DEPARTMENT OF MECHANICAL ENGINEERING HEAT AND MASS TRANSFER-2251 UNIT-I (TWO MARKS QUESTIONS) CONDUCTION 1. Define heat transfer?

2. Mention the significance of the study of heat transfer. 3. Give so e e!a "#es for heat transfer in engineering. $. %hat is the difference &et'een ther odyna ics and heat transfer? (. %hat are the different ). Define conduction? *. Define convection? +. Define radiation? ,. Define heat f#u!. 1-. .tate /ourier #a' of heat conduction. 11. Define ther a# conductivity. 12. Discuss the effects of te "erature on ther a# conductivity. 13. .tate the assu "tions fo##o'ed in /ourier0s series #a' of conduction 1$. %hat are the significance of /ourier0s #a' 1(. Mention the various factors affecting the ther a# conductivity of a 1). .tate the de"endence of ther a# conductivity on te "erature. 1*. Define ther a# conduction resistance. 1+. %rite the genera# heat conduction e1uation in Cartesian co2ordinates 1,. %rite the genera# heat conduction e1uation in Cartesian co2ordinates for an isotro"ic ateria#. 2-. %rite the genera# heat conduction e1uation in Cartesian co2ordinates for an isotro"ic ateria# 'ithout interna# heat generation. ateria#. odes of heat transfer?

21. %rite the genera# heat conduction e1uation in "o#ar Co2ordinates for an isotro"ic ateria#. 22. %rite the genera# heat conduction e1uation in s"herica# co2ordinates. 23. Define steady state heat conduction 2$. Define transient heat conduction 2(. Define transient heat conduction 2). %rite the genera# differentia# e1uation in Cartesian co2ordinates for a steady state heat conduction through an isotro"ic ateria# 'ithout interna# heat generations 2*. Difference &et'een ther odyna ics and heat transfer. 2+. Define the &asic #a' governing heat transfer 2,. Define ther a# conductivity of 3-. Define ther a# resistance 31. %rite do'n the three 3di ensiona# heat conduction e1uation in rectangu#ar coordinate syste 32. Distinguish &et'een steady state and un steady heat conduction 33. %rite the effects of ther a# conductivity 3$. %hat is the overa## heat transfer co2efficient 3(. Define critica# radius of insu#ation 3). %hat is ean &y fin ateria#s

3*. %hat are the ty"es of fins 3+. Ca#cu#ate the rate of heat transfer "er unit area through a co""er "#ate of $( thic4 5'hose face is aintained at 3(-6and other face at (-6.ta4e 473*-%8 4. 3,. Define efficiency fin $-. Define effectiveness of fin $1. Define "enetration de"th. $2. Define se i2infinite so#id. $3. 9o' 'i## you increase the res"onse of a ther ocou"#e?

$$. %hat are 9eis#er chart? $(. %hat are the ethods avai#a&#e to so#ve the transient heat conduction "ro&#e s?

$). Define coo#ing "rocess. $*. Define #u "ed heat ca"acity ana#ysis. $+. %rite the re#ation &et'een efficiency of the fin and effectiveness of the fin. $,. Mention so e of the a""#ications of transient heat conduction. (-. %hat are the a""#ications of fins? (1. Mention so e co (2. Define :iot nu &er. (3. ;ist do'n the three ty"es of &oundary conditions. ($. %rite do'n the e1uation for conduction of heat through a ho##o' cy#inder ((. 'rite do'n the e1uation for conduction of heat through a s#a& or "#ane 'a## (). < te "erature difference of (-- C is a""#ied across a fire2c#ay &ric45 1-c thic4 having a ther a# conductivity of 1%8 =. /ind the heat transfer rate "er unit area (*. Define Ne'ton >i4h an0s #a' (+. %hich one of the fo##o'ing is not a ateria# "ro"erty? on ty"es of fin configurations avai#a&#e.

(,. Na e so e good and so e "oor conductors of heat. )-. .tate the a""#ications of fins. )1. %hat are the factors affecting the ther a# conductivity? )2. .tate Ne'ton0s #a' of coo#ing. )3. %hat is #u "ed ca"acity ana#ysis? )$. Ca#cu#ate the rate of heat transfer "er unit area through a co""er "#ate $( thic45 'hose one face is aintained at (-oC.ta4e the 4 of the co""er as 3*-%8 oC. )(. < "#ane 'a## is 1(thic4 and its 'a## area is $.( 2.if its conductivity is ,.3(%8 oC and surface te "erature are steady at 1(-oCand $(oC5 deter ine the heat f#o' across the "#ane 'a##.

