Thermal Resistance Of Spherical Composite Wall Of 2 Layers In Series With Convection Calculator

Thermal Resistance of Spherical Composite Wall Formula:

\[ R_{th} = \frac{1}{4\pi} \left( \frac{1}{h_i r_1^2} + \frac{1}{k_1} \left( \frac{1}{r_1} - \frac{1}{r_2} \right) + \frac{1}{k_2} \left( \frac{1}{r_2} - \frac{1}{r_3} \right) + \frac{1}{h_o r_3^2} \right) \]

Inner Convection Heat Transfer Coefficient (h_i):

W/m²·K

Radius of 1st Concentric Sphere (r₁):

Thermal Conductivity of 1st Body (k₁):

W/m·K

Radius of 2nd Concentric Sphere (r₂):

Thermal Conductivity of 2nd Body (k₂):

W/m·K

Radius of 3rd Concentric Sphere (r₃):

External Convection Heat Transfer Coefficient (h_o):

W/m²·K

Thermal Resistance of Sphere (R_th):

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1. What is Thermal Resistance of Spherical Composite Wall?

The thermal resistance of a spherical composite wall with 2 layers in series with convection represents the overall resistance to heat flow through a multi-layered spherical system that includes both conductive layers and convective boundaries. It quantifies how effectively the composite wall resists heat transfer.

2. How Does the Calculator Work?

The calculator uses the thermal resistance formula:

Where:

\( R_{th} \) — Thermal resistance of sphere (K/W)
\( h_i \) — Inner convection heat transfer coefficient (W/m²·K)
\( r_1 \) — Radius of 1st concentric sphere (m)
\( k_1 \) — Thermal conductivity of 1st body (W/m·K)
\( r_2 \) — Radius of 2nd concentric sphere (m)
\( k_2 \) — Thermal conductivity of 2nd body (W/m·K)
\( r_3 \) — Radius of 3rd concentric sphere (m)
\( h_o \) — External convection heat transfer coefficient (W/m²·K)

Explanation: The formula accounts for both conductive resistance through the two material layers and convective resistance at the inner and outer surfaces of the spherical composite wall.

3. Importance of Thermal Resistance Calculation

Details: Accurate thermal resistance calculation is crucial for designing thermal insulation systems, predicting heat transfer rates, and optimizing energy efficiency in spherical containers, pressure vessels, and other spherical thermal systems.

4. Using the Calculator

Tips: Enter all values in appropriate SI units. Ensure all input values are positive and physically meaningful. The radii should be in increasing order (r₁ < r₂ < r₃) for proper calculation.

5. Frequently Asked Questions (FAQ)

Q1: What is the significance of the 1/4π factor?
A: The 1/4π factor accounts for the spherical geometry and ensures the thermal resistance is properly scaled for three-dimensional spherical heat transfer.

Q2: How does this differ from planar thermal resistance?
A: Spherical thermal resistance considers the curvature of surfaces and the varying surface area with radius, unlike planar resistance which assumes constant cross-sectional area.

Q3: What are typical values for thermal resistance?
A: Thermal resistance values vary widely depending on materials and geometry, from fractions of K/W for good conductors to hundreds of K/W for effective insulators.

Q4: Can this formula be extended to more than 2 layers?
A: Yes, the formula can be extended by adding more terms for additional conductive layers following the same pattern.

Q5: What are the limitations of this calculation?
A: This calculation assumes steady-state conditions, constant thermal properties, perfect spherical symmetry, and neglects radiation heat transfer effects.