Question

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

Answer 1

778.4°C

Step-by-step 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∞ +
`(q)/(h\pi Di)`

Ts =
`30+(294)/(25*(22)/(7)*(5)/(1000) )`

`Ts=30+(294)/(0.3928) \\`

`Ts =30+748.4\\Ts = 778.4`

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