che 342 practice set i i

7/25/2019 Che 342 Practice Set i i

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The Cooper Union

Dept of Chemical Engineering

ChE342 Heat and Mass Transfer Practice Set Problem II

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"ater is boiling in a 2#$cm$diameter al%min%m pan &k ' 23( ")m*+, at -#.C!Heat is transferred steadil/ to the boiling 0ater in the pan thro%gh its 1!#$cm$thic at bottomat a rate of 11 "! If the inner s%rface temperat%re of the bottom of the panis 1.C5 determine &a, the boiling heat transfer coe6cient on the inners%rface of the pan and &b, the o%ter s%rface temperat%re of the bottom ofthe pan! &2#4 ")m2!+7 1!3o,

2!

8 transparent 9lm is to be bonded onto the top s%rface of a solid plate insidea heated chamber! :or the bond to c%re properl/5 a temperat%re of (1.C is tobe maintained atthe bond5 bet0een the 9lm and the solid plate! The transparent 9lm has athicness of mm and thermal cond%cti;it/ of 1!1# ")m*+5 0hile the solidplate is 3 mm thic and has a thermal cond%cti;it/ of !2 ")m*+! Inside theheated chamber5 the con;ection heat transfer coe6cient is (1 ")m2*+! If thebottom s%rface of the solid plate is maintained at #2.C5 0hat are thetemperat%re inside the heated chamber and the s%rface temperat%re of thetransparent 9lm< 8ss%me thermal contact resistance is negligible! &2(oC713oC,

3!


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8 2$m = !#$m section of 0all of an ind%strial f%rnace b%rning nat%ral gas isnot ins%lated5 and the temperat%re at the o%ter s%rface of this section ismeas%red to be 1.C! The temperat%re of the f%rnace room is 31.C5 and thecombinedcon;ection and radiation heat transfer coe6cient at the s%rface of the o%ter

f%rnace is 1 ")m2

*+! It is proposed to ins%late this section of the f%rnace0all 0ith glass 0ool ins%lation &k ' 1!13 ")m*+, in order to red%ce the heatloss b/ -1 percent!8ss%ming the o%ter s%rface temperat%re of the metal section still remains atabo%t 1.C5 determine the thicness of the ins%lation that needs to be%sed! The f%rnace operates contin%o%sl/ and has an e6cienc/ of ( percent!The price of the nat%ral gas is >!1)therm & therm '1#5#11 ? of energ/content,! If the installation of the ins%lation5 costs >2#1 for materials andlabor! Ho0 long 0ill it tae for the ins%lation to pa/ for itself from the energ/it< &1!43- /r or #!3 months,

4The 0all of a refrigerator is constr%cted of 9berglass ins%lation &k =1!13#")m*+, sand0iched bet0een t0o la/ers of $mm$thic sheet metal &k =#!")m*+,! The refrigerated space is maintained at 3.C5 and the a;erage heattransfer coe6cients at the inner and o%ter s%rfaces of the 0all are 4 ")m2*+and - ")m2*+5 respecti;el/! The itchen temperat%re a;erages 2#.C! It isobser;ed that condensation occ%rs on the o%ter s%rfaces of the refrigerator0hen the temperat%re of the o%ter s%rface drops to 21.C! Determine theminim%m thicness of 9berglass ins%lation that needs to be %sed in the 0allin order to a;oid condensation on the o%ter s%rfaces!&@ ' 1!11144A m or1!44( cm,

Sheet metal

+itchen at Befrigerated space 2#oC at 3oC

mm mm

$$$

$$ @ $

$$

#!T0o #$cm$diameter5 #$cm$long al%min%m bars &k '(A ")m*+, 0ith gro%nds%rfaces are pressed against each other 0ith a press%re of 21 atm! The barsare enclosed in an


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ins%lation slee;e and5 th%s5 heat transfer from the lateral s%rfaces isnegligible! If the top and bottom s%rfaces of the t0o bar s/stem aremaintained at temperat%res of #1.C and 21.C5respecti;el/5 determine &a,the rate of heat transfer along the c/linders %nder stead/ conditions and &b,the temperat%re drop at the interface! &42!4 "7 A!4oC,

A!

Consider an engine co;er that is made 0ith t0o la/ers of metal plates! Theinner la/er is stainless steel &k ' 4 ")m+, 0ith a thicness of 1 mm5 andthe o%ter la/er is al%min%m &k2 ' 3( ")m+, 0ith a thicness of # mm! othmetal plates ha;e a s%rface ro%ghness of abo%t 23 mm! The al%min%m plateis attached on the stainless steel plate b/ scre0s that e=ert an a;eragepress%re of 21 MPa at the interface! The inside stainless steel s%rface of theco;er is e=posed to heat from the engine 0ith a con;ection heat transfercoe6cient of 1 ")m2+ at an ambient temperat%re of #1.C! The o%tsideal%min%m s%rface is e=posed to a con;ection heat transfer coe6cient of 2#")m2+ at an ambient temperat%re of 41.C! "hat is the heat %= thro%ghthe engine co;er< &(1 "! Contact resistance at the surface is about 0.2% oftotal thermal resistance,(!

