Is the heat transfer equation inaccurate?

Hi Joel,

we validated the heat transfer model a couple times, so I am confident it's ok in the source code. But I can double-check for the next release
Can you send me the papers with the equations high-lighted to my email address (it's given in the header of any file in the src directory)

Best wishes
Christoph

Hello!

I realize this was 5 years ago, but I was looking into these details when I found Joel's post. I think he may be correct.

It seems to me the liggghts equation for particle-particle conduction overestimates heat conduction by a factor of pi^0.5, compared to the cited paper.

I will try to lay out the reasoning:

The paper cited by liggghts is Chaudhuri et al., 2006 (Modeling of heat transfer in granular flow in rotating vessels).
The form of the equation they write in that paper is different than what appears in liggghts, as they have combined it with some solid mechanics properties, but Chaudhuri didn't develop the heat transfer model - they just used the equation developed by Batchelor and O'Brien, 1977 (Thermal or Electrical Conduction Through a Granular Material). So we should actually check that paper for the equation.

The original model by Batchelor and O'Brien is:
q = 2 * k * contact_radius * (T_i - T_j)

The equation in the liggghts documentation and source code is as follows (I just factored out the 2 in the first term):
q = ( 2 *k_i*k_j / (k_i + k_j) ) * 2 * (contact_area)^0.5 * (T_i - T_j)

The first term ( 2 *k_i*k_j / (k_i + k_j) ) accounts for different thermal conductivities, and it collapses down to just k if k_i and k_j are equal. Making this simplification:
q = 2* k * (contact_area)^0.5 * (T_i - T_j)

Now, comparing this to the original Batchelor and O'Brien equation, the only difference is the liggghts version has the term contact_area^0.5 vs. the term contact_radius in the original.

The contact_area and contact_radius should be related with the area of a circle, A = pi*r^2. Rearranging, contact_radius = (contact_area/pi)^0.5.

Substituting this in for the contact radius in the Batchelor/O'Brien equation shows that the correct equation should be:
q = 2* k * (contact_area/pi)^0.5 * (T_i - T_j)
which differs from the liggghts equation by a factor of (1/pi^0.5). Leaving out this factor of 0.564 would cause a very large overestimation in heat transfer compared to the cited work.

With the equations now laid out simply, can the liggghts team check this work and the implementation? Is there something else that I (and evidently Joel) are missing?

Much thanks for checking!

Evan