A long 1-cm-diameter electric cable is imbedded in a concrete wall (k = 0.13 W/(m K)) which is 1 m*1 m, as shown in the sketch. If the lower surface is insulated, the surface of the cable is 100°C and the exposed surface of the concrete is 25°C, estimate the rate of energy dissipation per meter of cable.
GIVEN
A long electric cable imbedded in a concrete wall with cable diameter (D) = 1 cm = 0.01 m
Thermal conductivity of the wall (k) = 0.13 W/(m K)
Wall dimensions are 1 m by 1 m, as shown in the sketch below
The lower surface is insulated
The surface temperature of the cable (Ts) = 100°C
The temperature of the exposed concrete surfaces (To) = 25°C
FIND
The rate of energy dissipation per meter of cable (q/L)
ASSUMPTIONS
The system is in steady state
The thermal conductivity of the wall is uniform
Two dimensional heat transfer
SKETCH
By symmetry, only half of the flux plot needs to be drawn
The number of heat flow lanes (M) = 2 ? 14 = 28
The number of curvilinear squares per lane (N) = 6
Therefore, the shape factor is
For steady state, the rate of energy dissipation per unit length in the cable must equal the rate of heat transfer per unit length from the cable which, from is
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