Solutions of 1D Fourier Heat Equation

material

pure Fe (s)

initial temperature (°C)

100

time (s)

0.5

This Demonstration shows heat flow through a 1m bar of selected composition, based on solutions of the 1D Fourier heat equation. Select the material and initial temperature to see the heat flow over time by moving the "time (s)" slider. As the time progresses, thermal energy initially concentrated at the center spreads out along the length of the bar.

References

[1] R. C. Daileda, "The Two-Dimensional Heat Equation." Partial Differential Equations, Lecture 12, Trinity University, 2012. ramanujan.math.trinity.edu/rdaileda/teach/s17/m3357/lectures/lecture12.pdf.

[2] Panda the Red, "The Heat Equation, Explained," Cantor's Paradise (blog). (Jun 30, 2019) www.cantorsparadise.com/the-heat-equation-a76d7773a0b5.

External Links

Steady-State 1D Conduction through a Composite Wall

Heat Flow through a Pipe

Heat Transfer in Fins

Permanent Citation

Nathaniel White, Erika Anderson

"Solutions of 1D Fourier Heat Equation"
http://demonstrations.wolfram.com/SolutionsOf1DFourierHeatEquation/
Wolfram Demonstrations Project
Published: April 8, 2022