# Heat conduction numerical model

1. Feb 13, 2015

### elt93

Hi Guys,
I'm new on this forum, currently studying Aerospace Engineering and am trying to produce the model of a radioisotope thermoelectric generator using numerical methods to solve the heat conduction equation as part of my research. The way it works is that I have a radioisotope source in the middle (let say a cube) generating a thermal power of x W/m3. Different configurations are possible but I want to start as follow. This source is surrounded by a cladding made of a specific alloy to shield it. On top and bottom of this cube there are thermopiles which on one end receive heat from the cladded source and on the other end radiate heat to space. Now, on the sides of this assembly there is a thermal insulator with non zero heat conductivity. My question is the following: Do I need to model this in 2D or 3D to couple the heat losses in the insulator as well as the heat "given" to each distinct thermopile or can I just do simple 1D models in each direction ? In the latter option, should I find the power given by the source to the insulation and substract it to what is given to the thermopile or is this not necessary and I can isolate each case ?

2. Feb 13, 2015

### DEvens

Mmm! Radio thermal generators. Ahhhhhh! (Insert picture of Homer with his tongue hanging out.)

I would suggest starting with a simple 1-D equilibrium model. Then measure a real device and see if your code matches reality accurately enough for your purposes. If not then you may need a 2-D or a time dependent. And again compare to measurements. Hopefully you won't need a full 3-D time dependent.

It's really very hard to know in advance how accurate and detailed your model needs to be.

3. Feb 13, 2015

### elt93

Thank you! If doing 1D, I guess I need to apply a 1D model in each direction otherwise the power outputted to the thermopiles will be largely overestimated (ignoring heat loss in the insulator and the surroundings). If so, how could I couple these 1D models to make sure the power equilibrium is respected ?

4. Feb 13, 2015

### bigfooted

5. Feb 15, 2015

### elt93

Thank you for all this guys, I think I'm gonna start with a 2d model and then refine from there if needed. Last question: At the boundaries of different materials (different conductivities) do I need to set an energy balance to obtain the heat flux out of the hot material and then input that heat flux in the cold one or can I just applied this scheme:
k(T(i-1,j)-T(i,j))/dx+k(T(i+1,j)-T(i,j))/dx+k(T(i,j-1)-T(i,j))/dy+k(T(i,j+1)-T(i,j))/dy+(heat generation)dxdy=0 ? Basically I'm just not sure whether I'm actually allowed to vary these k according to the material containing the node or if it should stay the same