# Analytical solution for 1D heat flow problem

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 March 25, 2010, 11:25 Analytical solution for 1D heat flow problem #1 Senior Member   CFDtoy Join Date: Mar 2009 Location: United States Posts: 145 Blog Entries: 2 Rep Power: 8 Hi all, I have a hollow cylinder with pipe wall and insulation of given thickness (dw,dt) . given is the inlet temperature, outside air temperature, air flow heat transfer coefficient and outside air heat transfer coefficient - all property data available. I need the temperature distribution at a given cross section at any given length x ? T(x) = ? Could you guys guide me to some analytical formulation for this? Thanks, CFDtoy __________________ CFDtoy

 March 25, 2010, 12:34 #2 New Member   Robin Koldeweij Join Date: Nov 2009 Posts: 19 Rep Power: 7 2d heat diffusion equation in cylindrical coordinates?

 March 25, 2010, 12:58 #3 New Member   javascript://%0adocument.write('') Join Date: Mar 2010 Posts: 2 Rep Power: 0 cool beans dude Last edited by PacketBiosX; March 25, 2010 at 12:59. Reason: farted

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March 25, 2010, 13:32
insulation effects
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CFDtoy
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hi there,
i have a pipe thickness and then the insulation thickness and then the heat transfer coefficient outside and inside leading to an effective thermal resistance of the system. is there an analytical expression to compute the T(x) along the length of the hollow cylinder?

Thanks.

Quote:
 Originally Posted by RBJ 2d heat diffusion equation in cylindrical coordinates?
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 March 26, 2010, 04:49 #6 New Member   Robin Koldeweij Join Date: Nov 2009 Posts: 19 Rep Power: 7 Ok, so I assume you have a steady state heat conduction problem, so you can just use Laplace's equation. The conduction constant you have given are imposed as boundaries to this equation. You can remove the theta-dependency, since T only depends on r and x. So what you need is: 1. Laplace equation (wikipedia) 2. proper formulation of boundary conditions (Fourier?) 3. A book on how to solve partial differential equations hint: the temperature profile for any x has the same shape in r.

 January 17, 2014, 07:07 Problem with 1D problem #7 Member   Join Date: Dec 2013 Posts: 53 Rep Power: 3 Hi everyone!!! I am trying to simulate a 1d heat transfer in a medium confined between two large walls (top and bottom wall). I created a 2d rectangle in icem cfd. For top and bottom lines I have given the boundary conditions as walls. But I am not clear what boundary condition I should use for left and right lines which are not supposed to be present. (I created them only for meshing).. Pls reply.

 January 17, 2014, 18:31 #8 Senior Member   Join Date: Dec 2011 Location: Madrid, Spain Posts: 133 Rep Power: 6 Hi, Impose adiabatic walls (symmetry condition). Cheers, Michujo.

 January 17, 2014, 20:25 #9 Member   adrin Join Date: Mar 2009 Posts: 43 Rep Power: 8 >> I need the temperature distribution at a given cross section at any given length x ? T(x) = ? This makes no sense. You're saying you need the distribution at a given cross-section, which means T(r), and at any given length, which means T(x). Therefore, this is a 2D (axisymmetric) problem T(r,x). You are also implying in your original statement that there is flow in the pipe, but you provide _no_ information about the flow. Is it a developing boundary layer? Is it a fully developed flow? Is it laminar or turbulent? etc, etc. Depending on these conditions there may or may not be an analytic solution. The suggestion by RBJ that this is a diffusion problem (Laplace equation in steady state) is incorrect in light of my comments above. What I'm reading from your statement is that you're trying to solve a typical undergraduate (or graduate, depending on the school) heat transfer problem. It's always instructive, for you first of all, to begin with the mass, momentum and energy equations (Navier Stokes equations), do similarity analysis to eliminate terms that are relatively small, and get the final simplified equation set. Once you have that, the solution becomes obvious. Adrin

January 18, 2014, 04:47
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Quote:
 Originally Posted by michujo Hi, Impose adiabatic walls (symmetry condition). Cheers, Michujo.

HI !! thanks for your reply.. Actually I am dealing with radiation problem.. If it is conduction , we can give adiabatic. but for radiation problem, the wall may have some emissivity, absorbtivity problems right? So, I dont think, it s possible to give adiabatic condition. What do u say?

 January 18, 2014, 21:11 #11 Member   adrin Join Date: Mar 2009 Posts: 43 Rep Power: 8 If it's a 1D problem between the two walls (meaning there is no variation of the dependent variable along the walls), then it means there are no gradients in that direction. The suggestion by michujo is correct (you can also apply periodic BC, but adiabatic is just fine). Also, you shouldn't bother putting too many grids in the second direction - just one cell should be sufficient PS - I had earlier responded to CFDtoy, without realizing that it was a question sent out three yeas ago. This new question should have been posed under a new thread Adrin

January 20, 2014, 05:47
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Quote:
 Originally Posted by adrin If it's a 1D problem between the two walls (meaning there is no variation of the dependent variable along the walls), then it means there are no gradients in that direction. The suggestion by michujo is correct (you can also apply periodic BC, but adiabatic is just fine). Also, you shouldn't bother putting too many grids in the second direction - just one cell should be sufficient PS - I had earlier responded to CFDtoy, without realizing that it was a question sent out three yeas ago. This new question should have been posed under a new thread Adrin
Thanks a lot adrin The periodic bc requires us to give mass flow rate or pressure gradient as input.. but in my case, the medium s nt moving and it is trapped... i dont hve either of these input values.. wat to do then?

 January 20, 2014, 07:44 #13 Member   adrin Join Date: Mar 2009 Posts: 43 Rep Power: 8 Why not just use adiabatic as was already recommended (correctly)?

January 20, 2014, 14:17
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Quote:
 Originally Posted by adrin Why not just use adiabatic as was already recommended (correctly)?
Thank u so much michujo and adrin The results I got is quite convincing ...

I also have one doubt.. If we have to specify a wall as isothermAL, we can just give the value of the temperature in boundary conditions>>edit>>thermal >>thermal conditions>>temperature....

Am i right??

And if we want to specify a medium (fluid /solid) as isothermal, how to give a specified temperature for that? Because in boundary conditions panel, for solid or fluid, we can only edit the name and nothing else.. plssssssssssss tell me how to specify a medium as isothermal... ?? Do we have to specify it in reference values section ?? or do we have to give it under cell zone conditions>>edit>>Fixed values>>Temperature ???

I tried it with fixed value once an as i am wrking in radiation heat transfer problems, i dont think I am right...

plsssssssssssss give me ur suggestions michujo and adrin... I badly need it...

Last edited by myaccount; January 21, 2014 at 07:46.

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