CH00 HEA RANSFER UNI I HEA CONDUCION Couse mateial Adapted fom:. Waen., McCabe, Julian. C. Smith and Pete Haiott, Unit Opeations of Chemical Engineeing, 7th Edn., McGaw Hill Intenational Edition, NewYo 005.. Holman. J.P., Heat ansfe, 9th Edn., ata McGaw Hill Boo Co., New Delhi, 008.. R.C.Sachdeva, Fundamentals of Engineeing Heat and Mass ansfe, 4 th Edition,New Age Intenational Publishes,00 4. www.che.utexas.edu/couse/che60/lectue_notes/chapte_.ppt CONENS Intoduction to vaious modes of heat tansfe, Fouie s law of heat conduction, effect of tempeatue on themal conductivity, steady-state conduction, compound esistances in seies, heat flow though a cylinde, citical adius of insulation in pipes. Intoduction to unsteady state conduction
Intoduction Pactically all the opeations that ae caied out by the chemical enginees involve the poduction o absoption of enegy in the fom of heat. he study of tempeatue distibution and heat tansfe is of geat impotance to enginees because of its almost univesal occuence in many banches of science and engineeing. he fist step in the optimal design of heat exchanges such as boiles, heates, efigeatos and adiatos is a detailed analysis of heat tansfe. his is essential to detemine the feasibility and cost of the undetaing, as well as the size of equipment equied to tansfe a specified amount of heat in a given time. Diffeence between themodynamics and heat tansfe hemodynamic tells us (i) How much heat is tansfeed (ii) How much wo is done (iii) Final state of the system Heat tansfe tells us: (i) How much heat is tansfeed(with what modes) (ii) At what ate heat is tansfeed (iii) empeatue distibution inside the body.. INRODUCION O VARIOUS MODES OF HEA RANSFER he vaious modes of heat tansfe ae (i) conduction (ii) convection (iii) adiation. Conduction Heat tansfe by the actual but invisible movement of molecules with in the continuous substance due to tempeatue gadient is nown as conduction. Convection When a cuent o macoscopic paticle of fluid cosses a specific suface, it caies with it a definite quantity of enthalpy. Such a flow of enthalpy is called convection. Convection is the mode of heat tansfe in which the heat flow is associated with the movement of fluid. Radiation ansfe of enegy though space by electomagnetic waves is nown as adiation.
Fig.. Modes of Heat ansfe.. APPICAIONS OF HEA RANSFER Enegy poduction and convesion -steam powe plant, sola enegy convesion etc. Refigeation and ai-conditioning Domestic applications -ovens, stoves, toaste Cooling of electonic equipment Manufactuing / mateials pocessing -welding, casting, soldeing, lase machining Automobiles / aicaft design
.. Conduction It is the tansfe of intenal enegy by micoscopic diffusion and collisions of paticles o quasi-paticles within a body due to a tempeatue gadient. he micoscopically diffusing and colliding objects include molecules, electons, atoms, and phonons. hey tansfe disoganized micoscopic inetic and potential enegy, which ae jointly nown as intenal enegy. Conduction can only tae place within an object o mateial, o between two objects that ae in diect o indiect contact with each othe. On a micoscopic scale, heat conduction occus as hot, apidly moving o vibating atoms and molecules inteact with neighboing atoms and molecules, tansfeing some of thei enegy (heat) to these neighboing paticles. In othe wods, heat is tansfeed by conduction when adjacent atoms vibate against one anothe, o as electons move fom one atom to anothe..4. FOURIER S AW OF HEA CONDUCION Accoding to Fouie s law of heat conduction, heat flux is popotional to tempeatue gadient. d -A dx Whee Rate of heat tansfe, W = hemal conductivity, W/mK o W/m C A = Heat tansfe aea, m d = empeatue gadient, C/m dx EFFEC OF EMPERAURE ON HERMA CONDUCIVIY hemal conductivity is the physical popety of the substance. It depends upon tempeatue gadient. Fo pue metals themal conductivity deceases with incease in tempeatue. Fo gases and insulatos themal conductivity inceases with incease in tempeatue. Fo small anges of tempeatue, may be consideed constant. Fo lage tempeatue anges, themal conductivity can be appoximated by an equation of the fom = a + b, whee a and b ae empiical constants. 4
