Chapter 15 Steady Heat Conduction3-110 Circular aluminum fins are to be attached to the tubes of a heating system. The increase in heat transfer from the tubes per unit length as a result of adding fins is to be determined. Assumptions1Steady operating conditions exist.2 The heat transfer coefficient is constant and uniform over the entire fin surfaces. 3 Thermal conductivity is constant. 4 Heat transfer by radiation is negligible. PropertiesThe thermal conductivity of the fins is given to be k= 186 W/m⋅°C.Analysis In case of no fins, heat transfer from the tube per meter of its length is 180°C 25°C ADLQhATTbno fin2no finno fin22m mmW / mCmCW====−=°−°=∞ππ10 051015714001571180 25974(.)().&()(.)(.)()The efficiency of these circular fins is, from the efficiency curve, 97.008.0m)C)(0.001W/m186(CW/m402001.0005.0222.10.025)2/001.0(03.0)2/(m005.02/)05.006.0(2/)(finoo21212=η⎪⎪⎪⎪⎭⎪⎪⎪⎪⎬⎫=⎟⎠⎞⎜⎝⎛+=⎟⎠⎞⎜⎝⎛+=+=+=−=−=kthtLrtrDDLHeat transfer from a single fin is W53.11C)25180)(m001916.0)(C.W/m40(97.0)(m001916.
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