An electric wire, 2 m long (2L) and 1 mm in radius (r), has its length...

 

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An electric wire, 2 m long (2L) and 1 mm in radius (r), has its length insulated against flow of heat and current. The two ends of the wire and its middle are connected to two separate power sources so that a current I: (= 0.2 amp) flows through one-part (left half of the wire) and a current I2 (= 0.15 amp) flows through the other (right half of the wire). The ends of the wire are maintained at Ta = 30 C, which is the ambient temperature. The electrical resistance of the material (p) of the wire is 1.5 ohm/m and its thermal conductivity (k) is 100 W/m/C. The wire temperature is uniform over its cross section. Determine (a) The temperature distribution, T(x) and T2(x), in the wire at steady state in terms of , B, L and Ta, where =-1/(2k) and =-12/(2k). T1, 11 and T2, 12 are the local temperature and volumetric rate of heat generation in the left and right half of the wire respectively. (b) The temperature at the middle of the wire, (c) The location and value of the maximum temperature in the wire. Insulated electric wire with different current flow in two halves. Insulation T. I Wire 12 -Ta Insulation L-1 m 2L=2m x An electric wire, 2 m long (2L) and 1 mm in radius (r), has its length insulated against flow of heat and current. The two ends of the wire and its middle are connected to two separate power sources so that a current I: (= 0.2 amp) flows through one-part (left half of the wire) and a current I2 (= 0.15 amp) flows through the other (right half of the wire). The ends of the wire are maintained at Ta = 30 C, which is the ambient temperature. The electrical resistance of the material (p) of the wire is 1.5 ohm/m and its thermal conductivity (k) is 100 W/m/C. The wire temperature is uniform over its cross section. Determine (a) The temperature distribution, T(x) and T2(x), in the wire at steady state in terms of , B, L and Ta, where =-1/(2k) and =-12/(2k). T1, 11 and T2, 12 are the local temperature and volumetric rate of heat generation in the left and right half of the wire respectively. (b) The temperature at the middle of the wire, (c) The location and value of the maximum temperature in the wire. Insulated electric wire with different current flow in two halves. Insulation T. I Wire 12 -Ta Insulation L-1 m 2L=2m x