Steady-State Conduction It is the fom of conduction which happens when the tempeatue diffeence diving the conduction is constant so that afte an equilibium time, the spatial distibution of tempeatues (tempeatue field) in the conducting object does not change any futhe. In steady state conduction, the amount of heat enteing a section is equal to amount of heat coming out. Unsteady state conduction It is the fom of conduction which happens when the tempeatue diffeence diving the conduction is not constant so that afte an equilibium time, the spatial distibution of tempeatues (tempeatue field) in the conducting object changes as a function of time..5. HEA RANSFER HROUGH A PANE WA et us conside a plane wall of thicness, themal conductivity, inside suface tempeatue i, outside suface tempeatue o. et Q be the ate of heat tansfeed though the plane wall. By Fouie s law of heat conduction d -A dx () Q dx 0 o = - A d () i Integating eqn(), we get Fig.. Plane wall A i o ().6. HEA RANSFER HROUGH A HOOW CYINDER et us conside a hollow cylinde as shown in fig.. he inside adius of the cylinde is, the outside adius is, and the length of the cylinde is. he themal 5
conductivity of the mateial of which the cylinde is made is. he tempeatue of the outside suface is, and that of the inside suface is. By Fouie s law of heat conduction d -A d () d Q = - d () Integating eqn(), we get () Fig.. Hollow cylinde OGARIHMIC MEAN RADIUS AND ARIHMEIC MEAN RADIUS ogaithmic mean adius is the adius that when applied to the integated equation fo a flat wall, will give the coect ate of heat flow though a thic walled cylinde. It is given by the expession o i o i Aithmetic mean adius is used fo thin walled cylinde. A o i whee, = log mean adius A = Aithmetic mean adius o = oute adius i = inne adius 6
.7. COMPOUND RESISANCES IN SERIES (I) Heat ansfe hough A Composite Plane Wall et us conside a flat wall constucted of a seies of layes as shown in fig.4. et the thicness of the layes be,, and the aveage themal conductivities of the mateials of which the layes ae made be,, espectively. et us conside a hot fluid at a tempeatue a and heat tansfe coefficient h a inside the wall and cold fluid at a tempeatue b and heat tansfe coefficient h b outside the wall. et,, and 4 be the inteface tempeatues. It is desied to deive an equation fo calculating the ate of heat flow though the seies of esistances. Rate of heat flow fom the hot fluid to the inne suface of the wall By Newton s law of cooling h a A ( a ) () By eaanging eqn(),we get (a - ) h a A Fig.4.Composite wall Rate of the heat flow though the I laye By Fouie s law of heat conduction A () By eaanging eqn(),we get A Rate of the heat flow though the II laye By Fouie s law of heat conduction A () 7
By eaanging eqn(),we get A Rate of the heat flow though the III laye By Fouie s law of heat conduction A By eaanging eqn(4),we get A 4 4 Rate of heat flow fom the oute suface of the wall to the cold fluid By Newton s law of cooling h b A ( 4 b ) (5) By eaanging eqn(5),we get 4 h A b b (4) Oveall ate of heat flow = oveall tempeatue dop oveall themal esis tan ce Oveall ate of heat flow a b h A A A A h A a b (6) 8
