Outer Surface Temperature of Spherical Wall Calculator

Formula Used:

\[ T_o = T_i - \frac{Q}{4\pi k} \left( \frac{1}{r_1} - \frac{1}{r_2} \right) \]

Inner Surface Temperature (Ti):

Heat Flow Rate (Q):

Thermal Conductivity (k):

W/m·K

Radius of 1st Concentric Sphere (r₁):

Radius of 2nd Concentric Sphere (r₂):

Outer Surface Temperature (Tₒ):

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1. What is the Outer Surface Temperature of Spherical Wall?

The Outer Surface Temperature of a spherical wall represents the temperature at the external surface of a spherical shell, calculated based on heat transfer principles through concentric spheres with different radii.

2. How Does the Calculator Work?

The calculator uses the spherical heat conduction formula:

\[ T_o = T_i - \frac{Q}{4\pi k} \left( \frac{1}{r_1} - \frac{1}{r_2} \right) \]

Where:

\( T_o \) — Outer Surface Temperature (K)
\( T_i \) — Inner Surface Temperature (K)
\( Q \) — Heat Flow Rate (W)
\( k \) — Thermal Conductivity (W/m·K)
\( r_1 \) — Radius of 1st Concentric Sphere (m)
\( r_2 \) — Radius of 2nd Concentric Sphere (m)
\( \pi \) — Archimedes' constant (≈3.14159)

Explanation: This formula calculates the temperature drop across a spherical wall due to heat conduction, considering the spherical geometry and material properties.

3. Importance of Temperature Calculation

Details: Accurate temperature calculation is crucial for thermal analysis, insulation design, and ensuring structural integrity in spherical vessels, tanks, and other spherical components exposed to heat transfer.

4. Using the Calculator

Tips: Enter all values in appropriate units. Thermal conductivity and radii must be positive values, and the two radii must be different. Ensure consistent units throughout.

5. Frequently Asked Questions (FAQ)

Q1: What if the radii are equal?
A: The formula requires different radii (r₁ ≠ r₂) as it represents heat transfer through a spherical wall with finite thickness.

Q2: Can this be used for hollow spheres?
A: Yes, this formula is specifically designed for heat conduction through hollow spherical walls.

Q3: What are typical applications?
A: Spherical tanks, pressure vessels, insulated containers, and any spherical structures involving heat transfer.

Q4: How does thermal conductivity affect the result?
A: Higher thermal conductivity reduces the temperature difference for the same heat flow rate, while lower conductivity increases the temperature drop.

Q5: What units should be used?
A: Use Kelvin for temperatures, Watts for heat flow rate, W/m·K for thermal conductivity, and meters for radii to ensure consistent results.