Temperature Inside Plane Wall At Given Thickness X With Symmetrical Boundary Conditions Calculator

Formula Used:

\[ t1 = -\frac{qG \cdot b^2}{2 \cdot k} \cdot \left(\frac{x}{b} - \left(\frac{x}{b}\right)^2\right) + T1 \]

Internal Heat Generation (qG):

W/m³

Wall Thickness (b):

Thermal Conductivity (k):

W/m·K

Thickness (x):

Surface Temperature (T1):

Temperature 1 (t1):

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1. What Is The Temperature Inside Plane Wall At Given Thickness X With Symmetrical Boundary Conditions Formula?

This formula calculates the temperature distribution inside a plane wall with internal heat generation and symmetrical boundary conditions. It provides the temperature at any given thickness x from the center of the wall.

2. How Does The Calculator Work?

The calculator uses the formula:

\[ t1 = -\frac{qG \cdot b^2}{2 \cdot k} \cdot \left(\frac{x}{b} - \left(\frac{x}{b}\right)^2\right) + T1 \]

Where:

\( t1 \) — Temperature at thickness x (K)
\( qG \) — Internal heat generation (W/m³)
\( b \) — Wall thickness (m)
\( k \) — Thermal conductivity (W/m·K)
\( x \) — Thickness from center (m)
\( T1 \) — Surface temperature (K)

Explanation: The formula accounts for parabolic temperature distribution in a wall with uniform internal heat generation and symmetrical boundary conditions.

3. Importance Of Temperature Calculation

Details: Accurate temperature calculation is crucial for thermal analysis, heat transfer studies, and designing thermal insulation systems in various engineering applications.

4. Using The Calculator

Tips: Enter all values in appropriate units. Ensure thickness x is between 0 and wall thickness b. All values must be positive.

5. Frequently Asked Questions (FAQ)

Q1: What are symmetrical boundary conditions?
A: Symmetrical boundary conditions mean both surfaces of the wall are maintained at the same temperature, creating a symmetrical temperature profile.

Q2: What is the maximum temperature location?
A: For symmetrical boundary conditions with internal heat generation, the maximum temperature occurs at the center of the wall (x = 0).

Q3: What are typical applications of this formula?
A: This formula is used in analyzing heat transfer in electrical conductors, nuclear fuel rods, chemical reactors, and other systems with internal heat generation.

Q4: What are the limitations of this formula?
A: This formula assumes steady-state conditions, constant thermal properties, uniform internal heat generation, and symmetrical boundary conditions.

Q5: How does internal heat generation affect temperature distribution?
A: Internal heat generation creates a parabolic temperature profile with maximum temperature at the center and minimum at the surfaces.