Question

A cylinder of a motorcycle made of alluminum alloy with k=186W/mk hasa length of 0.15m and outside diameter D=50mm. Under typical operating condition the outer surface of the cylinder is at 500K and is exposed to air at 300K, with h=50W/m^2.k. Five annular fins cast with the cylinder increases the cooling of the cylinder. Fins are of thickness of 6mm, and length of 20mm. Determine percent increase of the cooling of the cylinder due to fins.

* The answer is between 200-300%

Answer 1

Area of fins Af = 2r_2c²  - 2r₁²

= 2*3.14*0.048*0.048 - 2*3.14*0.025*0.025

= 0.01050 m2

Total finned surface area A = NAf + Ab

A = NAf + ( 2r₁H - 2r₁N_t )

= 0.05270 + (2*3.14*0.0250*0.15 - 2*3.14*0.0250*0.030)

= 0.07160 m2

r2c/r1 = 1.92

Lc = 0.023 m

Ap = 1.380 * 10^-4 m2

Lc^1.5 (h/kAp)^0.5 = 0.15 (ref - yunus cengel - 10.43)

Efficiency of the fin = 0.95

Heat transfer rate due to fins

Q = hA [1 - (NAf/A) (1-nf)] T

= (50*0.0760) [1 - (0.0527/0.0716) * 0.05] * 200

= 690.0 W

Heat transfer rate without fins

Q2 = hAT

= h*(2*3.14*r1*H)*T

= 50*(2*3.14*0.0250*0.150)*200

= 236.0 W

Change in heat transfer rate

= 690.0 - 236.0 = 454.0 W

percent increase of the cooling of the cylinder due to fins

= 454*100/236

= 192%