The effect of bifurcation on numerical calculation of conjugate heat transfer with radiation

- Unexpected behavior of numerical solution of conjugate heat transfer problems is demonstrated and discussed through solution of a simple example.
- Discussion is presented of whether and how the presence of bifurcation/chaos in the solution of the quartic character of conjugate heat transfer formulations may or may not reflect the actual physical behavior of the system being modeled.

The behavior of numerical solutions to conjugate heat transfer problems when thermal radiation is significant is discussed. Hidden behavior that can prevent convergence of numerical techniques is shown through a simple example and comparison with analytical solution of the resulting quartic equation. The paper illustrates why the nonlinear form of the governing energy equations can present unexpected behavior in numerical solutions, and this can prevent converged solutions in many cases. Discussion of whether apparent bifurcation/chaos in the solution has meaning in this class of problems is discussed.