Lecture 3.pdf

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Chem & Biological Engineering
CE 318
Professor Chong Cheng

(Heat CE 318: - Transport Process 2 and Mass Transfer) Lecture 3.1-D Steady-State Conduction Heat Transfer Scope: l) 1-D systems includes flatslab,hollow cylinder, and hollow sphere. For each ofthese systems, only one dimensional geometrical parameter (xor r)is requiredto describe theshape" l-r T:. ,T' ----X---------> Note: For a system, ifthe pointswith the same dimensional geometrical parameter one are not equivalent to each other, thenitis nota I-D system. For example: Tr 2) Steady-stateswithout heatgeneration will be discussed inthis lecture.Therefore, : heat in heat out Theoretical Starting Point: Fourier'sLaw of Heat Conduction q/A : -k(dT/dx) or qlA: -lr(dT/dr) Note: l) For any material, itsthermal conductivity may have dependence on temperature. Within a moderate ternperature range.approximately there would be k: a+ bT or k: a+bT+cT2 2) Although A isconstant for ID slab, A changes with r values for hollow cylinders or spheres (A:2nLr for cylinders;A: 4n? forspheres). Goal: To solve heattransfer rateand temperature plot for l-D conduction systems. Cr"w I Gr,llorl.i,un L -fin 5i.6 {t' wa"l,( " i I j I ,/ - -t ! l:ll- p*"i.*'t [r,w : A- d.x It ihc{.n A a"i B r,,'cer'htc,n{ , r}&'L vl I: I l rL/v -ql R't1 '\ _AA L \X, t-/ I lr t'i 1'lt-uP r^T 4t " , Il n -r- i/i\ ^Lr- ^L, ).- \ lL-T lt / RA tr q- lr - lr &rtVQ- *- tt-t tL t'- aX lx,-x,) i b.A / ir-n ltsirtnne iF ) +* o-e/ uA o i,: o ftzuwt \ ndl - Jtutt Lx tx -o,rxl/-, 11 -I I l, rxlr JNlTr- T*T *-"-- = fu-tu, ra.-Y, ) ptt t.4./ /'. I>- lt t'"'L' / ^F/KA /n'tti*. i-Lrcvryfat*f4p lrL It tt |4 v/-,"^"t I (L t- \v-L: lf u^lurte,l*,t* l- v*"s l;*^rt'y *rrL ''.'.. *'-t 1f! re,t'i | \1 1 J L
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