# Modeling a simple heating element

1. Mar 10, 2010

### tarmon.gaidon

1. The problem statement, all variables and given/known data

Hey Everyone,

I am working on a physics project in which we need to look at a basic physics model. I have a couple of quick questions regarding conduction and heat generated through a resistor.

So I basically have a wire acting as a resistor that I want to run current through. (A basic heating element, something similar to the nichrome wire in the rear windshield of a car.) I want to find out how much power needs to be dissipated from the wire in order to melt snow. Where I am getting stuck is trying to figure out how conduction comes into play. The wire would be against the inside of a plastic cover and would be melting snow on the other side of the material.

From what I understand you can calculate the conduction based on the temperatures of the hot surface and the cold surface. (The inside and outside of the material.) How would I go about relating the power dissipated by the wire with the temperature of the inside of the material. Can I directly relate the power and the energy required to raise the temperature of the wire?

Also can I use conduction to say how much the ambient temperature would raise on the side of the material with the heating element?

2. Relevant equations
Heat flow = kA($$\Delta$$T/ Length)
P = V^2/R
Energy required to raise the temp of the wire = mq($$\Delta$$T)
Energy required to melt the snow = mq($$\Delta$$T) + m(heat of fusion)

Any input would be appreciated,
Rob