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Neumann Boundary Condition for thermal radiation between two bodies

Posted 4 months ago
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Hi All,

I'm trying to formulate and solve a pde which models thermal radiation between two bodies using a Neumann boundary condition.

I've created a mesh and want to capture the thermal radiation heat transfer between element 106 and element 19 in the boundary mesh wireframe plot below.

enter image description here

I've modelled convective BCs as follows:

GconvPistComb = NeumannValue[hPistComb*(TPistHeat - temp[z, r]), ElementMarker == 106];
GconvBlkCool = NeumannValue[hCoolWater1*(TWater1 - temp[z, r]), ElementMarker == 75]

The pde with just these included looks like:

pde = {1/r D[-kMesh r D[temp[z, r], r], r] + D[-kMesh D[temp[z, r], z], 
     z] == GconvPistComb + GconvBlkCool

If I were modelling the thermal radiation from ambient gas to element 19 I would use the following Neumann BC in which TAmb is a pre-defined fixed value:

GradAmbTest = 
      NeumannValue[Epsilon Sigma (TAmb - temp[z, r])^4, 
       ElementMarker == 19];

How can I replace TAmb with an expression that represents the solved temperature field for Element 106?

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