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Heat transfer through cable

Heat transfer through cable

Heat transfer through cable

(OP)
Hello, I've received a task, and couldn't find the right way to solve the problem.
The question is taken from Heat Transfer 10th edition by JP Holman :
4-141
The 4.0-mm-diameter stainless-steel wire shown in Figure P4-141 is initially at
20◦C and is exposed to a convection environment at 20◦C where h may be taken
as 200 W/m2 · ◦C. An electric current is applied to the wire such that there is
a uniform internal heat generation of 500 MW/m3. The left side of the wire is
insulated as shown. Set up the nodal equations and stability requirement for calculating the temperature in the wire as a function of time, using increments of
r=0.5 mm and φ=π/4.Take the properties of stainless steel as k = 16 W/m · ◦C,
ρ = 7800 kg/m3, and c = 0.46 kJ/kg · ◦C.

Appreciate any kind of help.

RE: Heat transfer through cable

Is this school homework?
It looks like it...

RE: Heat transfer through cable

a 4.0mm cable is very small and even though half of the wire is insulated, my initial approach would be to assume (rightly or wrongly) that the internal temperature at any point in time is uniform throughout the cross section of the wire. I would not bother figuring out the nodal equations throughout the cross section and on the surface area of the wire having a diameter of 4mm.

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