Modeling a simple heating element

[tarmon.gaidon]

Homework Statement

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?

Homework 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

 

[jbsteele]

The Attempt at a SolutionTo answer your questions, yes you can use conduction to calculate how much the ambient temperature would raise on the side of the material with the heating element. The equation for heat flow through conduction is Heat flow = kA(\DeltaT/ Length), where k is the thermal conductivity, A is the area of the material, \DeltaT is the difference in temperature between the hot and cold sides of the material, and length is the thickness of the material. You can also relate the power dissipated by the wire directly to the energy required to raise the temperature of the wire. The equation for power is P = V^2/R, where V is the voltage and R is the resistance of the wire. The energy required to raise the temperature of the wire is given by the equation Energy required to raise the temp of the wire = mq(\DeltaT), where m is the mass of the wire, q is the specific heat capacity of the wire, and \DeltaT is the change in temperature. Finally, the energy required to melt the snow is given by the equation Energy required to melt the snow = mq(\DeltaT) + m(heat of fusion), where m is the mass of the snow, q is the specific heat capacity of the snow, and \DeltaT is the change in temperature. Hope this helps!