# Space-Time Transformation of Heat Conduction

## Model Data

**Type:**
heat transfer

**Physics Modes:**
heat transfer

**Keywords:**
heat diffusion
space time
validation

Transient heat diffusion in a *1 m* rod where one end is kept at T = 25 degrees
and the other subject to constant heat flux q_n = 1. This one-dimensional time
dependent problem is transformed to a static two dimensional one.

The computed results can both be compared with the analytical solution

$$ T_{ref} = (24+x) + \sum_{n=1}^\infty 8/(1-2n)^2/\pi^2cos((n-½)\pi x)e^{-((n-½)^2\pi^2)t}$$

and the equivalent one dimensional heat transfer in a rod example.

This model is available as an automated tutorial by selecting **Model Examples and Tutorials…** >
**Heat Transfer** > **Space-Time Transformation of Heat Conduction**
from the **File** menu, and also as the MATLAB simulation m-script example ex_heat_transfer8.
Step-by-step tutorial instructions to set up and run this model are linked below.