09 Nov '15 21:251 edit

I'm trying to bring a Steel wire in a plating line that has a diameter "D", and line velocity "v", through a temp differential "δT" over a distance "L"

Assuming Lumped capacitance ( neglecting temperature gradients in the wire), and heat transferred through the differential surface is predominantly accomplished via radiation with some heat transferred by way of convection, I apply a power balance to a differential element of wire and the relationship follows:

µ*Ac*v*c*dT = σ*ε*dAs*(Ts^4-T^4) + h*dAs*(Ts - T)

dT = 1/(µ*π*D^2/4*v*c)*(σ*ε*(Ts^4-T^4) + h*dAs*(Ts - T))π*D*dl

dT = 4/(µ*π*D*v*c)*(σ*ε*(Ts^4-T^4) + h*dAs*(Ts - T))*dl

The above can be numerically integrated to find T(l) (Temp as a function of position)

The question I have is how much power does it take to accomplish this for a wire at a distance "y" from the radiation source. I know the solution involves view factor, which is inversely proportional to y², but I'm pretty confused on how to apply it. Any help in clearing these ideas up would be appreciated.

Intuitively, the closer the wire is to the radiation source the less power I need to bring it through the temp change. Is the above relation a minimum if the wire were virtually touching the radiation source?

Assuming Lumped capacitance ( neglecting temperature gradients in the wire), and heat transferred through the differential surface is predominantly accomplished via radiation with some heat transferred by way of convection, I apply a power balance to a differential element of wire and the relationship follows:

µ*Ac*v*c*dT = σ*ε*dAs*(Ts^4-T^4) + h*dAs*(Ts - T)

dT = 1/(µ*π*D^2/4*v*c)*(σ*ε*(Ts^4-T^4) + h*dAs*(Ts - T))π*D*dl

dT = 4/(µ*π*D*v*c)*(σ*ε*(Ts^4-T^4) + h*dAs*(Ts - T))*dl

The above can be numerically integrated to find T(l) (Temp as a function of position)

The question I have is how much power does it take to accomplish this for a wire at a distance "y" from the radiation source. I know the solution involves view factor, which is inversely proportional to y², but I'm pretty confused on how to apply it. Any help in clearing these ideas up would be appreciated.

Intuitively, the closer the wire is to the radiation source the less power I need to bring it through the temp change. Is the above relation a minimum if the wire were virtually touching the radiation source?