(ii) Heat ansfe hough Coaxial Cylindes et us conside coaxial cylindes constucted of a seies of layes as shown in fig.5. et,, and 4 be the adii of the cylindes and the aveage themal conductivities of the mateials of which the layes ae made be,, espectively. et us conside a hot fluid at a tempeatue a and heat tansfe coefficient h a inside the cylinde and cold fluid at a tempeatue b and heat tansfe coefficient h b outside the cylinde. et,, and 4 be the inteface tempeatues. It is desied to deive an equation fo calculating the ate of heat flow though the seies of esistances. Fig.5.Coaxial cylindes Rate of heat flow fom the hot fluid to the inne suface of the wall By Newton s law of cooling h a A ( a ) () h a ( a ) By eaanging eqn(),we get (a - ) h a Rate of the heat flow though the I laye By Fouie s law of heat conduction () By eaanging eqn(),we get 9
0 Rate of the heat flow though the II laye By Fouie s law of heat conduction () By eaanging eqn(),we get Rate of the heat flow though the III laye By Fouie s law of heat conduction 4 4 (4) By eaanging eqn(4),we get 4 4 Rate of heat flow fom the oute suface of the wall to the cold fluid By Newton s law of cooling h b A ( 4 b ) (5) h b 4 ( 4 b ) By eaanging eqn(5),we get
(4 - b ) h b 4 Oveall ate of heat flow = oveall tempeatue dop oveall themal esis tan ce Oveall ate of heat flow h a a b 4 h b 4 (6).8. Insulation he addition of insulation mateial on a suface educes the amount of heat flow to the ambient. hee ae cetain instances in which the addition of insulation to the outside suface of cylindical of spheical walls does not educe the heat loss. Unde cetain cicumstances it actually inceases the heat loss up to a cetain thicness of insulation. It is well nown fact that the ate of heat tansfe will appoach zeo if an infinite amount of insulation ae added. his means that thee must be a value of adius fo which ate of heat tansfe is maximum.his value is nown as the citical adius of insulation, c..8.. CRIICA RADIUS OF INSUAION IN PIPES et us conside an insulating laye in the fom of a hollow cylinde of length. et i and o be the inne and oute adii of insulation. he themal conductivity of the mateial of which the laye is made be. et the inside suface of insulation be at a tempeatue i, and the outside suface at a tempeatue o be dissipating heat by convection to the suoundings at a tempeatue b with a heat tansfe coefficient h. hen the ate of heat tansfe Q though this insulation laye is Fig.6. Insulation laye
o i i b h o () he value of citical adius c, that is o fo which Q is a maximum may be obtained by equating dq/d o to zeo. 0 i b d d o o h o i h o i b 0(Since it is the diving foce) o () = 0 () o h o 0 = h = c he adius at which the ate of heat tansfe is maximum is nown as the citical adius of insulation.
.9.VARIABE HERMA CONDUCIVIY et us a hollow cylinde. he inside adius of the cylinde is i, the outside adius is o, and the length of the cylinde is. he themal conductivity of the mateial of which the cylinde is vaies with tempeatue as = o ( + ). he tempeatue of the outside suface is o, and that of the inside suface is i. By Fouie s law of heat conduction d -A d d - o ( + ) A d () o d Q = - o ( ) d () i o i Q o 0 i i o i o i o 0 i o i o ().0. Intoduction to Unsteady state heat tansfe A solid body is said to be in a steady state if its tempeatue does not vay with time. If howeve thee is an abupt change in its suface tempeatue o envionment it taes some time befoe the body to attain an equilibium tempeatue o steady state. Duing this inteim peiod the tempeatue vaies with time and the body is said to be in an unsteady o tansient state. he analysis of unsteady state heat tansfe is of geat inteest to enginees because of its widespead occuence such as in boile tubes, ocet nozzles, automobile engines, cooling of IC engines, cooling and feezing of food, heat teatment of metals by quenching, etc. Fo pactical puposes it is necessay to now the time taen to attain a cetain tempeatue when the envionment suddenly changes. he solution of an unsteady sate poblem will be moe complex than that of steady state one because of the pesence of anothe vaiable time, t.
