Deriving the Heat Equation in 2D & 3D (& in N Dimensions!) with Control Volumes and Vector Calculus

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  • เผยแพร่เมื่อ 3 พ.ย. 2024

ความคิดเห็น • 36

  • @shakennotstired8392
    @shakennotstired8392 2 ปีที่แล้ว +5

    Thanks professor. This is great staff. I am learning a lot. I am forever grateful for your effort

  • @ilpreterosso
    @ilpreterosso 2 ปีที่แล้ว +4

    A great review for me of contents from last semester!

  • @adityawagh1707
    @adityawagh1707 ปีที่แล้ว

    Love your videos Steve, they really help me understand the physics to a basic level. However seeing you in real life would be mind-bending, as the Steve we know is your mirrored persona.

  • @abrarsalekinraiyan3170
    @abrarsalekinraiyan3170 10 หลายเดือนก่อน +1

    Hearing that Steve properly learned all these after becoming a grad student, makes me feel a bit better that I didn't understand all these in undergrad 😅. And now as a grad student its coming together slowly for me

    • @Eigensteve
      @Eigensteve  10 หลายเดือนก่อน +1

      Glad to hear it :)

  • @tomctutor
    @tomctutor 2 ปีที่แล้ว +3

    Excellent derivation, I no doubt expect some examples will follow, thankyou!♒

    • @Eigensteve
      @Eigensteve  2 ปีที่แล้ว +3

      Yep yep, planning them now!

  • @erickleuro7928
    @erickleuro7928 2 หลายเดือนก่อน

    @13:40 my ¢5 cents to this amazing video, the partial derivative (with respect to time) can be moved inside the triple volume integral because the system is (or assumed to be) lineal and therefore obeys the principle of superposition; otherwise, this wouldn't be allowed

  • @ajitkumar-ip6hc
    @ajitkumar-ip6hc 2 ปีที่แล้ว +1

    Dear Steve, thank you for uploading your lectures it will be very helpful if you can make a video on Rayleigh-Benard convection simulation (DNS)

  • @ramkitty
    @ramkitty 2 ปีที่แล้ว +1

    i apply your teaching of vcalc to self physiotherapy and joint manipulation with the goal of equalizing tesions through muscle bundles by forcing applications at muscle attachment or roots.

  • @sammykmfmaths7468
    @sammykmfmaths7468 ปีที่แล้ว

    Thanks Professor 🎉🎉❤

  • @alirezaizadian1543
    @alirezaizadian1543 ปีที่แล้ว

    good job.thanks professor.

  • @Helmutandmoshe
    @Helmutandmoshe 2 ปีที่แล้ว

    I sure hope this series continues. Is there a plan for more videos?

  • @CyrusTabery
    @CyrusTabery 2 ปีที่แล้ว +2

    You forgot the thermal conductivity in Fourier’slaw. Also it maybe good to be clear when constant heat capacity and density assumption is needed. Finally nit pick : u is for vectors, use a different letter for temperature, T maybe? It maybe fun to show the dimensionless versions of the equations…

  • @oliviajulia7913
    @oliviajulia7913 ปีที่แล้ว

    Hi! Great content as always!
    Could you please do an example of this 3D heat equation including conduction, radiation and convection?
    It seems I can't find any example in the scientific literature... If you could refer to a source in the mean time where I could find this, it would be great!

  • @benanderson9189
    @benanderson9189 ปีที่แล้ว

    Towards the end once you've written the equation in its simplified form, why is alpha squared? Is this just a simple way of denoting that the coefficient of the laplacian of u is always positive?

  • @santoshpathak7303
    @santoshpathak7303 6 หลายเดือนก่อน

    (Time: 10: 50) Wow everybody is like me. I am gonna teach the same thing tomorrow and not sure how to explain that negative sign infront of the surface integral. I wanted to hear his explanation about it, he was so unhappy about his own explanation.

  • @maflojustin
    @maflojustin 2 ปีที่แล้ว +2

    21:30: you almost divided by 'zero'😄

  • @mingusbingus6746
    @mingusbingus6746 ปีที่แล้ว

    "I didn't learn about PDEs until I was a graduate student"- Same, I feel like I was cheated out of such a deep way of understanding the world.

  • @mathjitsuteacher
    @mathjitsuteacher 2 ปีที่แล้ว +2

    Hi Steve, what do I need to do a post doc with you?

    • @ramkitty
      @ramkitty 2 ปีที่แล้ว +1

      inquiring minds want to know

  • @JonasAstrom-zv1tu
    @JonasAstrom-zv1tu ปีที่แล้ว

    Sorry for a lightweight comment: you are writing in reverse, apparently without difficulty. I couldn't do that!

  • @MrFazeFaze
    @MrFazeFaze 2 ปีที่แล้ว

    great review! Would you be going into numerical methods too? i.e. FVM

  • @ba2tripleO
    @ba2tripleO 2 ปีที่แล้ว +1

    I think you forgot to add it to the playlist

    • @Eigensteve
      @Eigensteve  2 ปีที่แล้ว

      Good catch, thanks!!

  • @Nickzzzera_
    @Nickzzzera_ 2 ปีที่แล้ว

    Reynold's transport theorem

  • @snp27182
    @snp27182 ปีที่แล้ว

    Why not just say you are using the negative normal to the surface, rather than using the negative of the vector field? Theirs always a positive and negative normal to a surface after all.

  • @maudentable
    @maudentable ปีที่แล้ว

    Awesome 😂

  • @sheraz1001
    @sheraz1001 2 ปีที่แล้ว

    Could you please write a little bigger?

  • @ahmadababaei3254
    @ahmadababaei3254 2 ปีที่แล้ว

    Basically it's a wrong notation to have 2 or 3 integrals with a single differential parameter (dV or dS here).

    • @tomctutor
      @tomctutor 2 ปีที่แล้ว +1

      I don't know about pure mathematicians, but in physics dV and dS quite acceptable in context.

    • @ahmadababaei3254
      @ahmadababaei3254 2 ปีที่แล้ว

      @@tomctutor What I mean is if you have a single differential parameter (dV), then you need a single integral (over the volume V). An alternative notation would be using three differentials (dX dY dZ) with a triple integral sign.

    • @tomctutor
      @tomctutor 2 ปีที่แล้ว +3

      @@ahmadababaei3254 You sound like a pure maths type, as a physicist we get away with murder.🤠

    • @ahmadababaei3254
      @ahmadababaei3254 2 ปีที่แล้ว

      @@tomctutor :))) Actually what is presented here is quite accepted and can be found in all textbooks. Still, it doesn't make it right, right?

  • @byronwilliams7977
    @byronwilliams7977 2 ปีที่แล้ว

    FIRST !