)). < "#ane 'a## is 2(thic4 and its 'a## area is ).( 2.if its conductivity is 1-.3(%8 oC and surface te "erature are steady at 1(-oCand $(oC5 deter ine the te "erature gradient in the f#o' direction assu e that ?72,$(2.(% )*. Deter ine the heat f#o' across a "#ane 'a## of 1-c thic4ness 'ith a ther a# conductivity of +.( %8 = 'hen the surface te "erature are steady at 1--oc and 3-oC.the 'a## area is 3 2.a#so find the te "erature gradient in the f#o' direction. )+. Deter ine the heat transfer &y convection over a surface of -.( 2 if the surface is at 1)-oC and f#uid is at $-oC.the va#ue of convective heat transfer coefficient is 2(%8 2=. ),. < surface is at 2--oC and has an of 2 2.it e!changes heat 'ith another surface : at 3-oC &y radiation. The va#ue of factor due to the 'ith another surface at 3-oC &y radiation. The va#ue factor due to the geo etric #ocation and e issivity is -.$).deter ine the heat e!change. *-. < cu&e sha"ed so#id 2-c side having a density of 2(--4g8 3 and s"ecific heat of -.(24@84g= has a unifor heat generation rate of 1--4@8 3. If the heat received over its surfaces at2$-%5 deter ine the ti e rate of te "erature change of the so#id. *1. < 'ire1.( dia eter and 1(#ong is su& erged in 'ater at at os"heric "ressure. <n e#ectric current is "assed through a 'ire and is increased unti# the 'ater &oi#s at 1--oC .under the condition if convective heat transfer coefficient is $(--'8 2oC./ind ho' uch e#ectric "o'er ust &e su""#ied to the 'ire to aintain the 'ire surface at 12-oC *2. Dra' the A2B diagra *3. %hat is *$. %hat is for cyc#e o"eration. in heat transfer? in heat transfer?

eant &y c#osed syste eant &y o"en syste echanis

*(. %hat is the

used in conduction in so#ids?

*). Give any t'o odes of heat conduction in #i1uids and gases **. Na e any four ther a# conductivity ateria#s 'ith their ther a# conductivity. *+. Dra' any t'o ty"es of fins. Define heat? *,. %hy it is necessary to eva#uate fin "erfor ance and 'rite the eva#uation. +-. Give so e e!a "#es of heat transfer in engineering +1.Give so e e!a "#es of conduction in day to day #ife. ethods for fin

PART B (16 MARKS) CONDUCTION 1. CaD Derive the genera# heat conduction e1uation in Cartesian coordinates C&D <n e!terior 'a## of a house ay &e a""ro!i ate#y &y a -.1 #ayer of co on o &ric4 C47 -.* %8 CD fo##o'ed &y a -.-$ #ayer of gy"su "#aster C47 -.$+ %8 o CD. %hat thic4ness of #oose#y "ac4ed roc4 'oo# insu#ation C47 -.--)( %8 oCD shou#d &e added to reduce the heat #oss or gain through the 'a## &y +-E. 2. The te "erature distri&ution across a #arge concrete s#a& C47 1.2 %8 oC5 F 7 1.** G 1-23 28hD (-thic4 heated fro one side as easured &y ther ocou"#es a""ro!i ates to the re#ation t7 )-2(-!H12!2H2-!321(!$ 'hereIt0 is in oC and ! is in eters. Considering an area of ( 2 co "ute. 1. The heat entering and #eaving the s#a&s in ti e ti e. 2. The heat energy stored in unit ti e. 3. The rate of te "erature change at &oth sides of the s#a&s. $. The "oint 'here the rate of heating or coo#ing is a!i u . 3. CaD J!"#ain the different odes of heat transfer 'ith a""ro"riate e!"ressions. C i.D conduction CiiD. ConvectionC iii.D >adiation CivD. /ourier #a' of conduction. Cv.D .tefan2:o#tK ann #a' C&D Co "osite 'a## consist of 1- c thic4 #ayer of &ui#ding &ric45 =7 -.* %8 = and 3 c thic4 "#aster5 47 -.( %8 =. <n insu#ating ateria# of =7 -.-+ %8 = is to &e added to reduce the heat transfer through the 'a## &y $-E. /ind its thic4ness. $. Circu ferentia# a#u inu fins of rectangu#ar "rofi#e C1.( c 'ide and 1 thic4D are on to a ,engine cy#inder 'ith a "itch of 1. the height of the cy#inder is fitting the fins are 2--oC and 1(-oC res"ective#y. Ta4e a &ient at 3-oC and h CaverageD 7 1-- %8 2 =. Jsti ate the heat dissi"ated fro the finned and the unfinned surface areas of cy#inders &ody. (. CaD %hat do you understand &y critica# radius of insu#ationL o&tain an e!"ression for the sa e. C&D < cy#inder 1 #ong and ( c in dia eter is "#aced in an at os"here at $(oC. It is "rovided 'ith 1- #ongitudina# straight fins of ateria# having 47 12- %8 =. The height of -.*) thic4 fins is 1.2* c fro the cy#inder 5the heat transfer coefficient

