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Heat is uniformly generated at the rate of 4 x 105 W/m3 in a wall of thermal conductivity 25 W/m-K and thickness 60 mm. The wall is exposed to convection on both sides, with different heat transfer coefficients and temperatures as shown. There are straight rectangular fins on the right-hand side of the wall, with dimensions as shown (Lf = 16.25 mm) and thermal conductivity of 250 W/m-K. What is the maximum temperature that will occur in the wall? L t- 2 mm k = 25 W/m-K h=50 W/m2-K T 30°C h2= 12 W/m2-K T 2=15°C 8=2 mm 2L=60 mm k, 250 W/m-K Physical Properties Mathematical Functions Step 1 Your answer is correct Determine the value of fin efficiency 0.994 Attempts: 1 of 3 used Step 2 Your answer is incorrect Determine the fin area (neglecting the tip area) per unit depth, in m2/m. !m2/m Af = Attempts: 2 of 3 used Check Answer Save for Later Step 3 Your answer is incorrect. Determine the value of surface efficiency. n,=i ! Attempts: 1 of 3 used Save for Later Check Answer Step 4 Determine the temperature at the base of the fins, in °C. T2 = i °C Attempts: 0 of 3 used Save for Later Check Answer Step 5 Determine the maximum temperature in the wall, in °C. Tmax = °C eTextbook and Media Attempts: 0 of 3 used Check Answer Save for Later

Answer 1

The temp. disi botion in ganeration a way with unitarm Volume ic heat 2 Ts,2 Tex) ISI+TS,2 -1 2K 2 2. s-KANT dox L aLA-KAT,2- Ts, LL) 2 L s,2 = -KA dT aLA- lCA To,a-Ts (3) 2L 1sna hiA TT, ,) ,hAT2-T)9. Ts,= 2L Kh hA + 2 L 2 L Ts,2= K hiTI 2L 2L h,h ha 2L 2 L where A AtMo A NA (-) At A Re torming .the Calculations 2 R VTt 6.9m ma 14 Ac 2 SOx o.002 tanh( 6.1x o-o1625) tanh(m Lt) m2t 6-9O01615 2 Lt N2 wlt ( 8+ €JN. 2 x o o16 25 NA Su1.8 O.oo4 0 002 = 8.125 t S+t S Nw CSt4)NW A NA A At NA+ A A 8-415 3.615 8 125 (1- 0.9as)=8.58y A = h A 12 - 8-Sy = 1 0 3-0125 W/m2k 25 Lu/Mtin = 2L 90.으

t03-015 +47 x m xIS+ TsI 412 +103.0125)x50x 30 (2 X413 + 1D 3.0125) x 4 X1 x o. 03 414 x 10 3 O125 SOXIO3.O125 41730 193.41 C ( 2 x417 +so) X4x(OX0.03 (417 + So) x103.01LY x s + 417 x Sox30 +41x 103 01 L 50 x (03.01 15 417x SO eudient ot emp in eq. ) The Leration of max. Ts2-Ts, Xnan TCr-Te,) > 2 L 20P TS.,T,) 2 CT,2-TS.) Tmon 2 K 2 2 25 x(183-91-1939) 8 x lo-03)x 41 (183-91+ 13.3a) (0.03) 4x 10 X 2 x 25 0-928 + 118.94 7.2t - 186.668 C