Answer to Question #183120 in Mechanical Engineering for luke

Question #183120

A 2mm diameter electrical wire is insulated by a 2mm thick rubberized sheath (k=0.13W/m-K). The convection heat transfer coefficient at the outer surface of the sheath is 10W/m2-K and the temperature of the ambient air is 20C. What is the critical diameter of the insulation? (meters)


1
Expert's answer
2021-04-22T07:24:36-0400

Diameter of wire is 2 mm= "2\\times 10^{-3}"

Thermal heat conduction = k=0.13W/m-K,

thickness of sheath= t= "2\\times 10^{-3}" m, Ambient temperature= "T_a" = "20^o C"

insulation= 50"^o C"

Now net thermal resistance,

"R=\\frac{ln \\frac{r+t}{r}}{2 \\times \\pi k} + \\frac{1}{2 \\pi rh}"


"R=\\frac{ln \\frac{1+2}{1}}{2 \\times \\pi k} + \\frac{1}{2 \\pi 1\\times 10}"


R= 6.650 m2K/W

Maximum allowable power per unit length

Q'="\\frac{T_{in}- T_{\\infty}}{6.650}=\\frac{50-20}{6.65}= 4.511 \\frac{W}{m}"


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