Consider design B of 3.151. Over time, dust can collect in

Chapter , Problem 3.152

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QUESTION:

Consider design B of Problem 3.151. Over time, dust can collect in the fine grooves that separate the fins. Consider the buildup of a dust layer of thickness \(L_{d}\), as shown in the sketch. Calculate and plot the total heat rate for design B for dust layers in the range \(0 \leq L_{d} \leq 5 \mathrm{~mm}\). The thermal conductivity of the dust can be taken as \(k_{d}=0.032 \mathrm{~W} / \mathrm{m} \cdot \mathrm{K}\). Include the effects of convection from the fin tip.

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QUESTION:

Consider design B of Problem 3.151. Over time, dust can collect in the fine grooves that separate the fins. Consider the buildup of a dust layer of thickness \(L_{d}\), as shown in the sketch. Calculate and plot the total heat rate for design B for dust layers in the range \(0 \leq L_{d} \leq 5 \mathrm{~mm}\). The thermal conductivity of the dust can be taken as \(k_{d}=0.032 \mathrm{~W} / \mathrm{m} \cdot \mathrm{K}\). Include the effects of convection from the fin tip.

ANSWER:

Step 1 of 3

Given data:

The differential element equation as,

\(y_2^2 = 2x\)

\({y_2} = \sqrt {2x}\)

The differential element equation as,

\({y_1} = x\)

Consider the diagram shown below.

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