Thermal Radiation (Heat Transfer)

Unit VI Thermal RadiationThe Stephen-Boltzmann Law, The black body radiation, Shape factor and their relationships, eat e!chan"e between non black bodies, #lectrical network for radiati$e e!chan"e in an enclos%re of two or three "ray bodies, Radiation shields, &%mericals'(') Introd%ctionRadiation is a process in which heat is transferred from a re"ion of hi"her temperat%re to a re"ion of lower temperat%re when the re"ions or bodies are separated in space or e$en $ac%%m e!ists between them'In contrast to cond%ction and con$ection, medi%m is not mandatory for radiation to take place' Radiation is si"nificant mode of heat transfer in $ac%%m' The e!amples are heat transfer from the filament of a $ac%%m t%be and thro%"h the walls of e$ac%ated thermal flask' Radiation is also important in f%rnaces, comb%stion chambers, n%clear e!plosions, space applications etc'Thermal radiation is an electroma"netic radiation which is emitted by $irt%e of temperat%re of the s%rface' Its nat%re is the same as that of *-rays, $isible li"ht or radio wa$es' The distin"%ishin" feat%re of thermal radiation is its wa$elen"ths between +') and)++,' Visible li"ht wa$e len"ths lie between wa$es with the speed of li"ht i'e' - ! )+)+ cm.s' #lectroma"netic radiation is nothin" b%t wa$e carryin" ener"y'('/' Basic terms)' #missi$e 0ower, #It is defined as the total radiation emitted by a body per %nit area per %nit time'/' Stefan-Boltzmann LawIt states that the emissi$e power of a black body is proportional to fo%rth power ofits absol%te temperat%re or1 1T E or T Eb b = where 2 is a constant of proportionality and called Stefan-Boltzmann constant and its $al%e is 3'(4 ! )+-5 6.m/71'-' #missi$ity, 8It is the ratio of the emissi$e power of a body to the emissi$e power of a black body' It depends on temperat%re, wa$elen"th and the type of material'1' Radiation 0roperties, 9bsorpti$ity, :, Reflecti$ity, ; and Transmissi$ity, It is the total radiation incident %pon a s%rface per %nit area and per %nit time' Some part of the incident radiation may be absorbed, some part reflected band and some part transmitted thro%"h the body' Arom abo$e definitionP C #DQ") @ ) ? = + + = body opaque For G E JbAor black body) = = SoP C #b-' &et heat loss by Radiation from a >ray s%rfaceLet %s consider a control $ol%me with one of its s%rfaces e!chan"in" radiation with other s%rfaces o%tside control $ol%me' Let P be radiation ener"y lea$in" the control $ol%me and> the irradiation enterin" the control $ol%me' The B%antity P-> will be eB%al to the net radiation loss from the s%rface per %nit area per %nit time orJ C 9 ?P R >@If the s%rface is to be maintained at a constant temperat%re, an e!ternal so%rce m%st s%pply ener"y at the rate of J %nits to the s%rface' The process is shown in the dia"ram'&ow ( ) G E Jb + = )@ ) ?@ ?=bE JG@ ? G J A Q so =The eB%ation can be shown by an electrical network as shownin the fi"%re' =)bE JJ A Q?1@ eat Transfer by Radiation between two >ray S%rfacesTotal radiation lea$in" s%rface ), 9), P), a fraction 9) P)A)/ is recei$ed by s%rface /' =)bE JJ A QSimilarly, radiation lea$in" s%rface /, 9/ P/ and reachin" s%rface ) is 9/P/A/)' So net radiation e!chan"e between the two s%rfaces will be/) / / )/ ) ) )/F J A F J A Q =@ ?/ ) )/ ) )/J J F A Q or =