Clothing made of se;eral thin la/ers of fabric 0ith trapped air in bet0een5often called si clothing5 is commonl/ %sed in cold climates beca%se it islight5 fashionable5 and a ;er/ eecti;e thermal ins%lator! So it is no s%rprisethat s%ch clothing has largel/ replaced thic and hea;/ old$fashioned coats!Consider a Facet made of 9;e la/ers of 1!$mm$thic s/nthetic fabric &k =1!3 ")m*+, 0ith !#$mm$thic air space &k =1!12A ")m*+, bet0een thela/ers! 8ss%ming the inner s%rface temperat%re of the Facet to be 2.C andthe s%rface area to be !2# m25 determine the rate of heat loss thro%gh the

Facet 0hen the temperat%re of the o%tdoors is 1.C and the heat transfercoe6cient at the o%ter s%rface is 2# ")m2*+! "hat 0o%ld /o%r response be ifthe Facet is made of asingle la/er of 1!#$mm$thic s/nthetic fabric< "hat sho%ld be the thicnessof a 0ool fabric &k ' 1!13# ")m*+, if the person is to achie;e the same le;elof thermal comfort 0earing a thic 0ool coat instead of a 9;e$la/er siFacet< &(- "7 !32 mm,

!In an e=periment to meas%re con;ection heat transfer coe6cients5 a ;er/thin metal foil of ;er/ lo0 emissi;it/ &e!g!5 highl/ polished copper, isattached on the s%rface of aslab of material 0ith ;er/ lo0 thermal cond%cti;it/! The other s%rface of themetal foil is e=posed to con;ection heat transfer b/ o0ing %id o;er the foils%rface! This set%p diminishes heat cond%ction thro%gh the slab andradiation on the metal foil s%rface5 0hile heat con;ection pla/s theprominent role! The slab on 0hich the metal foil is attached to has athicness of 2# mm and a thermal cond%cti;it/ of 1!123 ")m*+! In a


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condition 0here the s%rro%nding room temperat%re is 21.C5 the metal foil isheated electricall/ 0ith a %niform heat %= of #111 ")m2! If the bottoms%rface of the slab is 21.C and the metal foil has an emissi;it/ of 1!125calc%late &a, the con;ectionheat transfer coe6cient if air is o0ing o;er the metal foil and the s%rface

temperat%re of the foil is #1.C7 and &b, the con;ection heat transfercoe6cient if 0ater is o0ing o;er the metal foil and the s%rface temperat%reof the foil is 31.C! &3(!3 ")m2!+7 4-- ")m2!+,

-!Consider a ;er/ long rectang%lar 9n attached to a at s%rface s%ch that thetemperat%re at the end of the 9n is essentiall/ that of the s%rro%nding air5i!e! 21.C! Its 0idth is #!1 cm7 thicness is !1 mm7 thermal cond%cti;it/ is211 ")m*+7 and base temperat%re is 41.C! The heat transfer coe6cient is 21")m2*+! Estimate the 9n temperat%re at a distance of #!1 cm from the baseand the rate of heat loss from the entire 9n! &2-!oC7 2!- ",

1!8 1!3$cm$thic5 2$cm$high5 and $cm$long circ%it board ho%ses 1 closel/spaced logic chips on one side5 each dissipating 1!14 "! The board isimpregnated 0ith copper 9llings and has an eecti;e thermal cond%cti;it/ of31 ")m*+! 8ll the heat generated in the chips is cond%cted across the circ%itboard and is dissipated from the bac side of the board to a medi%m at 41.C50ith a heat transfer coe6cient of 41 ")m2*+! &a, Calc%late the temperat%res

on the t0o sides of the circ%it board! &b, Go0 a 1!2$cm$thic5 2$cm$high5 and$cmlong al%min%m plate &k =23( ")m*+, 0ith A4 2$cm$long

al%min%m pin 9ns of diameter 1!2# cm is attached to the bac side of thecirc%it board 0ith a 1!12$cm$thic epo=/ adhesi;e &k ' ! ")m*+,!Determine the ne0 temperat%res on the t0o sides of the circ%it board&43!(oC5 43!(oC7 41!AoC541!AoC,

che 342 practice set i i

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