Isothermal Rectangular Parallelepiped Buried in Semi-Infinite Medium Calculator

Conduction Shape Factor Formula:

\[ S = 1.685 \times L_{pr} \times (\log_{10}(1 + \frac{D_{ss}}{W_{pr}}))^{-0.59} \times (\frac{D_{ss}}{H})^{-0.078} \]

Length of Parallelepiped (Lpr):

Distance from Surface to Surface of Object (Dss):

Width of Parallelepiped (Wpr):

Height of Parallelepiped (H):

Conduction Shape Factor (S):

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1. What Is The Conduction Shape Factor?

The Conduction Shape Factor is defined as the value used to determine the heat transfer rate for configurations which are very complex and require high calculation time. It provides a simplified approach to analyze heat conduction in irregular geometries.

2. How Does The Calculator Work?

The calculator uses the conduction shape factor formula:

\[ S = 1.685 \times L_{pr} \times (\log_{10}(1 + \frac{D_{ss}}{W_{pr}}))^{-0.59} \times (\frac{D_{ss}}{H})^{-0.078} \]

Where:

\( S \) — Conduction Shape Factor (m)
\( L_{pr} \) — Length of parallelepiped (m)
\( D_{ss} \) — Distance from surface to surface of object (m)
\( W_{pr} \) — Width of parallelepiped (m)
\( H \) — Height of parallelepiped (m)

Explanation: The equation calculates the conduction shape factor for an isothermal rectangular parallelepiped buried in a semi-infinite medium, accounting for geometric relationships between the object dimensions.

3. Importance Of Conduction Shape Factor Calculation

Details: Accurate conduction shape factor calculation is crucial for determining heat transfer rates in complex geometries, thermal analysis of buried objects, and designing efficient thermal management systems.

4. Using The Calculator

Tips: Enter all dimensions in meters. All values must be positive numbers greater than zero. Ensure consistent units for accurate results.

5. Frequently Asked Questions (FAQ)

Q1: What is a parallelepiped?
A: A parallelepiped is a three-dimensional figure formed by six parallelograms, similar to a rectangular prism but with parallelogram faces instead of rectangles.

Q2: When is this conduction shape factor formula applicable?
A: This formula is specifically designed for isothermal rectangular parallelepipeds buried in semi-infinite media, typically used in heat transfer analysis of underground structures.

Q3: What are typical values for conduction shape factor?
A: Conduction shape factor values vary widely depending on geometry, but typically range from fractions of a meter to several meters for practical engineering applications.

Q4: Are there limitations to this equation?
A: This equation assumes isothermal conditions and semi-infinite medium properties. It may be less accurate for extreme aspect ratios or non-ideal boundary conditions.

Q5: How does this relate to heat transfer calculations?
A: The conduction shape factor is used in the formula Q = k × S × ΔT, where Q is heat transfer rate, k is thermal conductivity, S is shape factor, and ΔT is temperature difference.