A long 1-cm-diameter electric copper cable is embedded in the center of a 25 cm square concrete block. If the outside temperature of the concrete is 25°C and the rate of electrical energy dissipation in the cable is 150 W per meter length, determine the temperatures at the outer surface and at the center of the cable.
GIVEN
FIND
The temperatures at the outer surface (Ts) and at the center of the cable (Tc)
ASSUMPTIONS
Two dimensional, steady state heat transfer
Uniform thermal conductivities
SKETCH
For steady state, the rate of heat transfer through the concrete block must equal the rate of electrical energy
dissipation. The heat transfer rate can be estimated with a flux plot of one quarter of the block:
The number of flow lanes (M) = 4 ? 6 = 24
The number of squares per lane (N) = 10
Therefore, the shape factor is
The rate of heat flow per unit length is given is
Solving for the surface temperature of the cable
From the temperature in the center of the cable is
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