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https://github.com/iammohith/heat-conduction-in-a-cylinder

This repository contains Python codes for analyzing heat conduction in a cylinder, focusing on analytical solutions for temperature distribution under various one-dimensional heat flow conditions. The scripts illustrate how temperature changes over space within the cylinder based on different boundary conditions and initial temperatures.
https://github.com/iammohith/heat-conduction-in-a-cylinder

analytical-solution heat-transfer python

Last synced: about 2 months ago
JSON representation

Host: GitHub
URL: https://github.com/iammohith/heat-conduction-in-a-cylinder
Owner: iammohith
License: mit
Created: 2020-04-15T13:33:24.000Z (over 4 years ago)
Default Branch: master
Last Pushed: 2024-10-19T11:13:27.000Z (3 months ago)
Last Synced: 2024-11-16T00:13:35.340Z (about 2 months ago)
Topics: analytical-solution, heat-transfer, python
Language: Python
Homepage:
Size: 19.5 KB
Stars: 0
Watchers: 2
Forks: 0
Open Issues: 0
Metadata Files:
- Readme: README.md
- License: LICENSE

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README

# Heat Conduction in a Cylinder

This repository contains Python code for simulating heat conduction in a long cylinder with various boundary conditions, thermal properties, and heat generation. The temperature distribution is calculated and visualized based on the governing heat conduction equations.

## Project Overview

This project explores the thermal behavior of a cylinder with radius $R$, subject to internal heat generation $Q_g$ and external thermal conditions. The wall temperature $T_w$ and the effect of thermal conductivity $K$ are taken into account to calculate the temperature distribution across the cylinder.

### Key Features:
- Solves heat conduction problems with heat generation within the cylinder.
- Visualizes temperature distribution using Python's `matplotlib` library.
- Supports various thermal boundary conditions and parameters like cylinder radius, heat generation, and thermal conductivity.

## Formulas Used

### 1. **Temperature Distribution with Heat Generation**

For a long cylinder with radius $R$ and wall temperature $T_w$, the temperature distribution is given by:

$$
T(r) = \frac{Q_g \cdot R^2}{4 \cdot K} \cdot \left(1 - \left(\frac{r}{R}\right)^2\right) + T_w
$$

Where:
- $T(r)$ is the temperature at radial distance $ r $ from the center.
- $Q_g$ is the heat generation per unit volume (W/m³).
- $K$ is the thermal conductivity of the cylinder material (W/m·K).

### 2. **Temperature Distribution with Fluid Interaction**

When the cylinder is immersed in a fluid with temperature $T_{\infty}$ and heat transfer coefficient $h_c$, the temperature distribution becomes:

$$
T(r) = \frac{Q_g \cdot R^2}{4 \cdot K} \cdot \left(1 - \left(\frac{r}{R}\right)^2\right) + T_{\infty} + \frac{Q_g \cdot R}{2 \cdot h_c}
$$

Where:
- $T_{\infty}$ is the surrounding fluid temperature (°C).
- $h_c$ is the convective heat transfer coefficient.

### 3. **Convective Heat Transfer Coefficient**

The heat transfer coefficient $h_c$ can be calculated as:

$$
h_c = \frac{Q_g \cdot R}{2 \cdot \theta}
$$

Where:
- $\theta = |T_w - T_{\infty}|$ is the absolute temperature difference between the wall and the fluid.

## Usage

1. **Clone the repository**:
```bash
git clone https://github.com/iammohith/Heat-Conduction-in-a-Cylinder.git
```

2. **Install dependencies**:
Make sure you have Python installed, and then install the required packages:
```bash
pip install numpy matplotlib
```

3. **Run the simulations**:
The Python scripts simulate different cases of heat conduction through the cylinder. To run a script, execute:
```bash
python script_name.py
```

4. **Modify Parameters**:
You can change parameters such as $T_w$, $T_{\infty}$, $R$, $Q_g$, and $K$ in the scripts to test different thermal scenarios.

## Visualizations

The temperature distributions are plotted using `matplotlib`. Each script generates a plot showing the temperature across the cylinder. Here's an example of a typical temperature distribution graph:
- **X-axis**: Distance from the center of the cylinder.
- **Y-axis**: Temperature at that distance.

## References

1. **Heat and Mass Transfer: Fundamentals & Applications**
*Afshin J. Ghajar and Yunus A Çengel*

2. **Heat and Mass Transfer**
*R.K. Rajput*

3. **Python Documentation**
Official Python documentation for libraries like `numpy` and `matplotlib`:
[Python Documentation](https://docs.python.org/3/)

## License

This project is open source and available under the [MIT License](LICENSE).