7/25/2019 Practice Problem Set 1 - Three Heat Transfer Techniques

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The Cooper Union Department of Chemical Engineering

ChE342 Heat and Mass transfer Practice Problems

1.A 0.3cmthic!" 12cmhigh" and 1#cmlong circ$it board ho$ses #0 closel%spaced logic chips on one side" each dissipating 0.0& '. (he board isimpregnated )ith copper *llings and has an e+ecti,e thermal cond$cti,it% of1& '-m/. All the heat generated in the chips is cond$cted across the circ$itboard and is dissipated from the bac! side of the board to the ambient air.'hat is the temperat$re di+erence bet)een the t)o sides of the circ$itboard. Answer: 0.042oC2.

t is )ell !no)n that )ind ma!es the cold air feel m$ch colder as a res$lt ofthe wind chill efect that is d$e to the increase in the con,ection heattransfer coecient )ith increasing air ,elocit%. (he )ind chill e+ect is $s$all%epressed in terms of the wind chill temperature 'C(" )hich is theapparent temperat$re felt b% eposed s!in. 5or o$tdoor air temperat$re of06C" for eample" the )ind chill temperat$re is276C at 20 !m-h )inds and 286C at &0 !m-h )inds. (hat is" a person eposedto 06C )ind% air at 20 !m-h )ill feel as cold as a person eposed to 276Ccalm air air motion $nder 7 !m-h. 5or heat transfer p$rposes" a standingman can be modeledas a 30cmdiameter" 190cmlong ,ertical c%linder )ith both the top and

bottom s$rfaces ins$lated and )ith the side s$rface at an a,eragetemperat$re of 346C. 5or a con,ection heat transfer coecient of 17 '-m2/"calc$late the rate of heat loss from this man b% con,ection in still air at 206C.'hat )o$ld %o$r ans)er be if the con,ection heat transfer coecient isincreased to 30 '-m2/ as a res$lt of )inds:'hat is the )ind chill temperat$re in this case: 336W, 672W, 6oC

3.

A concrete )all )ith a s$rface area of 20 m2and a thic!ness of 0.30 mseparates conditioned room air from ambient air. (he temperat$re of the

inner s$rface of the )all T1 is maintained at 27;C. a Determine the heatloss ' thro$gh the concrete )all for three thermal cond$cti,it% ,al$es of0.97" 1" and 1.27 '-m/ and o$ter )all s$rface temperat$res of T2 7 217"210" 27" 0" 7" 10" 17" 20" 27" 30" and 3# ;C a total of 11 data points for eachthermal cond$cti,it% ,al$e.(ab$late the res$lts for all three cases in onetable. Also pro,ide a comp$ter generated graph for the displa% of %o$r res$lts. (he res$lts for all

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three cases sho$ld be plotted on the same graph.! Disc$ss %o$r res$lts forthe three cases

4..n man% man$fact$ring plants" indi,id$als are often )or!ing aro$nd high

temperat$re s$rfaces. Eposed hot s$rfaces that are potential for thermalb$rns on h$man s!intiss$e are considered to be ha?ards in the )or!place. Metallic s$rface oftemperat$re abo,e 906C is considered etremel% high temperat$re in thecontet of thermal b$rn" )here s!in tiss$e damage can occ$rinstantaneo$sl% $pon contact )ith thehot s$rface. Consider an A@ 1010 carbon steel strip B 9#32 !g-m3 of 2mm thic! and 3 cm )ide that is con,e%ed into a chamber to be cooled at aconstant speed of 1 m-s. (he steel strip enters the cooling chamber at7896C. Determine the amo$nt of heat rate that needed to be remo,ed sothat the steel strip eits the chamber at 496C to a,oid instantaneo$s thermal

b$rn $pon accidental contact )ith s!in tiss$e. Disc$ssho) the con,e%ance speed can a+ect the heat rate needed to be remo,edfrom the steel strip in the cooling chamber. "#76 $W

Cooling

Chamber

@teel strip

1m-s

(inB 789oC (o$tB

49oC

7.

Consider a ho$se )ith a oor space of 200 m2and an a,erage height of 3 mat sea le,el" )here the standard atmospheric press$re is 101.3 !Pa. nitiall%

the ho$se is at a $niform temperat$re of 106C. o) the electric heater ist$rned on" and the heater r$ns $ntil the air temperat$re in the ho$se rises toan a,erage ,al$e of 226C. Calc$late ho) m$ch heat is absorbed b% the airass$ming some air escapes thro$gh the crac!s asthe heated air in the ho$se epands at constant press$re. Also" *nd the costof this heat if the $nit cost of electricit% in that area is 0.097-!'h.%03& $'()0.#%*

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&.FiG$id ethanol is a ammable $id and can release ,apors that formeplosi,e mit$res at temperat$res abo,e its ashpoint at 1&.&6C. n achemical plant" liG$id ethanolcp 7 2.44 !-!gI/" B 9#8 !g-m3 is being transported in a pipe )ith an

inside diameter of 7 cm. (he pipe is located in a hot area )ith the presenceof ignition so$rce" )here an estimated 20 !' of heat is added to the ethanol.Jo$r tas!" as an engineer" is to design a p$mping s%stem to transport theethanol safel% and to pre,ent *re ha?ard. f the inlet temperat$re of theethanol is 106C" determine the ,ol$me o) rate that is necessar% to !eepthe temperat$re of the ethanol in the pipe belo) its ashpoint. 0.00#+7m3s.

20 !'

FiG$id ethanol

(inB 10oC

(o$t

9.

A series of eperiments )ere cond$cted b% passing 40;C air o,er a long 27mm diameter c%linder )ith an embedded electrical heater. (he obKecti,e ofthese eperiments )as to determine the po)er per $nit length reG$iredW-- tomaintain the s$rface temperat$re of the c%linder at 300;C for di+erent air,elocities . (he res$lts of these eperiments are gi,en in the follo)ingtableL

m-s 1 2 4 # 12W -- '-m 470 &7# 8#3 1709 18&3

a Ass$ming a $niform temperat$re o,er the c%linder" negligible radiationbet)een the c%linder s$rface and s$rro$ndings" and stead% state conditions"determine the con,ection heat transfer coecient h for each ,elocit% .Plot the res$lts in terms of h '-m2/ ,s. m-s. Pro,ide comp$tergenerated graph for the displa% of %o$r res$lts and tab$late the data $sedfor the graph.! Ass$me that the heat transfer coecient and ,elocit% can be epressedin the form of h B Cn.. Determine the ,al$es of the constants C and n from

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the res$lts of part a b% plotting h ,s. on loglog coordinates and choosinga C ,al$e that ass$res a match at /1 m-s and then ,ar%ing n to get thebest *t.

#.

A spherical interplanetar% probe" )ith a diameter of 2 m" is sent o$t into thesolar s%stem. (he probe s$rface is made of material ha,ing an emissi,it% of0.8 and an absorpti,it% of 0.1. @ignals from the sensors monitoring the probes$rface temperat$res are indicating an a,erage ,al$e of 406C for a spacetemperat$re of 0 /. f the electronics inside the probe is generating heat at arate of 100 '-m3" )hat is the incident radiation rate on the probe s$rface. #47#+ W