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Area terms while using Axial Symmetry
Posted Dec 7, 2012, 3:57 p.m. EST 5 Replies
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Hello everyone,
I have what I beleive to be a somewhat simple question. I would like to model simple heat convection out of a cylindrical wire or water pipe. It really doesn't matter what it is, just that I want to model simple heat convection (natural convection of air) on a cylinder. I will use the following equation:
Where q is the heat transferred per unit time (W), A is the heat transfer area of the surface (
), 
is the convective heat transfer coefficient, and dT is the temperature difference between the surface of the interface and the bulk fluid.
I am planning on applying this to a Total heat flux section of a "Heat Flux" boundary condition of a 2D axisymmetric cylinder. I want to know what I should do about the "A" or area term above. Should I assume that when calculating, COMSOL will multiply the boundary condition by the angle theta? If it does do this, my "Area" term should simply be the length of the cylinder and Comsol would take care of the rest. If not, should I include the entire Area term in the expression? so I would end up entering the surface area of the cylinder (but without the area of the ends in my case).
In short, which of the two should I enter this for the total heat flux term:
1.
OR
2.
Thank you in advance for any help!!!
John
I have what I beleive to be a somewhat simple question. I would like to model simple heat convection out of a cylindrical wire or water pipe. It really doesn't matter what it is, just that I want to model simple heat convection (natural convection of air) on a cylinder. I will use the following equation:
Where q is the heat transferred per unit time (W), A is the heat transfer area of the surface (
), is the convective heat transfer coefficient, and dT is the temperature difference between the surface of the interface and the bulk fluid.I am planning on applying this to a Total heat flux section of a "Heat Flux" boundary condition of a 2D axisymmetric cylinder. I want to know what I should do about the "A" or area term above. Should I assume that when calculating, COMSOL will multiply the boundary condition by the angle theta? If it does do this, my "Area" term should simply be the length of the cylinder and Comsol would take care of the rest. If not, should I include the entire Area term in the expression? so I would end up entering the surface area of the cylinder (but without the area of the ends in my case).
In short, which of the two should I enter this for the total heat flux term:
1.
OR2.
Thank you in advance for any help!!!
John
5 Replies Last Post Dec 13, 2012, 1:29 a.m. EST
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Posted:
1 decade ago
Hi John
Indeed it's an important question and I find it far from trivial myself (at least not when I started to use COMSOL some years ago, and we are not alone having trouble, from what I notice on the Forum) but now I feel, as probably most fluent COMSOL users, that it's such an obvious thing that we forget to say or explain it [COMSOL doc writers: you could add some nice views and explanations about this in the users guide ;]
On important thing to understand is that COMSOL uses the integral expression approach, that is also the reason for the fuss about geometrical objects, their translformation into FEM entities (Domain, of spatial dimension n, and Boundaries of dimension n-1) onto which the physics and boundary conditions respectively are applied, and only thereafter we talk about mesh and discretization, differently from older traditional FEM programmes.
Therefore on domains the expressions are given in denisties (per volume or [1/m^3] if we start with a domain = 3D space) you should read your physics as integration_over_volume(your_expression*dV) = ... and for BC respectively one spatial dimension below.
so your BC expression Q[W] = hc[W/m^2/K]*A[m^2]*DT[K] where DT is the temperature difference
you should rather think with q[W/m^2]=Q/A)
integration_over_boundary(q*dA) = integration_over_boundary(hc*DT*dA)
And remind yourself that dV volume is basically dx*dy*dz i 3D cartesian space (or viathe Jacobian transformed into any user coordinate space) and dA is a surface element typically dx*dy for a plane surface perpendicular to Z or dy*dz for a surface perpendiuclar to X etc
In 2D-axi you need to take into account the "loop length" 2*pi*r which is in fact part of the Jacobian for the cartesian to cylindrical transformation expression
It's worth to dig into the COMSOL sub-node expressions (turn them on in the preferences)
Hope this helps on the way
--
Good luck
Ivar
Indeed it's an important question and I find it far from trivial myself (at least not when I started to use COMSOL some years ago, and we are not alone having trouble, from what I notice on the Forum) but now I feel, as probably most fluent COMSOL users, that it's such an obvious thing that we forget to say or explain it [COMSOL doc writers: you could add some nice views and explanations about this in the users guide ;]
On important thing to understand is that COMSOL uses the integral expression approach, that is also the reason for the fuss about geometrical objects, their translformation into FEM entities (Domain, of spatial dimension n, and Boundaries of dimension n-1) onto which the physics and boundary conditions respectively are applied, and only thereafter we talk about mesh and discretization, differently from older traditional FEM programmes.
