Question

W kg m-K m3 Two-Dimensional Steady and transient Conduction - Heat Sink Aluminum fins with triangle profiles (k = 290 p = 2800 ,C= 900 shown in the accompanying figure, are used to remove heat from a surface kg-K whose temperature is T, = 150°C. The temperature of the surrounding air is 20°C. The natural heat transfer coefficient associated with the surrounding air is h = 190, Determine the temperature distribution along a fin. w m-K Air To, h 20 mm 1 5 150°C 90 mm w m-K 2800 kg m3 kg-K A) Aluminum Heat sinks of rectangular profile (k = 290 ,p= C = 870 are commonly used to remove heat from a surface whose temperature is Ts 150°C. The temperature of the surrounding air is 20°C. The natural heat transfer coefficient associated with the surrounding air is h = 168 Determine the temperature distribution along a fin. = W m-K

Answer 1

I 320. mole P = 2800 rs - - 3 TS = 150c, c-900 I rs-k h = - 190 W Too -200 Qund A { Si Gomm 90 mm -L XL no Gencual differential eqn: Acous damn ] dr. ] - hercare (T-T) = 0 The fin profile can be descobed as 9(W) = (^) PER) e 2 (H+w) 66 2 [29() +w] = 2 Szt (1) + w] 2w AC) = HW = 56.C) 00 1 - T-TO a la (Aca) do hP(A) 020 K 86 an H H=240 d da ( do) 2wh O20 Sb wa L dn L 2hL 020 ndo dn dh I am condo) B.C: 1) 220 2) dot, kob m2 LB m² = 2h kob finite o=finite T=Ts =) O - Os 0.C with bessel's cas compare

treneralized Bessel og d + Can it bak).s=0 b-0, jo, din am 2-P+] BI-P 2 P-1 1 √(-p)2 4b o 2-pt i Pla [ c, In (on't) at Cz kn (wn' 2014 Fo (2M VEX) + Cz ko (2m ron] c. Io (2m rat ko (amin) pl wiring Bc0) finite = c. Io (0) + Coko (0) But i ko (0) - od Now o=c, To (2m ra) Using B.C CI) Os = c, Io (2mL) =) G- Temperature profile : 100s Io (amin) Io (2mL) values : L=0.09m Os = TS-TOO - es Io (2mL) 150 - 20 Boc m = B2h kob 2x190 320 x 0,04 - 5.4486 130 Io (2X5.4486 0.09x) Io (2x5,4486X0.09) 0 = 130 T. ( 8.26952) I. (0.98)