Maximum Temperature in Solid Sphere Calculator

Formula Used:

\[ T_{max} = T_w + \frac{q_G \times R_s^2}{6 \times k} \]

Surface Temperature of Wall (T_w):

Internal Heat Generation (q_G):

W/m³

Radius of Sphere (R_s):

Thermal Conductivity (k):

W/(m·K)

Maximum Temperature (T_max):

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1. What is the Maximum Temperature in Solid Sphere?

The Maximum Temperature in Solid Sphere calculation determines the highest temperature point within a solid sphere with uniform internal heat generation. This is crucial for thermal analysis and design in various engineering applications.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ T_{max} = T_w + \frac{q_G \times R_s^2}{6 \times k} \]

Where:

\( T_{max} \) — Maximum Temperature (K)
\( T_w \) — Surface Temperature of Wall (K)
\( q_G \) — Internal Heat Generation (W/m³)
\( R_s \) — Radius of Sphere (m)
\( k \) — Thermal Conductivity (W/(m·K))

Explanation: The formula calculates the maximum temperature at the center of a solid sphere with uniform internal heat generation, considering surface temperature and material properties.

3. Importance of Maximum Temperature Calculation

Details: Accurate maximum temperature calculation is essential for thermal management, material selection, and preventing thermal failure in spherical components with internal heat generation.

4. Using the Calculator

Tips: Enter surface temperature in Kelvin, internal heat generation in W/m³, radius in meters, and thermal conductivity in W/(m·K). All values must be positive.

5. Frequently Asked Questions (FAQ)

Q1: Where is the maximum temperature located in a solid sphere?
A: The maximum temperature occurs at the center of the sphere for uniform internal heat generation.

Q2: What assumptions are made in this calculation?
A: The calculation assumes steady-state conditions, uniform internal heat generation, constant thermal conductivity, and spherical symmetry.

Q3: How does thermal conductivity affect maximum temperature?
A: Higher thermal conductivity reduces the maximum temperature by facilitating better heat dissipation from the center to the surface.

Q4: What applications use this calculation?
A: This calculation is used in nuclear reactor design, electronic cooling, chemical reactors, and any spherical components with internal heat generation.

Q5: How does sphere radius affect maximum temperature?
A: Larger radius increases maximum temperature due to increased distance for heat conduction from center to surface.