Therefore on domains the expressions are given in denisties (per volume or [1/m^3] if we start with a domain = 3D space) you should read your physics as integration_over_volume(your_expression*dV) = ... and for BC respectively one spatial dimension below.
so your BC expression Q[W] = hc[W/m^2/K]*A[m^2]*DT[K] where DT is the temperature difference
you should rather think with q[W/m^2]=Q/A)
integration_over_boundary(q*dA) = integration_over_boundary(hc*DT*dA)
And remind yourself that dV volume is basically dx*dy*dz i 3D cartesian space (or viathe Jacobian transformed into any user coordinate space) and dA is a surface element typically dx*dy for a plane surface perpendicular to Z or dy*dz for a surface perpendiuclar to X etc
In 2D-axi you need to take into account the "loop length" 2*pi*r which is in fact part of the Jacobian for the cartesian to cylindrical transformation expression
It's worth to dig into the COMSOL sub-node expressions (turn them on in the preferences)
Hope this helps on the way
--
Good luck
Ivar
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Posted:
1 decade ago
Ivar,
That helps me immensely! Thank you! I also would appreciate some documentation on that topic!
Along those lines, though, I have another question; and I have seen this arise in more areas than in the one example I am giving you.
For the Heat Flux node, I have three different options, General Inward Heat Flux, Inward Heat Flux, and Total Heat Flux. The first two have the same unit which is [W/m^2] and the total flux has simply [W]. For my original problem, I will probably use the Inward Heat Flux, as the formula it gives (it includes a dT term) is exactly what I am looking for.
But, what if I wasn't so lucky and had to pick the "Total Heat Flux." It's unit is [W], so does that mean I should enter in the entire heat flux of the cylinder or should I again depend on COMSOL doing an integral over the surface of the cylinder for me?
Thank you,
John
That helps me immensely! Thank you! I also would appreciate some documentation on that topic!
Along those lines, though, I have another question; and I have seen this arise in more areas than in the one example I am giving you.
For the Heat Flux node, I have three different options, General Inward Heat Flux, Inward Heat Flux, and Total Heat Flux. The first two have the same unit which is [W/m^2] and the total flux has simply [W]. For my original problem, I will probably use the Inward Heat Flux, as the formula it gives (it includes a dT term) is exactly what I am looking for.
But, what if I wasn't so lucky and had to pick the "Total Heat Flux." It's unit is [W], so does that mean I should enter in the entire heat flux of the cylinder or should I again depend on COMSOL doing an integral over the surface of the cylinder for me?
Thank you,
John
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Posted:
1 decade ago
Hi
The Heat Flux BC has 3 modes: turn on the "preferences Equation view" and see how COMSOL handles them.
By default COMSOL proposes heat densities in W/m^2 as a "field variable" that applies over the selected boundary.
But as for many cases in "engineering" we know the overall power, and the geometry defines the surface, COMSOL has added the "total power" choice, that is a lumped BC value (scalar or time dependent value). Within the BC node COMSOL calculates the total surface for you and applies an average power value of the Q0/Area.
The inward heat flux choice is convecting cooling/heating approach here "h" might be a field or just a scalar (or time dependent
--
Good luck
Ivar
The Heat Flux BC has 3 modes: turn on the "preferences Equation view" and see how COMSOL handles them.
By default COMSOL proposes heat densities in W/m^2 as a "field variable" that applies over the selected boundary.
But as for many cases in "engineering" we know the overall power, and the geometry defines the surface, COMSOL has added the "total power" choice, that is a lumped BC value (scalar or time dependent value). Within the BC node COMSOL calculates the total surface for you and applies an average power value of the Q0/Area.
The inward heat flux choice is convecting cooling/heating approach here "h" might be a field or just a scalar (or time dependent
--
Good luck
Ivar
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Posted:
1 decade ago
Thanks, Ivar! That helped my question! I now see exactly how Comsol is calculating the flux.
John
John
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Posted:
1 decade ago
Hi
still the numerics of the flux solving is still delicate (check also the KB knowledge base of the main site) Your mesh, locally to abrupt diffusion type drive changes is critical (HT or chemistry or ...) particularly in time stepping solver cases, as critical sizes for material properties, time stepping and mesh density are linked by the physics
--
Good luck
Ivar
still the numerics of the flux solving is still delicate (check also the KB knowledge base of the main site) Your mesh, locally to abrupt diffusion type drive changes is critical (HT or chemistry or ...) particularly in time stepping solver cases, as critical sizes for material properties, time stepping and mesh density are linked by the physics
--
Good luck
Ivar