A stainless steel pin fin 5-cm-long, 6-mm-OD, extends from a flat plate into a 175 m/s air stream as shown in the sketch. Estimate (a) the average heat transfer coefficient between air and the fin. (b) the temperature at the end of the fin. (c) the rate of heat flow from the fin.

Question

GIVEN

• A stainless steel pin fin in an air stream

• Pin length (L) = 5 cm = 0.05 m

• Pin diameter (D) = 6 mm = 0.006 m

• Air velocity (U?) = 175 m/s FIND

(a) The average heat transfer coefficient ( h c) (b) The temperature of the end of the fin (TL) (c) The rate of heat flow from the fin (qf)

ASSUMPTIONS

• Steady state

• Air approaching the fin has negligible turbulence

• Radiative heat transfer is negligible

• Steel is type 304

• Steel properties are uniform

PROPERTIES AND CONSTANTS

Thermal conductivity (k) = 0.0202 W/(m K) Kinematic viscosity (?) = 9.3 × 10–6 m2/s Prandtl number (Pr) = 0.71 From Appendix 2, Table 10, for Type 304 stainless steel ks = 14.4 W/(m K) at 20°C (Note that figure 1.6 shows very little increase in k for stainless steel in the range of 300°C to 700°C.)

Answer 1

(a) The Reynolds number is



Therefore, may be used. (Note that Pr/Prs = 1)





(b) for a fin of uniform cross-section with convection at the tip, the temperature

distribution is



The tip temperature is practically the same as the ambient temperature.

(c) The rate of heat transfer is.



COMMENTS

These results should be considered an estimate due to uncertainty in the air properties.

Also, due to the presence of the surface from which the fin protrudes, the flow is not uniform as

assumed by Equation (6.3), therefore, the heat transfer coefficient may vary.