Skin Effect Heat Tracing: Explanation & Example

 

Skin effect is a phenomenon in alternating current (AC) systems where the current tends to flow near the surface of a conductor, with the density of the current decreasing exponentially with depth inside the conductor. This effect is important when calculating heat tracing requirements because it affects the resistance of the conductor and the amount of heat generated.

Steps to Calculate Heat Trace Power with Skin Effect Consideration

1. Understand the Parameters:

• Pipe diameter (D): Outer diameter of the pipe.
• Power density (P): Heat generated per unit length of the cable.
• Voltage (V): Voltage used in the system.
• Conductor material: Usually copper or steel for heating cables.
• Resistance (R): The resistance of the wire will be impacted by the skin effect.
• Current frequency (f): AC frequency used (typically 50 or 60 Hz).
• Insulation: Thermal insulation on the pipe and cable affects the heat dissipation and therefore the power needed.

2. Calculate the Resistance per Meter of Heat Trace Cable: The resistance (R) of the heat trace cable, considering the skin effect, can be calculated by:

R=ρ/A​

Where:

• ρ = Resistivity of the material (typically copper or aluminum).
• A = Cross-sectional area of the conductor, affected by skin depth.

3. Determine Skin Depth: The skin depth δ\deltaδ is the distance from the surface of the conductor where the current density falls to 1/e1/e1/e (approximately 37%) of its value at the surface. It is calculated as:

δ= squre root (ρ/πfμ)​​

Where:

• ρ = Resistivity of the material.
• f = Frequency of the current.
• μ = Permeability of the material (for copper, μ=4π×10−7 H/m)

4. Heat Generation: The heat generated in the cable due to resistance is given by Joule’s Law:

Q=I²R

Where:

• I = Current through the conductor.
• R = Resistance of the conductor (including the effects of skin effect).

5. Power Calculation: The power required for the heat trace system can be calculated using:

P=V²R​

Where:

• V = Voltage supplied to the heat tracing cable.
• R = Resistance of the cable, considering the skin effect.

Example Calculation

Let’s assume the following parameters:

• Pipe diameter D=0.1m
• Heating cable is made of copper (ρ=1.68×10−8 Ω⋅m).
• AC frequency f=60 Hz
• Voltage supplied V=120V
• Cable is designed to carry a current of I=5A

Step 1: Calculate the skin depth

δ = square root (ρ/πfμ) 

= square root (1.68×10⁻⁸)/(π×60×4π×10⁻⁷) ≈ 0.017 m

This means that the current flows within 0.017 meters (1.7 cm) of the surface of the conductor.

Step 2: Calculate resistance (simplified)

For simplicity, let’s assume the cable’s cross-sectional area A is designed to account for the skin effect. Let’s use a resistance R=0.5 Ω for the given length.

Step 3: Heat Generation (Joule Heating)

Now, using the current I=5A and resistance R=0.5 Ω:

Q = I²R 

= 5²×0.5 = 25×0.5 = 12.5 W

This is heat tracing cable output (W/m).

Step 4: Power Calculation

Given the voltage V=120 V and resistance R=0.5 Ω:

P = V²R 

= 120²x0.5 = 14400x0.5 = 28800W = 28.8kW

Thus, the power required for the heat tracing system is 28.8kW.