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# Deriving an expression for the heat flux as a function of radius (HARD!)? watch

1. Hi guys, I have the answer but I don't know know the thought process behind it, can you help me?
The cylindrical coordinates are:
1/r (r dT/dr) + g/λ = 0

the answer is in the attachment. But how do I get from the above equation to it?
(I accidentally cut abit off. The rest reads: heat flux = -λ dt/dr = g0r/2 ).

Many Thanks
Attached Images

2. (Original post by Mr Mondai)
Hi guys, I have the answer but I don't know know the thought process behind it, can you help me?
The cylindrical coordinates are:
1/r (r dT/dr) + g/λ = 0

the answer is in the attachment. But how do I get from the above equation to it?
(I accidentally cut abit off. The rest reads: heat flux = -λ dt/dr = g0r/2 ).

Many Thanks
I'm confused what you're stuck with. You have the equation you mentioned in the post, which I bolded. You re-arrange, integrate w.r.t r, then use the conditions that when , thus you can find the constant of integration.

Are you familiar with how to integrate?
3. (Original post by Phichi)
I'm confused what you're stuck with. You have the equation you mentioned in the post, which I bolded. You re-arrange, integrate w.r.t r, then use the conditions that when , thus you can find the constant of integration.

Are you familiar with how to integrate?
I'm sorry if I sound abit thick, but: aren't all the r's on the same side? and when you integrate 1/r you get ln (r) ?, then integrating r dT/dr = r ?
Again, sorry but I'm having a very hard time with this
4. ahhhhh my mistake, I have attached a pic of the question (b), now
5. (Original post by Mr Mondai)
ahhhhh my mistake, I have attached a pic of the question (b), now
The equation you initially gave is not what they used. They times through by r, then just integrate, where are you stuck?

Spoiler:
Show

Integrate w.r.t r

Given when you can find that

6. (Original post by phichi)
the equation you initially gave is not what they used. They times through by r, then just integrate, where are you stuck?

Spoiler:
Show

integrating w.r.t r

given when you can find that

ahhhhhhhhh thank you!!!! I understand it now! Thank you for your help :d
7. (Original post by Mr Mondai)
ahhhhhhhhh thank you!!!! I understand it now! Thank you for your help :d
I changed it slightly as LaTeX broke on me, but you're purely misreading the equation I assume. No worries

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