# sm3_12 - PROBLEM 3.12 KNOWN Dimensions and thermal...

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Unformatted text preview: PROBLEM 3.12 KNOWN: Dimensions and thermal conductivities ofthe components ofa Fuel cell membrane. FIND: The effective thermal conductivity in the x-direction for various carbon nanotuhe loadings. SCHEMATIC: X tgm=0.10mm i— L —-| ASSUMPTIONS: ( l) Steady-state conditions. (2) Constant properties. ANALYSIS: The equivalent thermal circuit is as follows. Therefore, “Ix —T|‘T3 — AT -AT 1 + l + l + l :qx_kcﬂ;x‘:tAT (1’2) Continued... PROBLEM 3.12 (Cont) Equating Eqs. (1) and [2) yields kemx — + ; wt L L L L L 1(ng (2501)“! + kmtpcw kcltl-Dthw + k nﬂtclw] 1 kemx = inﬂated. + 1cth + ado—ma. + awed] wheret = tpc+2tcl+2tgdl=020mm+2><001Irmr+2><0.l mm=0.42nmr For f: t], keﬂlx = 1 2X1.3me4l(><0.l><lC|'3m+0.25merK><0.2><lO'3m 0.42 x10-3 m +2>< 1 wxmxx 0.01 x 10-3 m+0 = 0.79 th-K < For f: 0.3, 2X1.3me~K><0.l><lO'3 m+0.25me‘K><0.2><lO'3 m +2>< 1 me-KXU -0.3)><0.01 x 10'3 m +2 x 3000 Wﬂm‘KX (0.3) x 0.01 >< 10'3 m = 43.5 th-K < Similarly, kamx = 15.1 lqu2 -K and 29.3 \va2 *K for f= 0.] and 0.2, respectively. COMMENTS: (1) Addition of a small amount ofhigh thermal conductivity carbon nanotubes increases the ability of the membrane to conduct energy in the x-direction. {2) The effective thermal conductivity in the y-direction will not be signiﬁcantly affected by the carbon nanotuhes, since the thermal resistance posed by the polymer core will have the most inﬂuence on the value of kg”. ...
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