Effective Thermal Conductivity Calculator

Formula Used:

\[ k_{Eff} = \frac{Q_s \times (r_2 - r_1)}{4 \times \pi \times r_1 \times r_2 \times \Delta T} \]

Heat transfer Between Concentric Spheres (Q_s):

Inside Radius (r₁):

Outer Radius (r₂):

Temperature Difference (ΔT):

Effective Thermal Conductivity (k_Eff):

Unit Converter ▲

Unit Converter ▼

From:	To:

1. What is Effective Thermal Conductivity?

Effective Thermal Conductivity is the rate of heat transfer through a unit thickness of the material per unit area per unit temperature difference. It quantifies how well a material conducts heat.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ k_{Eff} = \frac{Q_s \times (r_2 - r_1)}{4 \times \pi \times r_1 \times r_2 \times \Delta T} \]

Where:

\( k_{Eff} \) — Effective Thermal Conductivity (W/m·K)
\( Q_s \) — Heat transfer Between Concentric Spheres (W)
\( r_1 \) — Inside Radius (m)
\( r_2 \) — Outer Radius (m)
\( \Delta T \) — Temperature Difference (K)
\( \pi \) — Archimedes' constant (≈3.1416)

Explanation: This formula calculates the effective thermal conductivity for heat transfer between concentric spheres, accounting for the geometric configuration and temperature gradient.

3. Importance of Thermal Conductivity Calculation

Details: Accurate thermal conductivity estimation is crucial for thermal insulation design, heat exchanger optimization, and material selection in various engineering applications.

4. Using the Calculator

Tips: Enter heat transfer in watts, radii in meters, and temperature difference in kelvin. All values must be positive, and outer radius must be greater than inner radius.

5. Frequently Asked Questions (FAQ)

Q1: What is the significance of concentric spheres in this calculation?
A: Concentric spheres represent a common geometric configuration in heat transfer applications, particularly in insulation systems and spherical heat exchangers.

Q2: How does temperature difference affect thermal conductivity?
A: For most materials, thermal conductivity is relatively constant with temperature, but significant temperature differences may affect material properties.

Q3: What are typical values for thermal conductivity?
A: Thermal conductivity varies widely: metals (15-400 W/m·K), water (0.6 W/m·K), air (0.026 W/m·K), insulation materials (0.02-0.1 W/m·K).

Q4: Are there limitations to this equation?
A: This equation assumes steady-state conditions, uniform material properties, and neglects radiation and convection effects.

Q5: When should this calculation be used?
A: This calculation is particularly useful for analyzing heat transfer in spherical geometries, such as insulated tanks, spherical reactors, or planetary heat transfer problems.