# sm3_11 - PROBLEM 3 l l KNOWN Drying oven wall having...

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Unformatted text preview: PROBLEM 3. l l KNOWN: Drying oven wall having material with known thermal conductivity sandwiched between thin metal sheets. Radiation and convection conditions prescribed on inner surface: convection conditions on outer surface. FIND: (21} Thermal circuit representing wall and processes and (b) Insulation thickness required to maintain outer wall surface at T0 = 40°C. SCHEMATIC: 2 insulation, It = 0.05 WIm—K q“: 100 WM WW5 To =4ooc Tm Tl To Top —’. *W-“W‘W‘ 4—. q' Rat Ra Ram q" =soo°c Tm = 25°C qu h.= ~30 wtmz-K ho = 10 thLK ASSUMPTIONS: {I} Steady-state conditions, (2) One-dimensional conduction in wall. {3) Thermal resistance of metal sheets negligible,(4) Negligible contact resistance. ANALYSIS: (a) The thermal circuit is showu above. Note labels for the temperatures. thennal resistances and the relevant heat ﬂuxes. {b} Perform energy balances on the i~ and o nodes ﬁnding T —Ti 1‘ T 3‘1—'+-9,—i+q¥ad=0 (1) R cd cv,i Ti ‘To + Twp ‘To » .. = 0 (2) cd Rcv,o where the thermal resistances are R§v1i=lfhi=0.0333 mz-wa (3) gd=uk=uuos mz-Krw (4) R3V10=Hh0=0100 mszz‘W (5) Substituting numerical values, and solving Eqs. (1 ) and {2} simultaneously, ﬁnd L286 mm ‘4 COMMENTS: (I) The temperature at the inner surface can be found from an energy balance on the i-node using the value found for L. MJF M4. = 0 T- : 293 3°C Evan Red + Rcv.i I It follows that T.- is close to Tacj since the wall represents the dominant resistance ofthe system. {2) Verify that ql: = 50 W fm2 and q; = —150 W fmz. ls the overall energy balance on the system satisﬁed? ...
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