Stage 1
One-dimensional model
Established an axial temperature profile and an initial thermocouple energy balance.
Academic case study · Heat transfer
Hencken burner thermal analysis.
One-dimensional and axisymmetric finite-difference models of thermocouple heating by conduction, convection, and radiation.
- Model
- 1D and 2D axisymmetric
- Method
- Finite differences · SOR
- Physics
- Conduction · convection · radiation
- Maturity
- Analysis complete
01 · Problem
Thermocouple temperature inside the burner.
Heat-transfer model
The analysis estimated the temperature a thermocouple assembly could reach inside a Hencken burner. The energy balance included heating from the surrounding gas and radiation, along with conduction through the thermocouple structure.
The initial model established the dominant terms, but it could not represent radial gradients or the interaction between the bead, stem, and surrounding environment.
Reason for the 2D modelThe axisymmetric formulation resolved radial gradients that were missing from the one-dimensional model.
02 · Numerical approach
One-dimensional and axisymmetric models.
The model combined conduction, convection, and radiation terms. The numerical solution was checked with convergence and sensitivity studies.
Stage 2
Axisymmetric model
Added radial resolution so the bead and stem geometry affected the predicted temperature field.
Solver
Gauss–Seidel SOR
Iterated the finite-difference field and used bisection where the nonlinear radiation terms required it.
Checks
Sensitivity and limitations
Evaluated the effect of assumptions and parameter values on the result.
03 · Result
Model prediction and recommended range.
The 2D model predicted a peak temperature of 2385 K. Because that value depends on the model assumptions and was not experimentally validated, the report recommended a conservative range of 1900–2000 K.
2385 K model predictionThis is a simulation result, not a certified hardware limit. The recommended range remained 1900–2000 K.
04 · Methods used
Finite-difference thermal analysis.
- Converted the heat-transfer problem into a finite-difference system.
- Added a 2D axisymmetric model when the 1D assumptions became limiting.
- Included internal radiation with conduction and convection.
- Used sensitivity results and stated limitations to interpret the prediction.