Discussion Forum

Hi

your model is fully symmetric so you could even use just a partof it.

Well how do you define your "heat transfer coefficient ? is it k[W/m/K] ? and with respect to what ? :
cylinder thickness, radius, sphere radius, assumed placed in the middle of the cylinder ?

Then I would set a constant temperature T0 at one face (upper or lower) of the cylinder, set a constant power of 1[W] on the lower surface, and run a stationary study, even with parameters to change Lcyl, Rcyl, and/or Rsph and plot out

Average T on the Q=1[W] surface and deduce (with correct units) the result:

k_eq = 1[W] / Lcyl / (Aveop1(T)-T0)

To validate, you couls check that when you put all material PMMA and all ALN and run the same study you get k_eq = k_pmma and keq=k_aln respectively, and that k_aln>k_eq>k_pmma

even you should expect to have some rule of the type 1/k_eq = Const1/k_pmma+Const2/k_aln where Const1 and 2 are related to the geometry sizes

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Good luck
Ivar

Thanks for your help. Thermal expansion co efficient value, cylinder dimensions are given in the paper it self. In the Literature by increasing volume fraction of ALN in PMMA, they calculated thermal conductivity value. PMMA thermal conductivity value is low compare to ALN. By increasing ALN concentration value in PMMA ,Thermal conductivity of the composite will increase.
for the validation i followed the same procedure as per you mentioned i got the same value.
Using comsol , how to define volume fraction value of ALN (1% , 2% of volume fraction of ALN) in PMMA. Previously I had calculated PMMA volume(cylindrical shape (Pi*R^2*h)).Then I take 1% volume of cylinder =volume of the sphere(4/3 *pi*r^3).

In the input file i calculated 1% volume of cylinder= volume of sphere.


Rcy=6.35mm, Hcy=2mm. Rspehere=0.8mm for 1% volume calculation.

Could you help me whether I am following correct procedure for calculating volume fraction value.

If ALN particle size(sphere) should be less then 5um then what are the procedure i need to follow ?

Thanks for your help. Thermal expansion co efficient value, cylinder dimensions are given in the paper it self. In the Literature by increasing volume fraction of ALN in PMMA, they calculated thermal conductivity value. PMMA thermal conductivity value is low compare to ALN. By increasing ALN concentration value in PMMA ,Thermal conductivity of the composite will increase.
for the validation i followed the same procedure as per you mentioned i got the same value.
Using comsol , how to define volume fraction value of ALN (1% , 2% of volume fraction of ALN) in PMMA. Previously I had calculated PMMA volume(cylindrical shape (Pi*R^2*h)).Then I take 1% volume of cylinder =volume of the sphere(4/3 *pi*r^3).

In the input file i calculated 1% volume of cylinder= volume of sphere.


Rcy=6.35mm, Hcy=2mm. Rspehere=0.8mm for 1% volume calculation.

Could you help me whether I am following correct procedure for calculating volume fraction value.

If ALN particle size(sphere) should be less then 5um then what are the procedure i need to follow ?

Hi

OK but then you have 2 approaches, your method with one lumped sphere might be sovled by a FEM model as you built it,

but if you say you are mixing two materials in a homogenious way then you could probably use a rule of the type

k_eq = (1-pr_aln) * k_pmma + pr_aln * k_aln (for parallel conductances, and the "1/" for serial conductances)

where pr_aln is therelative material volumic ratio of the ALN , but it all depends on what you want to show

You could apply similar formulas for rho, and Cp

make it a try, and perhaps take a look at the COMSOL approach for two mixed material in i.e. porous matrerial examples

Have you checked articles like:
"Numerical analysis of effective thermal conductivity of mixed solid materials" Zhang Yinping, Liang Xingang, Materials & Design, Volume 16, Issue 2, 1995, Pages 91–95, the first that showed up on a quick google search ;)

or www.owlnet.rice.edu/~ceng402/proj02/sleung/finalproject.htm
or www.ias.ac.in/matersci/bmsaug2004/373.pdf

Obviously if your material is not only mixing, but also chemically reacting, you wil get different results, and the simple formulas above will no longer hold, in details, but then you need also to adapt your FEM with other material properties

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Good luck
Ivar

Thanks for your help. with this i had attached one file about my doubt and simulation file .Could you let me know my mistake.

Hi

I'm not sure there is anything "wrong" apart that I would not define any boundary layer, just leave the "domains"

Now you have 3 variables: radius of sphere, radius of cylinder and height of cylinder, while the other formulas from the articles, are related to a sphere inside (and same "centre" of) a cube hence only two variables cube length and sphere radius.

To check the formula you need to reproduce exactly the same conditions, it works rather well for a stationary case (cube and sphere) see attached model (4.3a) but then there are two remarks, first for dynamics none of these formulas (and only a correct FEM model) will give you the right values, and what about the BC you use, I have tried both fixed T on bottom, constant average power on top, and fixed T on top and on bottom, with a fixed DT. for the stead state conductance one get the same average value, but looking closer on the heat flux values, or the T variation on the constant flux side one see quite some variations in flux to get the same constant temperature.
Ideally I should set periodic T values at the two/four vertical Boundaries, in addition to isolation/symmetry but with a regular mesh these conditions should be rather equivalent anyhow

My model has a 2D (cylinder in cube), and 3D true sphere in cube model, only the later agrees well with the formula

For your case you need to adapt the cylinder radius to the cylinder height and then adapt the values to your volume fraction
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Good luck
Ivar