ansient heat conduction poblems can be divided into peiodic heat flow and non peiodic heat flow poblems. Peiodic heat flow poblems ae those in which the tempeatue vaies on a egula basis, eg., the vaiation of tempeatue of the suface of the eath duing a twenty fou hou peiod.. In the non peiodic type, the tempeatue at any point within the system vaies non linealy with time..0.. Systems with negligible intenal esistance umped Heat Analysis Heat tansfe in heating and cooling of a body is dependent upon both the intenal and suface esistances. he simplest unsteady state poblem is one in which the intenal esistance is negligible, that is, the convective esistance at the suface bounday is vey lage when compaed to the intenal esistance due to conduction. In othe wods, the solid has an infinite themal conductivity so that thee is no vaiation of tempeatue inside the solid and tempeatue is a function of time only. his situation cannot exist in eality because all the solids have a finite themal conductivity and thee will always be a tempeatue gadient inside wheneve heat is added o emoved. Poblems such as heat teatment of metals by quenching, time esponse of themocouples and themometes, etc can be analysed by this idealization of negligible intenal esistance. he pocess in which the intenal esistance is ignoed being negligible in compaison with its suface esistance is called the Newtonian heating and cooling pocess. In Newtonian heating and cooling pocess the tempeatue thoughout the solid is consideed to be unifom at a given time. Such an analysis is called the lumped heat capacity analysis..0.. Systems with negligible suface esistance Anothe class of tansient poblems met with in pactice is one in which the suface esistance is negligible compaed to the oveall esistance. his amounts to saying that the convective heat tansfe coefficient at the suface is infinity. Fo such a pocess the suface tempeatue emains constant fo all the time and its value is equal to that of ambient tempeatue. 4
P.No.. A funace wall consists of two layes,.5cm of fie bic(=.cal/h m o C)and.5cm of insulating bic (=0.5cal/h m o C). he tempeatue inside the funace is 650 o C and the inside heat tansfe coefficient is 60cal/h m o C. he tempeatue of the suounding atmosphee is 7C and the outside heat tansfe coefficient is 0cal/h m C. Detemine the ate of heat of loss pe squae mete of the wall. Solution: -.5 x 0 - m -.5 x 0 - m -. cal/h m o C - 0.5 cal/h m o C h a - 60 cal/h m o C h b - 0cal/h m C a 650 C b 7 C a b h A A A h A a b Q / A = 46.8 W / m P.No.. A pipe caying steam at 0 C has an I.D. of 5cm. he convection coefficient on the inside wall is 60W/m K. he pipe wall thicness is 5mm and the themal conductivity is 5W/mK. he outside is exposed to a chemical at 0C with a convection coefficient of 5W/m K. If the pipe wall is coveed with two insulation layes, the fist cm thicness with =0.W/mK and the second 4cm thicness with = 0.5W/m K. Detemine the ate of heat tansfe. Solution : 4-75 x 0 - m - 90 x 0 - m - 0 x 0 - m - 60 x 0 - m - 5 W / m K 5
6-0. W / m K - 0.5 W / m K h a - 60 W / m K h b 5 W / m K 4 4 h h b a b a 46. W
ASSIGNMEN: Composite Wall. A composite wall consists of a 7cm thic fiebic laye ( =. W/m o C) and a cm thic odinay bic laye ( = 0.70 W/m o C). he inside and outside suface tempeatues of the walls ae 400 o C and 45 o C espectively. Calculate the heat loss pe unit aea of the wall. Also calculate the tempeatue between the odinay bic and the fiebic layes.. A steam boile funace is made of a laye of fieclay ( = 0.5 W/m K).5cm thic and a laye of ed bic( = 0.7 W/mK) 50cm thic. If the wall tempeatue inside the boile funace is 00C and that on the outside wall is 50 o C, detemine the amount of heat loss pe squae mete of the funace wall.. he wall of a cold stoage consists of thee layes, an oute laye of odinay bic of 5cm thic, a middle laye of co,0cm thic, and inne laye of cement,6cm thic. he themal conductivities of the mateials ae: bic = 0.7 W/m o C, co = 0.04 W/m o C, cement = 0.7 W/m o C. he tempeatue of the oute suface of the wall is 0 o C, and the inne is -5 o C. Calculate ate of heat tansfe pe unit aea of the wall and inteface tempeatues. 