Thermal Resistance For Conduction At Tube Wall Calculator

Thermal Resistance Formula:

\[ R_{th} = \frac{\ln\left(\frac{r_2}{r_1}\right)}{2\pi k l} \]

Outer Radius of Cylinder (r₂):

Inner Radius of Cylinder (r₁):

Thermal Conductivity (k):

W/m·K

Length of Cylinder (l):

Thermal Resistance (Rₜₕ):

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1. What is Thermal Resistance for Conduction at Tube Wall?

Thermal resistance for conduction at tube wall quantifies the resistance to heat flow through a cylindrical wall. It's a crucial parameter in heat transfer analysis for pipes, tubes, and cylindrical containers.

2. How Does the Calculator Work?

The calculator uses the thermal resistance formula:

\[ R_{th} = \frac{\ln\left(\frac{r_2}{r_1}\right)}{2\pi k l} \]

Where:

\( R_{th} \) — Thermal resistance (K/W)
\( r_2 \) — Outer radius of cylinder (m)
\( r_1 \) — Inner radius of cylinder (m)
\( k \) — Thermal conductivity (W/m·K)
\( l \) — Length of cylinder (m)
\( \pi \) — Mathematical constant pi (≈3.1416)

Explanation: The formula calculates the resistance to heat conduction through a cylindrical wall, accounting for the logarithmic nature of radial heat flow.

3. Importance of Thermal Resistance Calculation

Details: Accurate thermal resistance calculation is essential for designing efficient heat exchangers, insulation systems, and thermal management solutions in various engineering applications.

4. Using the Calculator

Tips: Enter all values in SI units (meters for dimensions, W/m·K for thermal conductivity). Ensure outer radius is greater than inner radius, and all values are positive.

5. Frequently Asked Questions (FAQ)

Q1: Why is the formula logarithmic instead of linear?
A: Heat flow through cylindrical walls follows a logarithmic distribution due to increasing surface area with radius, unlike flat walls where it's linear.

Q2: What are typical thermal resistance values?
A: Values vary widely depending on materials and dimensions. Insulating materials have higher resistance, while conductive metals have lower resistance.

Q3: How does wall thickness affect thermal resistance?
A: Thicker walls generally increase thermal resistance, but the relationship is logarithmic rather than linear.

Q4: Can this formula be used for composite walls?
A: For multiple cylindrical layers, thermal resistances add in series, similar to electrical resistances.

Q5: What are the limitations of this formula?
A: Assumes steady-state conditions, constant thermal conductivity, and no internal heat generation within the wall material.