manufacturer plans to use steel wire (ks = 25 Wm-1 K-1 ) in a household appliance. For safety considerations, we would like an estimate of the smallest electric current that is required to melt the wire. The bare wire is exposed to 20°C air with convective heat transfer coefficient of 15 Wm-2 K-1 and has diameter of 2.0 mm and electrical resistance of 0.20 W/m (i.e., per meter of wire). Thermal energy is produced within the wire at the rate I2 Re , where I is the electrical current through the wire and Re is the wire’s electrical resistance. I = 0.643 Solve the microscopic energy balance in the steel wire with a prescribed temperature Ts at the wire surface, as well as the requirement that temperature be finite at the center of the wire, to find an expression for the temperature at the center of the wire in terms of the surface temperature Ts . Use your result to estimate the electric current at which the wire begins to melt.
manufacturer plans to use steel wire (ks = 25 Wm-1 K-1 ) in a household appliance. For safety
considerations, we would like an estimate of the smallest electric current that is required to melt the wire.
The bare wire is exposed to 20°C air with convective heat transfer coefficient of 15 Wm-2 K-1 and has
diameter of 2.0 mm and electrical resistance of 0.20 W/m (i.e., per meter of wire). Thermal energy is
produced within the wire at the rate I2 Re , where I is the electrical current through the wire and Re is the
wire’s electrical resistance. I = 0.643
Solve the microscopic energy balance in the steel wire with a prescribed temperature Ts at the wire
surface, as well as the requirement that temperature be finite at the center of the wire, to find an
expression for the temperature at the center of the wire in terms of the surface temperature Ts . Use your
result to estimate the electric current at which the wire begins to melt.
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