Neumann Boundary Condition for thermal radiation between two bodies

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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.

MathematicaThermalRadiationQuestion.png
MathematicaThermalRadiationQuestion.png571×347 6.68 KB

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?