Heat Equation Derivation: Cylindrical Coordinates 

Cengel's 5th ed: "After lengthy manipulation, we obtain [Conduction Equation in cylindrical coordinates]" In my opinion, the author of the book clearly had no respect for the reader's intellectual capacity. This is pretty straight forward, even though I could not think of it myself at first.

In the second term of the final equation, why is it written (1/r)(d/dr)(kr dT/dr) instead of just (d/dr)(k dT/dr)? Why not eliminate the r from that term?

Awesome video, had the exact concepts that I was looking for! Been working on a problem involving heat conduction in spherical coordinates, and was able to take the method here and apply it to my specific problem. Thanks for the clear explanation, really appreciate the effort that went into this video!

at 6:45 you substitute from fourier's law but you pull the "r" that is with the d(phi) into the parenthesis for the first term (d/dr term) but that is not the case for the other two terms...why is that?

Will work on having this up soon. Thanks for the suggestion!

Hello How are you doing brother ? Why don't you drive for ? Heat Equation : spherical Coordinates Would you mind do a video explaining the derivation Please guys give me like in order to let (LearnChemE) to see my comment ..and do a video for this type of an equation best regards

big respect for you man. love from Iran

Thank you...from an ..Indian.....😊.....Very helpful and time consuming video.......make more videos like this 😀......

do you have the same video but in spherical coordinates?

Hey, really nice video! I want to add why there's a "r" in dV=rdθdrdz. In other way, it's dV=dAdz=(rdθ)(dr)dz and (rdθ)(dr) comes from calculating the bottom area of a very small(differential) volume in cylindrical coordinates, analogous to dxdydz in Cartesian coordinates. So, how does (rdθ)(dr) become the bottom area in cylindrical coordinates, when it's shaped like a circular sector instead of a simple rectangle? That's because since we're calculating a differential scale, the circular sector shape could be regarded as a rectangle when calculating its area.

For the slow kits in the crowd, it would help if you did a quick example.

Thank you so much...this too tough for me to understand during the class discussion...now u just save me from being dead..😂

Fabulous explanation

I have a question: i the general equation you have 1/r d/dr multiplied by (kr dt/dr). shouldn't the r's cancel out?

why doesn't the (1/r) cancel with the r in the first term of the equation?

The second part of your statement is correct but the first isn't. The differential distance is already included in the definition of q_Phi and it doesn't make sense to compute the taylor series expansion with r*d Phi. Think about it, if you that were the case we wouldn't be able to write the taylor series expansion of an unknown function because we wouldn't know the factors to the differential we're multiplying. It's a great video, the only thing missing the one you pointed out.

You are great :) All we need now is the spherical coordinates

Clear explanation! Thanks

3D solution (programming done in MATLAB) of discretized momentum, energy and mass balances for an arbitrary gas phase reaction (pressure variations must be taken into account) taking place in a tubular reactor with baffles and equipped with a heat exchanger, please.

We are taking the differential element, then why rdθ why not ∆rdθ?

Great video !!! could you post one on spherical coordinates ??

Thanks u sir ur method is very good

How about in a one dimentional? thanks

You did a great job. Congratulations :)

please could you draw us an elemental volume for a sphere,like you drew here for cylindrical coordinates,i am having a hard time understanding the "rsin(theta)d(pHi)" dimension in the derivation for heat conduction in spherical coordinates,other videos dont have a clear explaination for it.

ρ*cp*dT/dt has as its units Kg*W/m^3 ... every other term's units are W/m^3 ... what's happening!!???

Great video man...:)

One thing sir plzz do it with label diagram

Please, we need ( heat conduction in spherical coordinates )

great video... thanks

Thank you!

very helpful. Thank you so much

why theres no polar coordinat there?

Thanks mate👍

thnku sir ,you are great

Thank you very much u saved me

Awesome !

great video thx

very helpful thanx a lot

Thanks man!!

really helpful

with the dr term why r is not canceled out bcx r is in both numerator and denominator.... ??????

I disliked the video because you had an error and you seemed to skip a bit of math at the end, which would have revealed the error. In the video you show that q_(Phi+d Phi)=q_Phi + partial of q_Phi wrt Phi, *d Phi, but the end should be r*d Phi, since as you stated we are dealing with a differential distance, and d Phi would only be a arc length...Then you do not explain in any way why the r for the radius term stays in but the den. r comes out in the Phi term.

than k you very much

THANK YOU

Spherical?

awesome!

thanx Alot More helpful

Thank you!

Spherical?