Question

Find the efficiency and heat flux per unit of width in W / m coming out of the following triangular fin:

t = 2mm = 6mm To = 250 °C w = Fin width Air To= 20 °C h = 40 W/m2.K w=Largeur de l'ailette K = 240W/m.K

Answer 1

Using the triangular fin analysis results we can solve this problem as below-
sol: The data provided in the question are as below- 250'0 fin Fin base temperature , To environment temperature, Too = 20'C. convective heat transfer co-efficient , h = 40 W/m²k. Fin thickness,t = 2 mm = (2x1013) mi Length ,L=6 mm = (68 10-3 m. Thermal conductivity of fin material, k = 240 W/mk We have to find out a) fin efficiency: b) heat flux per unit width > Assuming negligible radiation heat transter from the fin Steady state operations - fin efficiency : I, ( 2PVC) Pre I. (2PJI) where , P is the fin parameter and 2hfL and a ) n and given by p= kt f f = It ( 4 ) ? I + c 2x10-3 2 x 6*10-3 2-3)? 1.0138 3 -P= :- 2X 40 X1-0138 X 6x10 240 X 2X 10-3 = 1-00688 .. n = 1.00688 voxio I, ( 2x 1.00688 x 56x10-3 Io (2X1-00688 6X 103

1.00688 √ 6810 3 I, (0.1559852) Io (0.1559852) 1:00 688 x10.006 0.07823 1.00 6092) Besser Function of first kind calculation- I, (0.1559852) 99:697y. a). O. 07823 Io C011559852) 1:0060921 - -6 = Heat flux per unit width of the fin, Pkt ( To-Too) I, (2PVC) IL T. (2010) 1.00688x 240x2x10x (250–20) x I, (0.1559852) 6X10-3 = Io (0.1559852) ir 1435.063646 X 0.07-823 1006092) 111.585 Wind Ans (6) =