4. A funace wall consists of cm of efactoy fie clay bic (=W/m o C ).5 cm of the silica bic (=0.88W/m o C) and 6mm of ion plate (=45W/m o C).he fie side of the efactoy is at 50 o C and outside suface of steel is o C. Detemine the heat loss. 5. A funace wall is made of inside silica bic (=.858W/m o C) and outside magnetite bic (=5.8W/m o C). he thicness of the silica bic is cm and that of magnetite bic is 0 o C. he tempeatue of silica bic suface inside the funace is 00 o C and at the outside suface of magnetite is 0 o C. Find the heat loss pe squae mete of the funace wall. 6. he composite wall of a funace consists of an inne laye of silica bic,5cm thic ( =.04 W/m o C), and an oute laye of insulating bic,0cm thic (=0. W/m o C). he inside tempeatue of the funace is 800 o C and the inteface tempeatue is 705 o C. Calculate the ate of heat loss pe unit aea of the funace wall. 7. A wall of 0.5m thicness is to be constucted fom a mateial which has an aveage themal conductivity of.4w/mk. he wall is to be insulated with a mateial having an aveage themal conducting of 0.5W/mK, so that the heat loss pe squae mete will not exceed 450W. Assuming that the inne and oute suface tempeatues ae 00 o C and 5 o C espectively, calculate the thicness of insulation equied. 8. A wall cm thic is to be constucted fom a mateial which has an aveage themal conductivity of. W/mC. he wall is to be insulated with a mateial having an aveage themal conductivity of 0.5W/mC, so that the heat loss pe squae mete will not exceed 80W. Assuming that the inne and oute suface tempeatues of the insulated wall ae 00 and 0C, calculate the thicness of the insulation equied. 9. A composite wall is made of two layes of 0.0m and 0.5m thicness with sufaces held at 600 o C and 0 o C espectively. If the conductivities ae 0 and 50W/mK detemine the heat conducted. In ode to estict the heat loss to 5W/m anothe laye of 0.5m thicness. Detemine the themal conductivity equied. 7
0. A funace wall consists of 00mm of efactoy fieclay bic, 00mm of aolin bic, and 6 mm of steel plate. he fie side of the efactoy is at 50C, and the outside of the steel is at 0C. (a) Calculate the heat loss pe squae mete coss section of the wall. (b) Detemine the inteface tempeatues. fieclay =.50 W/m C; aolin bic = 0.8 W/mC ; steel = 45 W/m C.. An exteio wall of a house may be appoximated by a 0cm laye of common bic(=0.7w/mc) followed by a.75cm laye of gypsum plaste (=0.48W/mC).What thicness of loosely paced oc-wool insulation (=0.065W/mC) should be added to educe the heat loss though the wall by 80%?. he doo of a cold stoage plant is made fom two 6mm thic glass sheets( = 0.75W/mK) sepaated by a unifom ai gap( = 0.0W/mK) of mm. he tempeatue of the ai inside the oom is -0C and the ambient ai tempeatue is 0 o C. Assuming the heat tansfe coefficient between glass and ai to be.6 W/m K, detemine the ate of heat loss into the oom pe unit aea of the doo. Neglect convection effect in the ai gap. Coaxial cylindes. A thicwalled tube of stainless steel (= 9 W/mC)with cm ID and 4cm OD is coveed with a cm laye of asbestos insulation(= 0. W/mC).If the inside wall tempeatue of the pipe is maintained at 600C and outside wall tempeatue is maintained at 00C, calculate the heat loss pe mete length. Also calculate the tube insulation inteface tempeatue.. A hot steam pipe having an inside suface tempeatue of 50C has an inside diamete of 8cm and a wall thicness of 5.5mm. It is coveed with a 9cm laye of insulation having =0.5 W/m C, followed by a 4cm laye of insulation