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Luden [163]
3 years ago
8

The heat flux through a 1-mm thick layer of skin is 1.05 x 104 W/m2. The temperature at the inside surface is 37°C and the tempe

rature at the outside surface is 30°C.a. What is the thermal conductivity of the skin?b. A layer of clothing material with half the thermal conductivity of skin and twice the thickness of skin is placed on the outside surface of the skin. If the outside surface of the clothing is maintained at 30°C, what is the new heat flux from the skin and what is the temperature at the skin-insulation interface?
Engineering
1 answer:
miss Akunina [59]3 years ago
3 0

Answer:

a) Thermal conductivity of skin: k_{skin}=1.5W/mK

b) Temperature of interface: T_{interface}=35.6\°C

Heat flux through skin: \frac{Q}{A}=2100W/m^2

Explanation:

a)

k=\frac{QL}{A(T_{2}-T_{1})}

Where: k is thermal conductivity of a material, \frac{Q}{A} is heat flux through a material, L is the thickness of the material, T_{1} is the temperature on the first side and T_{2} is the temperature on the second side

k_{skin}=\frac{QL}{A(T_{2}-T_{1})}

k_{skin}=\frac{Q}{A}*\frac{L}{(T_{2}-T_{1})}

k_{skin}=1.05*10^{4}*\frac{1*10^{-3}}{(37-30)}

k_{skin}=1.5W/mK

b)

k_{insulation}=\frac{k_{skin}}{2}

k_{insulation}=\frac{1.5}{2}

k_{insulation}=0.75W/mK

The heat flux between both surfaces is constant, assuming the temperature is maintained at each surface.

\frac{Q}{A}=\frac{k(T_{2}-T_{1})}{L}

\frac{k_{skin}(T_{skin}-T_{interface})}{L_{skin}}=\frac{k_{insulation}(T_{interface}-T_{insulation})}{L_{insulation}}

\frac{1.5*(37-T_{interface})}{0.001}=\frac{0.75*(T_{interface}-30)}{0.002}

55500-1500T_{interface}=375T_{interface}-11250

1875T_{interface}=66750

T_{interface}=35.6\°C

\frac{Q}{A}=\frac{k_{skin}(T_{skin}-T_{interface})}{L_{skin}}

\frac{Q}{A}=\frac{1.5*(37-35.6)}{0.001}

\frac{Q}{A}=2100W/m^2

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2. A well of 0.1 m radius is installed in the aquifer of the preceding exercise and is pumped at a rate averaging 80 liter/min.
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Question:

The question is not complete. See the complete question and the answer below.

A well that pumps at a constant rate of 0.5m3/s fully penetrates a confined aquifer of 34 m thickness. After a long period of pumping, near steady state conditions, the measured drawdowns at two observation wells 50m and 100m from the pumping well are 0.9 and 0.4 m respectively. (a) Calculate the hydraulic conductivity and transmissivity of the aquifer (b) estimate the radius of influence of the pumping well, and (c) calculate the expected drawdown in the pumping well if the radius of the well is 0.4m.

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