Question

Circular pipe of 23.9 mm OD and 1.5 mm wall thickness and length 90 mm is used as a fin on a wall at 200°C. The outside is exposed to air at 35°C with a convection coefficient of 15 W/m2K. The conductivity of the material is 45 W/mK. Determine the heat loss from the fin and also the mid section and tip temperature.

Answer 1

iten data For circular fin D: 23.9 mm inside . 23.9 - 2 1 .5 - thickness = 1.5mm AC = (do-d}-] = I [23.9*-20.9?] = 105.5 mm2 pe lidl = T14 23.976?10.04: 6.75 vjóm (perimeter) = 90 mm m= he To = 200°c Too = 35°c Isy 6.75 x 103 h = is v 45x105.5X10 K = 45 me 4.61 ml:4.61 Yoq = 0.41 mics hence it is a finite length of Fin a co (heat loss) = I ka mga tanhmi finite fin 245 x 105.5TD 4.6x16 5 tonn (0.41) 0 = 1.4025 Watt To-To 200-3 = 165 - equation for finite Temperature distribution length of Gin is T-Too To- Ton : cosh(ml-mal (oshmi at = 45 mm i.e.mid section T-35 Cosh (4.6160.09-0.0451] 200-35 . cash (4.6149.04) T-35 - 1.021 1.287 1 = 189.93°c at mid section 200-35

Tip temp. Ti-Tool To - Too coshme Ti - 35 F 299 - 35 losh (4.61X0.09) TL = 186.75°C]