having = 0.5 W/mC. he outside tempeatue of insulation is 0C. Calculate the heat lost pe mete of length. Assume =47 W/mC fo the pipe.. A cylindical hot gas duct, 0.5m inside adius,has an inne laye of fieclay bic( =. W/m C) of 0.7m thicness. he oute laye, 0.4m thic is made of a special bic(=0.9 W/m C). he bicwo is enclosed by an oute steel cove which has a tempeatue of 65 C. he inside tempeatue of the composite cylindical wall of the duct is 400C. Neglecting the themal esistance of the steel cove, calculate the ate of heat loss pe mete of the duct and also the inteface tempeatue between the ceamic layes. 4. A 0cm O.D steam pipe caying satuated steam at tempeatue 95C is lagged to 0cm diamete with magnesia (= 0.07 W/mK) and futhe lagged with laminated asbestos (=0.08 W/mK) to 5cm diamete. he whole pipe is futhe potected by a laye of canvas. If the tempeatue unde the canvas is 0C, calculate the ate of heat loss on 50m length of pipe. 5. A pipe of I.D 5.4cm and O.D 6.8cm caies satuated steam at tempeatue 90C. he themal conductivity of the pipe wall is 5 W/mK. he pipe is insulated with a 0cm thic fibe glass blanet (=0.07 W/mK). If the oute suface tempeatue is 4 C, calculate the ate of heat loss ove a 0 m section of the pipe. 6. A steel pipe.4mm oute diamete,.8mm wall thicness caies satuated steam at o C. Pipe is insulted with 50mm laye of magnesia pipe coveing and outside this magnesia is 75 mm laye of co. Inside tempeatue of co is at o C. Calculate the heat loss pe mete length of the pipe and the tempeatue at 8
the boundaies between metal and magnesia and between magnesia and co. Data: steel =45W/m o C ; Mg, =0.0588W/m o C, Co, = 0.059W/m o C. 7. A multilaye cylindical wall of a funace is constucted of 4.5cm laye of insulating bic with themal conductivity of 0.08W/mK followed by a 9cm laye of common bic with themal conductivity of 0.08W/mK. he inne wall tempeatue is 500 o C and oute wall tempeatue is 70 o C.What is the heat loss though the wall, when the inne diamete of the funace is.m and the length of the wall is m? 8. A steel pipe (I.D. 4.4cm and O.D. 4.74cm) caies steam at 450 o C. he steel pipe is coveed with a.5cm laye of an insulating mateial (=0.09cal/h m o C).his is coveed with a 5cm laye of anothe insulating mateial (=0.06cal/h m o C ). If the tempeatue of the outemost insulation laye is 60 o C, calculate the heat loss in cal/h pe mete length of pipe and the laye contact tempeatues. Neglect esistance of the steam film and assume fo the steel pipe as 6cal/h m o C. 9. A steel pipe line (=50W/mK) of 00mm and O.D.0mm is to be coveed with two layes of insulation each having a thicness of 50mm.he themal conductivity of the fist insulation mateial is 0.06W/mK, and that of the second is 0.W/mK. Calculate the loss of heat pe mete length of pipe and the inteface tempeatue between the two layes of insulation when the tempeatue of the inside tube suface is 50 o C and that of the outside suface of the insulation is 50 o C. Combined Heat ansfe. A funace wall consists of two layes,.5cm of fie bic (=.cal/h m o C) and.5cm of insulating bic (=0.5cal/h m o C). he tempeatue inside the funace is 650 o C and the inside heat tansfe coefficient is 60Kcal/h m o C. he tempeatue of the suounding atmosphee is 7 o C and the outside heat tansfe coefficient is 0cal/h m o C.Neglecting the themal esistance of the mota joints detemine the ate of heat of loss pe squae mete of the wall.. he inne dimensions of a feeze cabinet ae 60cm x 60cm x 50cm(height). he cabinet walls consist of two mm thic enameled sheet steel (= 40W/mK) walls sepaated by a 4cm laye of fibeglass(=0.049w/mk) insulation. he inside tempeatue is to be maintained at -5 o C and the outside tempeatue on a hot summe day is 45 o C.Calculate the ate of heat tansfe assuming heat tansfe coefficient of 0 W/m K both on the inside and outside of the cabinet. Also calculate the oute suface tempeatue of the cabinet.. A steel tube having =46 W/mC has an inside diamete of cm and wall thicness of mm. A fluid flows on the inside of the tube poducing a convection coefficient of 500 W/mC on the inside suface, while a second fluid flows acoss the outside of the tube poducing a convection coefficient of 97 W/m C on the outside tube suface. he inside fluid tempeatue is C while the outside fluid tempeatue is 57C. Calculate the heat lost by the tube pe mete of length. 