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An electrical current of 700 A flows through a stainlesssteel cable having a diameter of 5 mm and an electricalresistance of 6104/m (i.e., per meter of cablelength). The cable is in an environment having a tem-perature of 30C, and the total coefficient associatedwith convection and radiation between the cable andthe environment is approximately 25 W/m2K.(a) If the cable is bare, what is its surface temperature

Respuesta :

ogorwyne

Answer:

778.4°C

Explanation:

I = 700

R = 6x10⁻⁴

we first calculate the rate of heat that is being transferred by the current

q = I²R

q = 700²(6x10⁻⁴)

= 490000x0.0006

= 294 W/M

we calculate the surface temperature

Ts = T∞ + [tex]\frac{q}{h\pi Di}[/tex]

Ts = [tex]30+\frac{294}{25*\frac{22}{7}*\frac{5}{1000} }[/tex]

[tex]Ts=30+\frac{294}{0.3928} \\[/tex]

[tex]Ts =30+748.4\\Ts = 778.4[/tex]

The surface temperature is therefore 778.4°C if the cable is bare

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