Inner Surface Temperature of Spherical Wall Calculator

Formula Used:

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

Outer Surface Temperature:

Heat Flow Rate:

Thermal Conductivity:

W/(m·K)

Radius of 1st Concentric Sphere:

Radius of 2nd Concentric Sphere:

Inner Surface Temperature:

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

The inner surface temperature of a spherical wall is the temperature at the inner surface of a spherical shell, calculated based on heat transfer principles through concentric spheres with different radii and thermal properties.

2. How Does the Calculator Work?

The calculator uses the formula:

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

Where:

\( T_i \) — Inner surface temperature (K)
\( T_o \) — Outer 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 difference between inner and outer surfaces of a spherical wall based on heat conduction through the material.

3. Importance of Temperature Calculation

Details: Accurate temperature calculation is crucial for thermal analysis, insulation design, and ensuring structural integrity in spherical vessels and containers subjected to temperature gradients.

4. Using the Calculator

Tips: Enter all values in appropriate units. Temperatures in Kelvin, heat flow rate in Watts, thermal conductivity in W/(m·K), and radii in meters. All values must be positive, and radii must be different.

5. Frequently Asked Questions (FAQ)

Q1: Why is this formula specific to spherical walls?
A: The formula accounts for the spherical geometry where heat flow follows an inverse square law with radius, different from planar or cylindrical geometries.

Q2: What are typical applications of this calculation?
A: Used in designing spherical pressure vessels, storage tanks, planetary models, and any spherical structure with heat transfer considerations.

Q3: 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 gradient.

Q4: What if the radii are equal?
A: The formula becomes undefined when radii are equal as it represents a single point rather than a spherical wall with thickness.

Q5: Can this be used for composite spherical walls?
A: For composite walls with multiple layers, additional calculations are needed to account for interface temperatures and different thermal conductivities.