) / / )/ ) / ) )/ /@ ?= = F A F A as J J F A) / // ))/ )/ ))/) )==F AJ JF AJ JQ so('4 #lectrical &etwork Aor Radiation #!chan"e in an #nclos%re of two or three >ray Bodies)' #lectrical &etwork for sol$in" radiation problems6e ha$e seen in last article that net heat lost by radiation from a "ray s%rface is "i$en byC AJ EQb. ) =' 6ritin" this eB%ation for s%rfaces ) and /, we obtain/ / // //) ) )) )). @ ) ? . @ ) ? AJ EQ andAJ EQb b==/ / ) )/ ) )@ ? Q J J F A Q Also = =S%bstit%tin" $al%es of J) and J/ in abo$e eB%ation, we obtain/ / // /)/ )/ )) ) )) ). @ ) ? . ) . @ ) ? AJ EF A J JAJ Eb b ==Arom this eB' Val%es of P) and P/ are calc%lated and $al%es of J) and J/ e$al%ated/ //)/ ) ) ))/ )/ )) ) )A F A AE EQ Qb b+ += =These eB%ations are shown on electrical network/' Radiation between two black s%rfaces connected by a refractory s%rfaceThe fi"%re shows a network for a system consistin" of two black s%rfaces ) and / which are connecti$e by a refractory s%rface R' Refractory s%rface R is not connected by any potential beca%se net radiation transfer by R is zero/ ) ) )/ ). ) . )). )) )R R F A R F A F A R ++ =@ ) ?/) / / / /F A F A F A NowR R R = =)/ ) / / / ) /, ) F A A F A so F FR R R = = + )/ ) /) /F A F A = )/ ) / ) )) ) F F so F F NowR R = = + )/ ) / )/ ))/ ))@ ) ?)) )F A A F AF ARso++ = @ / ? . @ ?)/ ) / ) )/ ) / )F A A A F A A A + =R E EQb b / ))/=@ ?// ))/ ) / )/)/ ) / ))/ b bE EF A A AF A A AQ +=)/ ) / )/)/ ) /)/ / ) )/ ) )//@ ?F A A AF A AF were E E F A Qb b += =-' Radiation e!chan"e between two "ray s%rfaces connected by a refractory s%rfaceThe electrical network for radiation between two "ray bodies connected by a refractory s%rfaces is shown in the fi"%re'The electrical network shown in the abo$e two dia"rams are eB%i$alent'/ //)/ ) ) ))/ ))/) ) )A F A AE EQ sob b+ +=/)/ ) /)/ ) / ))// )F A AF A A AFwere +=/),)/)/ / )FF A A A I!+= = =)/ / )/ ))/)//) )@ ?FE E AQb b++ += 1' Radiation e!chan"e for three "ray bodiesThe network for three "ray s%rfaces which see only each is shown in the fi"%re' Arom 7irchhoffHs law of c%rrent at only L%nction ' + = i9pplyin" the law at three L%nctions, we obtain followin" three eB%ationS+) ) )- ) )) -)/ )) /) ))) )=++F AJ JF AJ JAJ Eb+) ) )/- // -)/ )/ )/ /// /=++F AJ JF AJ JAJ Eb+) ) )/- /- /)- )- )- --- -=++F AJ JF AJ JAJ EbArom abo$e three eB%ations P), P/ and P- can be calc%lated' ere heat transfer by radiation can be calc%lated)- )- //-)- )- ))-)/ )/ ))/. ) . ),. ) F A J JQ andF A J JQF A J JQ===('5 Radiation Shields)' Introd%ctioneat transfer by radiation between s%rfaces can be red%ced considerably either by %sin" hi"h refracti$e s%rfaces ( ) ) or by %sin" radiation shields between the heat e!chan"in" s%rfaces' Thin plastic shields coated with hi"hly reflecti$e metallic films on both sides ser$e as a $ery effecti$e radiation shields' These shields do not deli$er or remo$e any heat from the system' They offer an additional resistance to the heat flow so that o$erall heat transfer is red%ced' These are %sed for the ins%lation of cryo"enic stora"etanks and in the meas%rement of temperat%re with thermometers and thermoco%ples' These are shielded to minimize radiation losses'/' eat transfer by radiation with radiation shieldsLet %s consider two parallel plates ) and / of each area 9 at temperat%res T) and T/ respecti$ely'@ ) ''? '''''''''')) )@ ?/ )1/1) )/ += T TAQIf a radiation shield with emissi$ity-is introd%ced between ) and /, then@ / '''''? '''''''''')) )@ ?,)) )@ ?/ -1/1- / -- )1-1) )- += += T TAQ T TAQSince radiation shields do not remo$e or deli$er heat from the systemAQAQFromAQAQAQ-/ )- )/ -/ )-, = = =@ - '''''''? '''''''''' '''''''''')) )@ ?)) )@ ?/ -1/1-) -1-1) += + T T T Tor@ 1 ''? '''''''''')) ))) ))) ))) )- ) / -- )1// -1)1- + + + + + += T TT or0%ttin" the $al%e of 1-T from eB' ?1@ in eB' ?-@, we obtain( )@ 3 '''''''? '''''''''' '''''''''')) ))) )/ - - )1/1) )/ + + += T TAQGi$idin" #B' 3 by #B'?)@ we "et( )( )@ ( '''? '''''''''' '''''''''')) ))) ))) )/ - - )/ ))/)/ + + + += witoutsieldQQ = = =- / )I!( ) ( ) witout sieldQ Q)/ )//)=Th%s when one radiation shield is inserted between two parallel plates, the radiation heat transfer is hal$ed and temperat%re of shield from #B' ?1@ is( )1/1)1-/)T T T + =Let %s consider the case where there are n shields between the two infinite parallel planes,all the planes ha$in" emissi$ity of ' Aor this case there will be ?nD)@ spaces created by total ?nD/@ parallel planes'witout sieldAQn AQso += ))