Question

1. A copper pin fin 2.5 mm in diameter protrudes from a wall at 100°C into air at 28°C. ( k=396 W/m-K.) The heat transfer is mainly by natural convection with a heat transfer coefficient of 12 W/m²×K. Calculate heat losses from the fin assuming the fin is infinitely long. If there is an array of 10 copper pin fins, how much power do they dissipate?

Answer 1

Given - ds 2.5mm 0.0025m fin is infinitely long, so the temp haiwank of tip of fin will be essentially that Too-28°c of the ambient fluid i At x=0 P= Too and ozo 100°C ke 396 W/mk o=P-To cłatło 20 For any fin case heat transfer rate through entire fin equal to heat conducted into the fin at it root: qoxa-ken en om co watt ---(1) We know that - P- To sem Oo - Toato e т-Та геmx (16 -) By differentiating the equation, we get on the = (-me-me (-Doo) —-(2) Putting the value of (2) in (1) qefin 2 -KA (-me muco-To al reco s hpkA (Coro) ha la W/m2K pa perimeter = TX0.0025 = 7.85X10-3m K = 396 W/mK A z profile area= X0.00252,4.91x100m2 Pos 100°c Pro = 28°C Pfin 2 ]12x7.85103*396x4.91x10-6 x(100-28) = 0.974 Watt Heat loss from an arrasp of 10 fine - 0.974X10 a 9.74 Watt Ans.