4. A steam pipe is coveed with two layes of insulation, the fist laye being cm thic and second 5cm. he pipe is made of steel(=58w/mk) having an I.D of 60mm and O.D of 70mm. he inside and outside film coefficients ae 0 and 5.8W/m K espectively. Calculate the heat lost pe mete of pipe if the steam tempeatue is 00 o C and the ai tempeatue is 50 o C. he themal conductivity of the two insulating mateials ae 0.7 and 0.09 W/mK espectively. 5. A steel tube ( = 4.6 W/mK) of 5.08cm ID and 7.6 OD is coveed with a.54cm laye of asbestos insulation(= 0.08W/mK). he inside suface of the tube eceives heat by convection fom a hot gas at a tempeatue of 6 o C with the heat tansfe coefficient 84W/m K,while the oute suface of the insulation is 9
exposed to the ambient ai at 8 o C with the heat tansfe coefficient of 7 W/m K.Calculate the loss of heat to ambient ai fo m length of the tube and also the inteface tempeatues. 6. A multilaye cylindical wall of a funace is constucted of 4.5cm laye of insulating bic with themal conductivity of 0.08W/mK followed by a 9cm laye of common bic with themal conductivity of 0.08W/m K. he inne wall tempeatue is 500C and oute wall tempeatue is 70C.(a) Calculate the heat loss though the wall, when the inne diamete of the funace is.m and the length of the wall is m.(b) Detemine the inteface tempeatues. 7. A steel pipe having an I.D.5.50mm and an O.D.60.mm and =9.7cal/h m o C caies steam at 50 o C. It is lagged with.7mm thic oc wool of themal conductivity 0.049cal/h m o C and the suounding ai is at 0 o C.If the heat tansfe coefficient fom the insulated pipe to the suounding ai is 6cal/h m o C, what will be the (a) heat loss pe mete length of pipe (b) tempeatue at the boundaies between the pipe wall and oc wool and (c) between the oc wool and suounding ai. 8. A pipe caying steam at 0C has an intenal diamete of cm and the pipe thicness is 7.5 mm. he conductivity of the pipe mateial is 49 W/m K. he convective heat tansfe coefficient on the inside is 85 W/m K. he pipe is insulated by one laye of insulation of 5 cm thicness having conductivity of 0.5 W/m K. he outside is exposed to ai at 5C with a convection coefficient of 8 W/m K. Detemine the heat loss fo 5m length and the inteface tempeatues. 9. A 5cm diamete steel pipe is coveed with a cm laye of insulating mateial having = 0. W/mC followed by a cm thic laye of anothe insulating mateial having = 0.06 W/mC. he entie assembly is exposed to a convection suounding condition of h = 60W/m C and = 5C. he outside suface tempeatue of steel is 400C. calculate the heat lost by the pipe insulation assembly fo a pipe length of 0m. 9. A steel pipe (= 44W/mK) of 5.08cm I.D and 7.6cm O.D is coveed with a.54cm laye of asbestos insulation (=0.08W/mK).he inside suface of the pipe eceives heat fom the hot gas at a tempeatue of 6 o C with the heat tansfe coefficient 84W/m K,while the oute suface of the insulation is exposed to the ambient ai at 8 o C with the heat tansfe coefficient of 7W/m K. Calculate the heat loss to ambient ai fo m length of the pipe and also calculate the inteface tempeatues. 