+
Solution of the Heat Diffusion Equation by the Method of Separation of Variables

Solution of the Heat Diffusion Equation by the Method of Separation of Variables

Rating:
Rating
(0)
Author: Miguel Ramirez
Description:

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.

(more)
See More

Try Our College Algebra Course. For FREE.

Sophia’s self-paced online courses are a great way to save time and money as you earn credits eligible for transfer to over 2,000 colleges and universities.*

Begin Free Trial
No credit card required

25 Sophia partners guarantee credit transfer.

221 Institutions have accepted or given pre-approval for credit transfer.

* The American Council on Education's College Credit Recommendation Service (ACE Credit®) has evaluated and recommended college credit for 20 of Sophia’s online courses. More than 2,000 colleges and universities consider ACE CREDIT recommendations in determining the applicability to their course and degree programs.

Tutorial

Solution of the Heat Diffusion Equation in One Dimension, by the Method of Separation of Variables

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

How to solve Partial Differential Equations via Separation of Variables, By Chris Tisdell

This video-lecture complements the previous video lecture:
"Solution of the Heat Diffusion Equation in one dimension by the Method of Separation of Variables"

Source: Chris Tisdell at YouTube: http://www.youtube.com/watch?v=sLaez4Fcfh8

Computing Fourier Series | MIT 18.03SC Differential Equations, Fall 2011

Computing Fourier Series
Instructor: David Shirokoff
View the complete course: http://ocw.mit.edu/18-03SCF11

License: Creative Commons BY-NC-SA
More information at http://ocw.mit.edu/terms
More courses at http://ocw.mit.edu

Source: MIT OpenCourseWare at YouTube: http://www.youtube.com/watch?v=jzzpxqVohhI

Manipulating Fourier Series | MIT 18.03SC Differential Equations, Fall 2011

Manipulating Fourier Series
Instructor: David Shirokoff
View the complete course: http://ocw.mit.edu/18-03SCF11

License: Creative Commons BY-NC-SA
More information at http://ocw.mit.edu/terms
More courses at http://ocw.mit.edu

Source: MIT OpenCourseWare at YouTube: http://www.youtube.com/watch?v=v4YcejwdQC0