# Heat transfer, heat from current

1. Oct 5, 2010

### Frostfire

Is there a relation that connects a current with the diameter of a material for efficient transfer of thermal energy.

I say diameter as I think its safe to assume heat leaves radially given a uniform material.

I am also looking for a relation between resistance of a material and heat generated under high current loads. I know the basic ones but I seem to remeber something about them not being accurate given high current

Any helps appreciated

2. Oct 24, 2010

### Mapes

What exactly do you mean by "efficient transfer of thermal energy" here? (Highest temperature per unit power? Voltage? Something else?) It will affect how you attack the problem.

You may have some luck searching "resistivity" + "temperature" for your material of interest.

3. Oct 24, 2010

### Frostfire

thermal energy per power was my first thought

4. Oct 24, 2010

### Mapes

OK, that's going to be relatively straightforward: the efficiency is just

$$\eta=\frac{I^2R_L}{I^2R_L+I^2R_S}=\frac{R_L}{R_L+R_S}=\frac{1}{1+R_SA/\rho L}$$

where $I$ is the current, $R_L=\rho L/A$ is the load resistance (the resistance of the heater), $R_S$ is the source resistance (the resistance of the power supply and wiring), $\rho$ is the resistivity of the heater material, and $L$ and $A$ are the length and cross-sectional area of the thermal heater.

This is essentially the principle of power matching; you maximize power transfer when the load resistance matches the source resistance and the source resistance is minimized. Does this answer your question?