Heat transfer, heat from current

[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

 

[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.

 

[Frostfire]

thermal energy per power was my first thought

 

[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?

 

[alphy]

There is indeed a relationship between the current and the diameter of a material for efficient transfer of thermal energy. This is known as the thermal conductivity of a material, which is a measure of how well a material can conduct heat. The thermal conductivity can be affected by several factors, including the diameter of the material.

In general, materials with larger diameters will have a higher thermal conductivity. This is because a larger diameter allows for more pathways for heat to flow through the material. This is known as the cross-sectional area, and it directly affects the thermal conductivity.

However, it is important to note that the thermal conductivity is not the only factor that affects heat transfer. The resistance of a material, which is a measure of how difficult it is for electricity to flow through the material, also plays a significant role. Under high current loads, the resistance of a material can increase, which can lead to the generation of more heat.

The relationship between resistance and heat generation under high current loads is known as the Joule heating effect. This effect states that the amount of heat generated in a material is directly proportional to the square of the current and the resistance of the material. This means that as the current and resistance increase, the amount of heat generated also increases.

It is important to note that the basic relationships between current, resistance, and heat generation may not be accurate under high current loads. This is because at high currents, the resistance of a material may not be constant and may vary with temperature. In addition, other factors such as the material's thermal expansion and thermal capacity may also affect heat generation.

In conclusion, the diameter of a material plays a role in efficient heat transfer, but it is not the only factor. The thermal conductivity and resistance of the material also play important roles, and these relationships may not be accurate under high current loads. It is essential to consider all these factors when studying heat transfer in materials.