0-3 horizontal oxidized teel pipe carrying team and having an OD of 0.683m ha a urface temperature of 37.9 K and i expoed to air at 97. K in a large encloure. Calculate the heat lo for 0.305 m of pipe from natural convection plu radiation. For the teel pipe, ue an emiivity of 0.79. nwer: 6.9/ 6./ 63
One final topic: Radiation Heat ranfer Between wo Infinite Plate Conider a uantity of radiation energy that i emitted from urface. Left plate at Right plate at emit reflect 3 aborb See: Geankopli, ection.b lo: Bird, Stewart, and Lightfoot, ranport Phenomena 960 Wiley PP6-8 emit 6 aborb 5 reflect 7 emit 3 Firt round urface Quantity of energy incident at urface : Quantity of energy aborbed at urface : Quantity of energy reflected from urface : Radiation Heat ranfer Between wo Infinite Plate hi energy goe back to urface. fraction reflected incident energy
Second round urface Quantity of energy aborbed at urface (econd round): Radiation Heat ranfer Between wo Infinite Plate fraction aborbed incident energy Quantity of energy reflected from urface (econd round): fraction reflected incident energy 5 hird round urface Radiation Heat ranfer Between wo Infinite Plate Quantity of energy aborbed at urface (third round): fraction aborbed incident energy Quantity of energy reflected from urface (third round): fraction reflected incident energy here i a pattern. 6 3
Radiation Heat ranfer Between wo Infinite Plate Now, calculate the radiation energy going from urface to urface : Later, calculate energy from to ; then ubtract to obtain net energy tranferred. energy aborbed at urface n n energy from 7 Radiation Heat ranfer Between wo Infinite Plate Radiation energy going from urface to urface : n n0 n How can we calculate? n x n0 nwer: S x 8
5 Radiation Heat ranfer Between wo Infinite Plate Radiation energy going from urface to urface : Final Reult 9 Faith. Morrion, Michigan Radiation Heat ranfer Between wo Infinite Plate Radiation energy going from urface to urface : Radiation energy going from urface to urface : NE Radiation energy going from urface to urface : 30
Radiation Shield Radiation Shield Left plate at Right plate at 3 Purpoe of Heat Shield: o reduce the amount of energy tranfer from (hotter) plate at to econd (cooler) plate at 3. Note: net, net,3 3 nalyi of Radiation Shield Radiation Shield We will aume that the emiivity i the ame for all urface. net, net,3 3 Now we eliminate between thee euation. Note: net, net,3 3 3 6
7 nalyi of Radiation Shield Radiation Shield 3 3 3 3 3 3 33 nalyi of Radiation Shield Radiation Shield 3 3 With one heat hield preent, fall by half compared to no heat hield. 3 N Heat Shield N Heat Shield With N heat hield preent, fall by a factor of /N compared to no heat hield. by the ame analyi, 3
CM30 ranport Procee and Unit Operation I Part : Profeor Faith Morrion Department of Chemical Engineering Michigan echnological Univerity CM30 - Momentum and Heat ranport CM30 Heat and Ma ranport www.chem.mtu.edu/~fmorrio/cm30/cm30.html 35 CM30 ranport Procee and Unit Operation I Part : Heat ranfer Summary Within homogeneou phae: Microcopic Energy Balance Steady olution rectangular: cylindrical: ln emperature and Newton law of cooling boundary condition (if i upplied) Unteady olution (from literature) Carlaw and Jeager Heiler chart 36 8
CM30 ranport Procee and Unit Operation I Part : Heat ranfer Summary cro phae boundarie: Microcopic Energy, Momentum, and Ma Balance Micro momentum: Micro energy: Simultaneou effect (complex) Solution are difficult to obtain (and often not really neceary) ue to obtain Data correlation for: forced convection, natural convection (ue in deign) radiation 37 CM30 ranport Procee and Unit Operation I Part : Heat ranfer Summary Heat ranfer Unit Operation Macrocopic energy balance Heat Exchanger double pipe (Δ Shell-and-tube Heat exchanger effectivene Evaporator/ Condener 38 9
CM30 ranport Procee and Unit Operation I Profeor Faith Morrion Department of Chemical Engineering Michigan echnological Univerity CM30 - Momentum and Heat ranport CM30 Heat and Ma ranport www.chem.mtu.edu/~fmorrio/cm30/cm30.html 39 0