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# Derivation of the Heat Diffusion Equation in One Dimension

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Author: Miguel Ramirez
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This tutorial is designed to explain to AP Calculus AB students, how to obtain the heat diffusion equation in one dimension combining conservation principles and the Fourier Heat Law, and how to solve this equation using the separation of variables method

Combining the Fourier Heat Law and the Conservation of Energy Principle, the heat diffusion equation, in one dimension, for a homogenous and isotropic media is obtained. Then, for homogenous boundary conditions, and using the Separation of Variables Method, a solution is obtained. Next, students will write the equivalent code in MS-Excel VBA (Visual Basic for Applications) for this solution, to visualize how this solution gives the values for temperature at given positions and times.

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Tutorial

## Derivation of the Heat Diffusion Equation in One Dimension

This is a mandatory to watch video for the AP Calculus AB End of Year Project: "Simulator for Heat Transfer Processes in STALM super Critical CO2 Printed Circuit Heat Exchanger"

Source: By M Ramirez

## Conservation of Mass, Lecture 2.1, By Victor Ugaz

This video lecture complements the previous video-lecture: "Derivation of the Heat Diffusion Equation in One Dimension"

Source: Victor Ugaz at You Tube: http://www.youtube.com/watch?v=-HQ4t8JX1TY

## Conservation of Mass, Lecture 2.2, By Dr. Victor Ugaz (Texas A&M)

This Video-lecture complements the previous video-lecture: "Derivation of the Heat Diffusion Equation in One Dimension"