Fundamentals of Heat ansfe Muhammad Rashid Usman Institute of Chemical Engineeing and echnology Univesity of the Punjab, ahoe. Figue taen fom: http:heatexchange-design.com0006heat-exchanges-6 Dated: 7-Jan-0
Heat conduction though a hollow cylinde Heat tansfe aea π
Heat conduction though a hollow cylinde Rate of heat tansfe π ln ( ) ( ) Rate of heat tansfe pe unit length ln π ( ) ( ) ln( ) π empeatue diffeence themal esistance
Heat conduction though a hollow cylinde: empeatue pofile What about tempeatue pofile in adial diection? ny idea about tempeatue pofile in axial diection! he answe is staight fowad. hin!
Heat conduction though a hollow cylinde: empeatue pofile + ln ln( ) 5
Heat conduction though a hollow cylinde: Poblem- glass pipe has an outside diamete of 6 in, and an inside diamete of 5 in, it will be used to tanspot a fluid which maintains the inne suface at 00 F, the outside tempeatue of the pipe is 75 F. What will be the ate of heat flow? 0.6 Btuh ft F. [p. 6, 5] nswe: 5.78 Btuh ft 6
Heat conduction though a hollow sphee Heat tansfe aea π 7
8 Heat conduction though a hollow sphee ( ) tansfe heat of Rate π esistance themal empeatue diffeence π aea unit pe tansfe heat Rate of
Heat conduction though a hollow sphee: empeatue pofile What about tempeatue pofile in adial diection? 9
Heat conduction though a hollow sphee-: empeatue pofile + 0
Heat conduction though a hollow sphee: Poblem- Calculate the heat loss pe m of outside suface aea fo a heated sphee 5 cm diamete coveed with 50 cm insulation with themal conductivity 0.057 calh m C. he inside and outside tempeatue of insulation ae 5 C and 80 C espectively. nswe: 60.7 calh m
hemal esistances in seies Heat conduction though a multilaye (composite) plane (flat) wall Heat conduction though a multilaye hollow cylinde Heat conduction though a multilaye hollow sphee
Heat conduction though a multilaye (composite) plane wall B C empeatue pofile x x B x C
Heat conduction though a multilaye (composite) plane wall Fo laye B: Fo laye : Fo laye C: Fo steady-state, it may be shown that x B B x x C C C C B B x x x
5 Heat conduction though a multilaye (composite) plane wall Fo the oveall change in tempeatue the esistance in seies all Sum of tempeatue diffeence Oveall ate Heat x x x C C B B + + ( ) O C C B B x x x + +
Heat conduction though a multilaye (composite) plane wall-: Poblem- [p. 9, 7] funace is constucted with 0.0 m of fiebic, 0. m of insulating bic, and 0.0 m of building bic. he inside tempeatue is 00 K and the outside tempeatue is 0 K. hemal conductivities ae of fiebic, insulating bic, and building bic ae shown in the Figue. Estimate the heat loss pe unit aea and the tempeatue at the junction of the fiebic and the insulating bic. 00 K 0 K. Wm K 0. Wm K 0.7 Wm K x 0.0 m x 0.0 m x 0.0 m 6
Heat conduction though a multilaye (composite) plane wall-: Poblem-5 [p., 8] Compute the ate of heat tansfe though the walls of a oom having inside and outside tempeatues 55. K and 97. K espectively. he walls of the oom ae made up of in concete, in co boad, and ½ in wood. he themal conductivities of the wall mateials ae concete 0.76 Wm K, coboad 0.0 Wm K, and wood 0.5 Wm K. lso, find the tempeatue at the inteface between the wood and co boad. 7
Heat conduction though a multilaye (composite) hollow cylinde- 8
9 Heat conduction though a multilaye (composite) hollow cylinde- Fo mateial B: Fo mateial : Fo mateial C: ( ) ( ) ln π ( ) ( ) ln B π ( ) ( ) ln C π ( ) ( ) ( ) ( ) ( ) ( ) ln ln ln C B π π π Fo steady-state, it may be shown that
0 Heat conduction though a multilaye (composite) hollow cylinde- C B + + π π π ) ln( ) ln( ) ln( ) ( Fo the oveall change in tempeatue the esistance in seies all Sum of tempeatue diffeence Oveall ate Heat C B + + π π π ) ln( ) ln( ) ln( ) ( O
Heat conduction though a multilaye (composite) hollow cylinde-: Poblem-6 [p. 98, 6] tube 60 mm oute diamete contains two layes of insulation & B. hicness of laye is 50 mm with themal conductivity 0.055 Wm C followed by a 0 mm laye B with themal conductivity 0.05 Wm C. If the tempeatue of the oute suface of pipe is 50 C and the tempeatue of the oute suface of laye B is 0 C. Calculate the heat loss in watts pe mete length.
Heat conduction though a multilaye (composite) hollow sphee Deive an expession fo heat conduction though a composite hollow sphee.
Refeences. Geanoplis, C.J. (00). anspot pocesses and sepaation pocess pinciples: includes unit opeations. th ed. Pentice-Hall Intenational, Inc.. Holman, J.P. (00). Heat tansfe. 0 th ed. McGaw-Hill Highe Education, Singapoe.. Cengel, Y.. (00). Heat tansfe: pactical appoach. nd ed. McGaw- Hill.. Incopea, F.P.; DeWitt, D.P.; Begman,..; avine..s. (007) Fundamentals of heat and mass tansfe. 6 th ed. John Wiley & Sons, Inc. 5. Ken, D.Q. (965). Pocess heat tansfe. McGaw-Hill Intenational Boo Co., Singapoe. 6. McCabe, W..; Smith, J.C.; Haiott, P. (99). Unit opeations of chemical engineeing. 5 th ed. McGaw-Hill, Inc., Singapoe. 7. Coulson, J.M.; Richadson, J.F.; Bachust, J.R.; Hae, J.H. 999. Coulson and Richadson s Chemical engineeing: Fluid flow, heat tasnfe and mass tansfe. vol.. 6 th ed. Buttewoth-Heinemann, Oxfod. 8. Staff of Reseach and Education ssociation. (98). he heat tansfe poblem solve. Reseach and Education ssociation, New Jesey.