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 with glycerol at 20°C flowing over the fin at 2 m/s. The plate temperature is 50°C.
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
• Glycerol velocity (U?) = 2 m/s
• Glycerol temperature (T?) = 20°C
• Plate temperature (Tp) = 50°C 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
• Turbulence in the glycerol approaching the fin is low
• Radiative heat transfer is negligible
• Steel is type 304
• Steel properties are uniform
• Variation of the thermal properties of glycerol and steel with temperature is negligible
PROPERTIES AND CONSTANTS
Thermal conductivity (k) = 0.285 W/(m K) Kinematic viscosity (?) = 1175 × 10–6 m2/s Prandtl number (Pr) = 12,609 for type 304 stainless steel ks = 14.4 W/(m K) at 20°C
(a) The Reynolds number is
Therefore, Equation may be used. (Note that Pr/Prs = 1)
(b)
Therefore, the tip temperature is practically the same as the ambient glycerol temperature.
(c) The rate of heat transfer,
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