Wow, as a physics student learning electromagnetism this helped a lot, because I could do analogous thinking in terms of potential, electric field and charge density. Thanks!!! :)
Nice Graphic representation, but I´m affraid That the Vector Arrows be greater in the center and lower on the edge, I mean fatter at center and gradually thiner.
that would be the case if you were talking about the temperature only but here we are talking about the rate of flow of heat which of course depends on the temperature difference. Here at the surface of the rod, the temperature difference(with the coolant) is much higher than within the rod. Hence the longer vector arrows.
A lesson on vectors and why I'm right. If you have basis vectors i, and j. If you dot i with itself you get ||i|| ||i|| cos(0) = 1*1* cos (o) = 1. The vectors drop out. See where I'm going?
Maybe not so, the temperature will fall off more rapidly near the edge interface to the conducting coolant medium. Therefore the magnitude of the vector field which graphically represents the flow of heat will be greater (longer) near the edge, shorter near the core or center.
Divergence refers to the flow of the heat. When the rod is heated, the heat will flow out from the center. When the rod cools, it slows down. Now, in your mind, pretend like I just told you that with a very sophisticated English accent. 😁 Oh, and don't you dare forget to pour yourself a piping hot spot of tea.🙃
Think of it like this , J is a vector field assume its radial so its vector field function will look similar to J(x,y)=[c*x,c*y] which means that at every point in space a vector J is associated with it whose component in x direction at that point is Jx(x,y)=c*x(i hat ) and y component Jy(x,y)=c*(j hat) Now J has units of energy per unit time In order to locate "source" of any vector field what you can do is take any region and enclose it with a surface ("closed surface") , when you find surface integral of vector field you will have have a scalar quantity which represents net quantity( which is represented by vector field) that has "flowed" out of that closed surface, Energy in our case The smaller the area more accurate the measurement or in simple terms how much that region behaves like "source".Now u just check any wikipedia page you can follow the maths from there
It's probably because you don't have a background in vector calculus and nuclear physics. He's talking about controlling the heat in them there rods bub.
@@yk_ramzesz20 The chain rule for partial derivatives brother. That's how you prove that the gradient vector is always perpendicular to the level curve. I'm just a lil o school teacher. LOL
![Div, Grad, and Curl: Vector Calculus Building Blocks for PDEs [Divergence, Gradient, and Curl]](/img/1.gif)
Wow, as a physics student learning electromagnetism this helped a lot, because I could do analogous thinking in terms of potential, electric field and charge density. Thanks!!! :)
Yes Yes of course Mr. Einstein, and we all know what you're up to?
Read Maxwell.
Divergence of J is utilized to find the scalar. Div is a dot product.
Curl - a measure of rotation, isn't mentioned in this video.
This should have mentioned that div(grad(F)) can be written as the laplacian(F) since it's such a commonly used operator
+The Flagged Dragon right it should.
thanx that helped alot in understanding my vector analysis course
Sure it did. Now tell us another LIE Dr. Who.
It's used in controlling intensity. Watts/m^2 is intensity.
like a point of positive electric charge emiting electric field vector field
Nice Graphic representation, but I´m affraid That the Vector Arrows be greater in the center and lower on the edge, I mean fatter at center and gradually thiner.
that would be the case if you were talking about the temperature only but here we are talking about the rate of flow of heat which of course depends on the temperature difference. Here at the surface of the rod, the temperature difference(with the coolant) is much higher than within the rod. Hence the longer vector arrows.
شرح جميل. .شكرا
Substitute the gradient of J1 and J2 into the upper equation and PRESTO
A lesson on vectors and why I'm right. If you have basis vectors i, and j. If you dot i with itself you get ||i|| ||i|| cos(0) = 1*1* cos (o) = 1. The vectors drop out. See where I'm going?
Maybe not so, the temperature will fall off more rapidly near the edge interface to the conducting coolant medium. Therefore the magnitude of the vector field which graphically represents the flow of heat will be greater (longer) near the edge, shorter near the core or center.
Not as good as the other two. I'm still a bit confused as to what divergence us 🤔
Divergence refers to the flow of the heat. When the rod is heated, the heat will flow out from the center. When the rod cools, it slows down. Now, in your mind, pretend like I just told you that with a very sophisticated English accent. 😁 Oh, and don't you dare forget to pour yourself a piping hot spot of tea.🙃
Pour lol
A better explanation is that divergence is the limit of flux. Divergence is essentially flux at a single point.
Terima kasih pak
The red analogue telephone (I guess it's a bad sign if it rings). The CRT computer monitors. I wonder how it's changed today.
J is the intensity vector.
Good video!
It is surprising how hot the fuel rods get, 900C in the centre.
The magnitude of J is the heat intensity.
Still, the divergence isn't clear to me.
Think of it like this , J is a vector field assume its radial so its vector field function will look similar to
J(x,y)=[c*x,c*y]
which means that at every point in space a vector J is associated with it whose component in x direction at that point is Jx(x,y)=c*x(i hat ) and y component Jy(x,y)=c*(j hat) Now J has units of energy per unit time
In order to locate "source" of any vector field what you can do is take any region and enclose it with a surface ("closed surface") , when you find surface integral of vector field you will have have a scalar quantity which represents net quantity( which is represented by vector field) that has "flowed" out of that closed surface, Energy in our case
The smaller the area more accurate the measurement or in simple terms how much that region behaves like "source".Now u just check any wikipedia page you can follow the maths from there
@@denishtrivedi3071 could you explain solenoidal vector?
Divergence is the limit of flux through an infinitesimal area. It is a scalar.
Only if I got money every time the old man blinked 😔
I feel that
This made no sense to me.
It's probably because you don't have a background in vector calculus and nuclear physics. He's talking about controlling the heat in them there rods bub.
@@guitarttimman dude I graduating from electrical engineering and I still don't understand how to do vector calculations from this video check Chegg
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@@yk_ramzesz20 The chain rule for partial derivatives brother. That's how you prove that the gradient vector is always perpendicular to the level curve. I'm just a lil o school teacher. LOL
great
Lol they have robotics that do all of that now, wow how times have changed...
Kappa
In Jesus' Name, Amen. God bless you ✨
Woke
shit.
+Goran Hazar use good language