Temperature profile inside a pellet

[oksuz_]

Hi,

As some of you may know, the temperature profile inside a pellet is determined by using the equation given below,

T_x=T_Rim+ρ(r_pellet²-x²)(4Kf)^-1

Where;
ρ is power density.
Kf is thermal conductivity.

The temperature profile is strictly dependent on the material used as a fuel. The figure given below shows this dependency,

Here, the fuel pellet diameter, r_pellet is 20 mm, and ρ is 250 W/cm^3.

What I want to know is that how the temperatures are different for each material at the center of the fuel pellet since the amount of the fission energy produced inside a fuel pellet depends only on which fuel (U-235, U-238, e.t.c.) is used. Different materials can cause different temperature profiles due to having different thermal conductivity, but I do not understand how temperatures are different at the center.

Maybe I am missing something. Any comments would be appreciated.

 

[drvrm]

Maybe I am missing something. Any comments would be appreciated.

while looking at literature i came across the following which may be of interest;

<https://www.nuclear-power.net/nucle...-generation/temperature-profile-nuclear-fuel/>

 

[anorlunda]

Do different isotopes of the same element have different thermal conductivities? I think no, but I can't find a source that says that explicitly.

 

[drvrm]

Do different isotopes of the same element have different thermal conductivities? I think no, but I can't find a source that says that explicitly.

quote;
<... in solving materials science problems related to nuclear fuel, researchers are usually interested in elemental composition of the fuel pellets, because the chemical and thermal physics properties are the same for different isotopes of one chemical element. Nevertheless, for modeling of the elemental composition one should perform calculation of the isotopic composition and carry out the summation over all isotopes of a given chemical element. ...>Prediction of the Material Composition of the VVER-type Reactor Burned Pellet with Use of Neutron-Physical Codes
Mikhail Ternovykh1, Ivan Saldikov1, Georgy Tikhomirov1, and Alexander Gerasimov2
1 National Research Nuclear University MEPhI (Moscow Engineering Physics Institute), Department of Theoretical and Experimental Physics of Nuclear Reactors, Kashirskoe shosse 31, Moscow, 115409, Russia
2 NRC Kurchatov’ Institute - Institute for Theoretical and Experimental Physics, Department of nuclear reactors, Moscow, Russia.

<https://www.knepublishing.com/index.php/KnE-Materials/article/download/1>

 

[256bits]

Different materials can cause different temperature profiles due to having different thermal conductivity, but I do not understand how temperatures are different at the center

The key us that you have a constant power source, rather than a constant temperature source such as a flame within the cylindrical pellet.
Take a look at the diagram of temperature profile once more.
For the metal, a good conductor, heat can flow readily from the interior to the exterior.
For the oxide, a poor conductor, heat does not flow as readily.
What does that tell you what should happen to the temperature in the interior.

 

[rpp]

It isn't an issue with what isotopes fission, it is an issue with the thermal conductivity of the material (metal, nitride, oxide, etc.).
Each of these materials have different thermal conductivities.

The metal has the highest thermal conductivity, so the heat will transport through a metal the easiest, and the peak temperature will be lower.
Oxides have a lower thermal conductivity, so the heat will transport less easily, and the peak temperatures will be higher.

If the physics doesn't make sense, look at the math. If you increase the thermal conductivity (Kf), it will lower the quantity on the right hand side, which will decrease the temperature. If you decrease the thermal conductivity, it will raise the quantity on the right and increase the temperature.

 

[oksuz_]

Thank you for all your replies.

I felt that it was related to thermal conductivity. However, I expected the temperature at the center was the same for all materials while there is a rapid temperature drop for a material that has a high thermal conductivity.

The equation given above manifests the temperature profile as it is given in the graph. However, I am not somehow satisfied.

Any more comment would be appreciated.

 

[gmax137]

temperature at the center was the same for all materials

Why would you expect that?

 

[oksuz_]

Why would you expect that?

The volumetric heat generation rate is same for all materials. Am I thinking wrong?

 

[gmax137]

well that's right. But at steady state, all of the heat generated has to be leaving the pellet, right? What determines that? How does the heat generated at radius r get out to the edge?