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Published bySydney Perkins Modified over 4 years ago

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Example 1:- An annular alloyed aluminum (k = 180 W/m . K ) fin of rectangular profile is attached to the outer surface of a circular tube having an outside diameter of 25 mm and a surface temperature of 250 oC. The fin is 1 mm thick and 10 mm long, and the temperature and the convection coefficient associated with the adjoining fluid are 25 oC and 25 W/m2 .K, respectively. (a) What is the heat rate per fin? (b) If 200 such fins are spaced at 5-mm increments along the tube length, what is the heat rate per meter of tube length?

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Example 2 ) The end of a rectangular bar surrounded by insulation is maintained at 100 oC and is exposed to ambient air as shown in the schematic. A linear array of pin fins (N =10) is affixed to the end surface to enhance the heat transfer rate from the bar. The pin fins (k = 65 W/m . K) are 3 mm in diameter and 12 mm long. The ambient air temperature is 25 oC, and the convection coefficient over the bar end surface and pin fins is equal to 10 W/m2 . K.

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Example 3) Compare the temperature distributions in a straight cylindrical rod having a diameter of 2 cm and a length of 10 cm and exposed to a convection environment with h=25 W/m2 ・ ◦C, for three fin materials: copper [k =385 W/m・ ◦C], stainless steel [k =17 W/m・ ◦C], and glass [k =0.8 W/m・ ◦C]. Also compare the relative heat flows and fin efficiencies.

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These values may be inserted into Equation of temperature distribution to calculate the temperatures at different x locations along the rod, and the results are shown in Figure Example 2-8. We notice that the glass behaves as a “very long” fin, and its behavior could be calculated. The fin efficiencies are calculated from Equation by using the corrected length approximation of Equation of corrected length given. We have

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**The parameters of interest for the heat-flow and efficiency comparisons are now tabulated as**

To compare the heat flows we could either calculate the values from Equations for a unit value of θ0 or observe that the fin efficiency gives a relative heat-flow comparison because the maximum heat transfer is the same for all three cases; i.e., we are dealing with the same fin size, shape, and value of h. We thus calculate the values of ηf from Equation and the above values of mLc.

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The temperature profiles in the accompanying figure can be somewhat misleading. The glass has the steepest temperature gradient at the base, but its much lower value of k produces a lower heat-transfer rate.

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