&et'een and at os"heric air is 1* %8 2=. Ca#cu#ate the rate of heat transfer and the te "erature at the end of /ins if surface te "erature of cy#inder is 1(-oC. ). CaD < stee# tu&e 'ith (c ID5 *.) c OD and 47 1(%8 oC is covered 'ith an insu#ative covering of thic4ness 2 c and 47-.2%8 oC. < hot gas at 33-oC 'ith h7$-- %8 oC. /#o's inside the tu&e. The outer surface of the insu#ation is e!"osed to coo# air at 3-oC 'ith h7)- %8 2oC. Ca#cu#ate the heat #osses fro the tu&e to the air for 1- of the tu&e and the te "erature dro"s resu#ting fro the ther a# rMsistance of the hot gas f#o'5 the stee# tu&e5 the insu#ation #ayer and the outside air. C&D The inner surface at r 7 a and the outer surface at r7& of a ho##o' cy#inder are at aintained at unifor te "erature T1 and T2 res". The ther a# conductivity of the so#id is constant deve#o" an e!"ression for the 1 di ensiona# steady state te "erature distri&ution in the cy#inder and for the radia# heat f#o' rate through the cy#inder over a #ength 9. *. CaD %hat is #u "ed ca"acity ana#ysis and o&tain the e!"ression for the te "erature distri&ution for sa e. &D < s#a& of a#u inu 1- c thic4 is origina##y at a te "erature of (-- oC is sudden#y i ersed in a #i1uid at 1--oC resu#ting in heat transfer coefficient of 12--%8 2=. Deter ine the te "erature at the center #ine and the surface one in after the i ersion <#so ca#cu#ate the tota# ther a# energy re oved "er unit area of the s#a& during this "eriod. The "ro"erties of a#u inu for the given condition are F7+.$G1- 2( 2 8sL N 7 2*-- 4g8 3L O7 21(%8 =L c7 -.,4g8=. +. CaD < co "osite 'a## consist of 1- c thic4 #ayer off &ric4.47-.* %8 = and 3c thic4 "#aster5 47-.( %8 =. <n insu#ating ateria# of 47-.-+ %8 = is to &e added to reduce the heat transfer through the 'a## &y $-E./ind its thic4ness. C&D <n a#u inu "#ate C471)-%8 oC5 N72*,-%8 oC5 C"7-.++4P84goCD of thic4ness ;73c and at a unifor te "erature of 222( oC is sudden#y i ersed at ti e t7- in a 'e## stirred f#uid aintained at a constant te "erature T F 72(oC. Ta4e732-oC.Deter ine the ti e re1uired for the centre of the "#ate to reach (-oC. ,. CaD < furnace 'a## consists of three #ayers. The inner #ayer of 1-c thic4ness is ade of fire&ric4 C471.-$%8 =D.The inter ediate #ayer of 2(c thic4ness is ade of asonry &ric4 C47 -.),%8 =D fo##o'ed &y a (c thic4 Concrete 'a## C471.3*%8 =. %hen the furnace is in continues o"eration the inner surface of the furnace is at +--oC 'hi#e the outer concrete surface is at (-oC. Ca#cu#ate the rate of heat #oss "er unit area of the 'a##5 the te "erature at the inter face of the fire&ric4 and asonry &ric4 and the te "erature at the interface of the asonry &ric4 and concrete. C&D <n e#ectrica# 'ire of 1-c #ength and 1 dia eter dissi"ates 2-- % in air at 2(oC.the convection heat transfer coefficient &et'een the 'ire surface and air is 1(

