1. What is the Temperature at Distance x Formula?

The temperature at distance x formula calculates the temperature at any point within a wall or solid material when the inner and outer surface temperatures are known. This linear temperature distribution assumes steady-state heat conduction through a homogeneous material.

2. How Does the Calculator Work?

The calculator uses the temperature formula:

Where:

• \( T \) — Temperature at distance x (K)
• \( T_i \) — Inner surface temperature (K)
• \( T_o \) — Outer surface temperature (K)
• \( x \) — Distance from inner surface (m)
• \( L \) — Total length/thickness of wall (m)

Explanation: The formula assumes linear temperature distribution through the wall material, which is valid for steady-state heat conduction through homogeneous materials with constant thermal conductivity.

3. Importance of Temperature Calculation

Details: Calculating temperature distribution in walls is crucial for thermal analysis, insulation design, energy efficiency calculations, and understanding heat transfer mechanisms in building materials and industrial applications.

4. Using the Calculator

Tips: Enter all temperatures in Kelvin, distances in meters. Ensure distance x is between 0 and total length L. All values must be positive, and x should not exceed L.

5. Frequently Asked Questions (FAQ)

Q1: When is this formula applicable?
A: This formula applies to steady-state heat conduction through homogeneous materials with constant thermal conductivity and no internal heat generation.

Q2: What if the material is not homogeneous?
A: For composite walls with different materials, the temperature distribution becomes piecewise linear and requires separate calculations for each material layer.

Q3: Can this be used for cylindrical or spherical walls?
A: No, this formula is specifically for plane walls. Cylindrical and spherical walls have logarithmic and inverse radial temperature distributions respectively.

Q4: What are the limitations of this approach?
A: This approach assumes constant thermal conductivity, no internal heat generation, and steady-state conditions. It doesn't account for transient effects or variable material properties.

Q5: How accurate is this calculation?
A: For homogeneous materials under steady-state conditions with constant thermal properties, this calculation provides exact results for temperature distribution.