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?
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!
Great question. We have to be careful with the math here. We are not multiplying those terms; we are taking the partial derivative of kr dt/dr with respect to r. The 1/r term is on the outside of that partial derivative. I hope that helps.
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.
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
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.
r cannot be taken out because r is a variable. For example you can take k out if you assume that the material is isotropic but you cant if k changes inside the material with direction (anisotropic), that is, it is a function of radius r. It is just like differentiation of (1/x)*d(x^2)/dx or d(2*x)/dx where you cant take x out because it needs to be differentiated.
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.
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.
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.
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?
Dana Plant r is constant wrt phi
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!
Will work on having this up soon. Thanks for the suggestion!
Any updates on the spherical coordinates?
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?
Thank you so much...this too tough for me to understand during the class discussion...now u just save me from being dead..😂
You are great :) All we need now is the spherical coordinates
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?
Great question. We have to be careful with the math here. We are not multiplying those terms; we are taking the partial derivative of kr dt/dr with respect to r. The 1/r term is on the outside of that partial derivative. I hope that helps.
Fabulous explanation
why doesn't the (1/r) cancel with the r in the first term of the equation?
We are taking the differential element, then why rdθ why not ∆rdθ?
How about in a one dimentional? thanks
You did a great job. Congratulations :)
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.
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
Clear explanation! Thanks
Great video !!!
could you post one on spherical coordinates ??
For the slow kits in the crowd, it would help if you did a quick example.
+Dustin Smith We'll see if we can make a new screencast for that. Thanks for watching!
Thanks u sir ur method is very good
why theres no polar coordinat there?
Great video man...:)
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.
ρ*cp*dT/dt has as its units Kg*W/m^3 ... every other term's units are W/m^3 ... what's happening!!???
with the dr term why r is not canceled out bcx r is in both numerator and denominator.... ??????
r cannot be taken out because r is a variable. For example you can take k out if you assume that the material is isotropic but you cant if k changes inside the material with direction (anisotropic), that is, it is a function of radius r. It is just like differentiation of (1/x)*d(x^2)/dx or d(2*x)/dx where you cant take x out because it needs to be differentiated.
thanks dear. (Y)
Jamal Khan when r is with phi we are able to take it out because r is constant as it is with partial change with phi ?
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.
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.
i forgot to thank you for this video..great help..thanks
i hope if you write ur email i will send u the volume element
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.
very helpful. Thank you so much
great video... thanks
Please, we need ( heat conduction in spherical coordinates )
Thank you very much u saved me
Thanks mate👍
One thing sir plzz do it with label diagram
thnku sir ,you are great
Spherical?
very helpful thanx a lot
great video thx
really helpful
Thank you!
Thanks man!!
Awesome !
THANK YOU
thanx Alot More helpful
awesome!
than k you very much
Spherical?
Thank you!