0. A pipe caying steam at 0 o C has an I.D. of 5cm. he convection coefficient on the inside wall is 60W/m K.he pipe wall thicness is 5mm and the themal conductivity is 5W/mK. he outside is exposed to a chemical at 0 o C with a convection coefficient of 5W/m K. If the pipe wall is coveed with insulation layes, the fist cm thicness with =0.W/mK and the second 4cm thicness with = 0.5W/mK, detemine the ate of heat tansfe and inteface tempeatue. A pipe caying steam at 0C has an intenal diamete of cm and the pipe thicness is 7.5 mm. he conductivity of the pipe mateial is 49 W/m K. he convective heat tansfe coefficient on the inside is 85 W/m K. he pipe is insulated by one laye of insulation of 5 cm thicness having conductivity of 0.5 W/m K. he outside is exposed to ai at 5C with a convection coefficient of 8 W/m K. Detemine the heat loss fo 5m length and the inteface tempeatues. 0
Citical adius of insulation. A tube of O.D..5 cm is to be insulated with a laye of asbestos of themal conductivity = 0. w/m o C. he conduction heat tansfe coefficient fom the suface of the asbestos to the ambient ai is h α = W/mC. Calculate the citical adius of insulation.. A steam pipe 0 cm I.D. and cm O.D. is coveed with an insulating substance (=w/m). he steam tempeatue and the ambient tempeatue ae 00 o C and 0 o C espectively. If the convective heat tansfe coefficient between the insulation suface and ai is 8W/m, find the citical adius of insulation. Fo this value, calculate the heat loss pe mete length of pipe and the oute suface temp. Neglect the esistance of the pipe mateial.. Calculate the citical adius of insulation fo asbestos (=0.7 W/m o c) suounding a pipe and exposed to oom ai at 0 o C with h=.0 W/m o C. Calculate the heat loss fom a 00 o C, 50 mm dia pipe coveed with the citical adius of insulation and without insulation. 4. Evaluate the thicness of ubbe insulation necessay in the case of a 0mm dia coppe conducto to ensue max. heat tansfe to the atmosphee, given the themal conductivity of ubbe as 0.55 W/mK and the suface coefficient as 8.5 W/m K. Estimate the max heat tansfe ate pe mete length of conducto if the tempeatue of ubbe is not to exceed 65 0 C while the atmosphee is at 0 o C. Vaiable themal conductivity. A plane wall of fieclay bic of thicness 5cm is having tempeatues 50 o C and 50 o C on its two sides. he themal conductivity of the fieclay bic is a function of tempeatue. (W/mK) = 0.88 (+0.0007). Calculate the ate of heat tansfe.. A fie clay wall 0cm thic has its two sufaces maintained at 000 o C and 00 o C. he themal conductivity vaies with temp. as (W/m) = 0.8 + 0.00058. Calculate the ate of heat flow.. Calculate the heat loss pe squae mete of the suface aea of a funace wall 5cm thic. he inne and oute suface tempeatues ae 400 o C and 40 o C espectively. he vaiation of the themal conductivity in W/mK with tempeatue in o C is given by the following equation: K = 0.00 0-6. 4. Compute the heat loss pe squae mete suface aea of a 40cm thic funace wall having suface temp. of 00 o C and 50 o C, if the themal conductivity of the wall mateial is given by = 0.005-5 0-6, is in o C. 5. he two faces of a slab at x = 0 and x = ae ept at t and t o C espectively. he '' of the mateial is given by as a tempeatue dependent value by = o (t - t o ) whee t o and o ae constants. Deduce the expession fo heat flow/unit aea. 6. Calculate the ate of heat tansfe in a slab of thicness 0 cm and aea 4.5 cm when the two faces ae maintained at 00C and 50C. he themal conductivity, can be expessed by the elation, = 6.8+7. 0 - W/m. 7. Deive an expession fo one dimensional heat tansfe in a hollow cylinde. he themal conductivity vaies with tempeatue as = o ( + ) 8. Deive an expession fo one dimensional heat tansfe in a hollow cylinde. he themal conductivity vaies with tempeatue as = o ( + + ) 9. A thic wall coppe cylinde has an inside adius of cm and the oute adius of cm. he inne and oute sufaces ae held at 0 o C and 90 o C
espectively. Assume vaies with tempeatue as (W/mK) =7.9[- 9.5 0-5 (-50)]. Detemine the heat loss pe unit length. ---------------------