%8 2=.Ca#u#ate the critica# radius of insu#ation and a#so deter ines the te "erature of the 'ire if it0s insu#ated to the critica# thic4ness of insu#ation. 1-. CaD <n a#u inu rod C472-$ %8 =D 2c in dia eter and 2-c #ong "rotrudes fro a 'a## 'hich is aintained at 3--oC.the end of the rod is insu#ated and the surface of the rod is e!"osed to air at 3- oC.the heat transfer coefficient &et'een the rod0s surface and air is 1-%8 =. Ca#cu#ate the heat #ost &y the rod and the te "erature of the rod at a distance of 1- c fro the 'a##. . 11. /ind out the a ount of heat transferred through an iron fin of #ength (5 'idth 1-and the thic4ness ( . <ssu e 47(+'8 oC and h712%8 2C for the ateria# of the fin and the te "erature at the &ase of the fin as +-oC <#so find the te "erature at the ti" of the fin if the at os"heric te "erature is 2-oC. 12. <n e#ectrica# 'ire of 1- #ength and 1 dia eter dissi"ates 2--% in air at 2(oc. The convection heat transfer coefficient &et'een the 'ire surface and air is 1(%8 2=. Ca#cu#ate the critica# radius insu#ation and a#so deter ine the te "erature of the 'ire if it0s insu#ated to the critica# thic4ness of insu#ation. 13. CaD Derive the heat conduction e1uation in the cy#indrica# co2ordinates using the e#e enta# vo#u e for a stationary isotro"ic so#id. C&D < 3 c thic4ness other. Deter ine the "ercentage decrease in heat transfer if &etter insu#ating ne!t to "i"e than it is the outer #ayer. <ssu e that the outside and inside te "eratures of co "osite insu#ation are fi!ed. ateria# is OD stea "i"e is to &e covered 'ith t'o #ayer of insu#ation each having a

of 2.( c . the average ther a# conductivity of one insu#ation is ( ti es that of the

1$. < co "osite 'a## is for ed of 2.( c co""er "#ate C473((%8 4D5a 3.2 #ayer of as&estosC47.11-%8 =D and a (c #ayer of fi&re "#ate C47.-$,%8 =D.The 'a## is su&@ected to an overa## te "erature difference of ()- o C C()- O C on the Cu "#ate side and - O C on the fi&re "#ate side D.Jsti ate the heat f#u! through this co "osite 'a## and the interface te "erature &et'een as&estos and fi&re "#ate. 1(. < .tee# tu&e of (c ID 5*.)c OD and 471(%8 = is covered 'ith an insu#ation of thic4ness 2c and ther a# conductivity 5-.2 %8 =.< hot gas at 33- O C and h7)-%8 2 =.<ssu ing a tu&e #ength of 1- 5find the heat #oss fro the tu&e to air. <#so find5across 'hich #ayer the #argest te "erature dro" occurs. 1). One end of #ong rod 1c dia eter having a ther a# conductivity of$(%8 = is "#aced in a furnace. The rod is e!"osed to air at 3- O C over its surface and the convection co2efficient is esti ated at 3(%8 2=.If the te "erature is read as 2)( O C at a distance of 3,.3 fro the furnace end5deter ine the &est te "erature of the rod.

1*. < "#ane sha"ed nuc#ear fue# e#e ent of 2$ thic4ness e!"osed on the sides to convection at 2-- O C 'ith a convective heat transfer co2efficient of ,--%8 2= generates heat at 2M%8 3.Deter ine CiD The surface te "erature5CiiD the a!i u te "erature in the "#ate and CiiiD the te "erature gradient at the surface. The ther a# conductivity of the ateria# is 2(%8 =. 1+. < stee# "i"e of -.$ dia. carrying oi# in the co#d region is "ro"osed to &e "rotected &y insu#ations < and : of +c and 1-c thic4ness 'ith conductivities of -.-3and -.3 %8 =. These are "urchased in re1uired vo#u es in "o'der for . During the e!ecution5 &y ista4e the ateria# : 'ith conductivity -.3%8 = 'as a""#ied first and then the other ateria#. Investigate the heat transfer rate in t'o situations.

1,. O&tain an e!"ression for the te "erature "rofi#e of an infinite#y #ong fin of unifor cross2 section fro &asic "rinci"#es and hence ca#cu#ate the heat transfer &y fin. 2-. < ther ocou"#e is oved fro one ediu to another ediu at a different te "erature5 sufficient ti e ust &e given to the ther ocou"#e to co e to ther a# e1ui#i&riu 'ith the ne' conditions &efore a reading is ta4en. consider a -.1 dia co""er ther ocou"#e 'ire origina##y at 1(-oC. /ind the te "erature res"onse Ci.e.5 an a""ro!i ate "#ot of te "erature Bs ti e for interva#s of C $- and 12- secondsD 'hen this 'ire is sudden#y i ersed in CiD 'ater at O $- C Ch7+-%8 2=DCiiDair at $-OC Ch7$-%8 2=D