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Zina [86]
3 years ago
15

A long homogeneous resistance wire of radius ro = 5 mm is being used to heat the air in a room by the passage of electric curren

t. Heat is generated in the wire uniformly at a rate of g=5'107 W/m as a result of resistance heating. If the temperature of the outer surface of the wire remains at 180°C, determine the temperature at r = 2 mm after steady operation conditions are reached. Take the thermal conductivity of the wire to be k = 8 W/m x °C.
Engineering
1 answer:
VARVARA [1.3K]3 years ago
6 0

Answer:

T = 212.8125°C

Explanation:

Given

radius of the wire, r_{0} = 5 mm 0.005 m

heat generated, g = 5 x 10^{7} W/m^{3}

outer surface temperature, T_{S} = 180°C

Thermal conductivity, k = 8 W / m-k

Now maximum temperature occurs at the center of the wire

that is at r=0,

Therefore, T_{o}=T_{S}+\frac{g\times r_{o}^{2}}{4\times k}

                  T_{o}=180+\frac{5\times 10^{7}\times 0.005^{2}}{4\times 8}

                 T_{o}=219.0625°C

Therefore, temperature at r = 2 mm

\frac{T-T_{S}}{T_{O}-T_{S}}= 1-\left (\frac{r}{r_{O}}  \right )^{2}

\frac{T-180}{219.0625-180}= 1-\left (\frac{2}{5}  \right )^{2}

Therefore, T = 212.8125°C

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