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The student is shown two radio choices: \"Yes\" and \"No\". One of them is correct.

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To cool a summer home, air is routed through a plastic pipe (k = $\\var{k}$ W/mK, Di = $\\var{Di}$ m, Do = $\\var{Do}$ m) that is submerged in a body of water. The water temperature is nominally at T = 17°C, and a convection coefficient of ho = $\\var{ho}$ W/m2K is maintained at the outer surface of the pipe. If air from the home enters the pipe at a temperature of Tm,i = 29°C and a mass flow rate of $\\var{m}$ kg/s, what pipe length L is needed to provide a discharge temperature of Tm,o = 21°C?

\n

\n

Let’s work through this assignment in parts:

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What mode of heat transfer is present between the air pipe outer surface and water?

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Conduction

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Do we have the convection coefficient between the air pipe outer surface and water?

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What mechanism of convection heat transfer is present between the air pipe inner surface and the air?

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Free convection

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Forced external flow convection

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Do we have the convection coefficient between the air pipe inner surface and the air?

\n
\n
\n
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What mechanism of heat transfer is present between the air pipe outer surface and its inner surface?

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Free convection

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Forced external flow convection

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Do we have a uniform surface temperature or a uniform surface heat flux condition on the inner surface of the pipe?

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Do we have a uniform surface temperature or a uniform surface heat flux condition on the outer surface of the pipe?

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\n
\n
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If we were to use a U value between the air in the pipe and the water outside of it, what would it include? (select all that applies)

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R conduction in the water

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R radiation in the inner surface of the pipe

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R radiation in the outer surface of the pipe

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Calculate the thermal resistance, R’, between the air pipe outer surface and its inner surface.

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Hint: You would need pipe conductivity, inner diameter and outer diameter.

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Calculate the thermal resistance, R’, between the air pipe outer surface and water.

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We need air flow properties. At what temperature, do we look up values? Provide your answer in K.

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What is the air specific heat that we use in our calculations? (only add the number, but not the unit in J/kg.K)

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The air absolute viscosity that we use in our calculations is ???.? x 10-7 N.s/m2

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What is the air conductivity that we use in our calculations? (only input the number without unit. In three significant figures, for example as 0.0111, in W/mK)

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What is the air Pr that we use in our calculations? (add the number in three significant figures.)

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Calculate the Reynolds number for the air flow.

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What type of flow do we have in the pipe?

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Assuming a fully developed flow throughout the pipe, what is the Nu number for the air flow?

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Calculate the convection coefficient between the air flow and the pipe inner surface.

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Calculate the thermal resistance, R’, between the air flow and the pipe inner surface.

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We know UAs = 1 / R and R’ = R/L. Use this to calculate UAs/L and enter it below (provide the number only, with three decimal figures, in W/K):

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What pipe length L is needed to provide a discharge temperature of Tm,o = 21°C?

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Hint: Find the relation between UAs , the water temperature, the inlet air temperature and the outlet air temperature. Use what you have found in previous parts to find L. (provide the number only, with one digit, in m)

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