Operation of Heat Equation in One Dimension

The heat equation is a partial differential equation that models the temperature changes across the dimensions of a body, with respect to time. It basically conveys that the temperature change at a particular point is directly proportional to the difference between the average neighbourhood temperature and it's own temperature. The proportionality constant being \( \alpha \):

\[ \frac{dT}{dt} = \alpha \left( \frac{\partial^2 T}{\partial x^2} + \frac{\partial^2 T}{\partial y^2} + \frac{\partial^2 T}{\partial z^2} \right) \]

In this simulation, we look at the operation of this equation along a single dimension

Generate Simulate

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Presets

1. Two rods at different temperatures: Generate
   
   
2. Linear gradient in temperature: Generate

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Note:

1. The temperature changes in the beginning are extremely rapid, after which the pace reduces
2. In certain cases, when the conductivity is high (> 0.9), temperatures briefly oscillate at several positions

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Developed by ChanRT | Fork me at GitHub