Thursday 16 July 2015

Heat Equation part 2 a slight modification

While writing the code for the previous post I slightly modified the code in order to add 2 ‘peaks of heat’. Now, by looking at what I wrote I am not quite sure that the solution is consistent (physically speaking). At first glance we can see that there are three ‘heat spots’. If you imagine of heating the rod in two spots and cooling it in between, the situation is the following:

im

By setting L = 3*pi and making some other small changes we obtain:



Physically we could interpret the result as follows:
the heat flows spontaneously towards areas where the temperature is lower, therefore the temperature should go up in the middle of the rod (since it has been cooled down and has a lower temperature compared its surroundings) and go down in the sides. Assuming that the left and right boundaries of the rod are kept at constant temperature through an ideal thermostat.


Why not  checking if this solution is mathematically and physically consistent?

5 comments:

  1. Cloud Computing has been the stage for emerging technologies and an increase in career opportunities for both fresher and professional.
    Cloud Computing Course Fees in Bangalore

    ReplyDelete

  2. Very informative blog! There is so much information here that can help thank you for sharing.
    Data Science Syllabus

    ReplyDelete
  3. Really impressed! Information shared was very helpful Your website is very valuable. Thanks for sharing..
    Business Analytics Course in Bangalore

    ReplyDelete
  4. I got to this amazing site not long ago. I actually captured with the piece of resources you have got here. Thanks for making such wonderful blog page.
    Business Analytics Course in Indore

    ReplyDelete
  5. amazing write , keep posting and if you are intresting in big data coder and code developer then checkout java classes in satara

    ReplyDelete