It looks like the error is due to an insufficiently constrained thermal model, which can happen when Fluent and Steady-State Thermal are not properly coupled. Here are a few things to check and try:

Potential Causes and Solutions

1. Ensure Proper Coupling Between Fluent and Thermal Solver

• Check that the interface between the solid and fluid domains is correctly defined. In ANSYS Workbench, the contact type should be "Coupled" (not just "Bonded" or "Frictionless").
• In ANSYS Fluent, enable Conjugate Heat Transfer (CHT) to ensure proper heat transfer between solid and fluid.

2. Boundary Condition Issues (Ill-posed Problem)

• The error suggests an ill-conditioned matrix, which means the thermal model might not have enough constraints to find a unique solution.
• Applying only a heat flux on the solid bottom and a convection condition on the fluid top might not fully constrain the system.Why does setting a constant temperature work?When you set a constant temperature, the solver has a fixed reference to balance the system. However, with only a heat flux and convection, the system might be underconstrained. What to try:Instead of only using heat flux, try specifying a small reference temperature somewhere in the solid domain (e.g., a small portion with a fixed temperature). Alternatively, check if defining a convective boundary condition on the bottom of the solid domain (instead of pure heat flux) improves the solution.

3. Check Mesh Quality and Contact Conductance

• If the mesh near the interface is too coarse, heat transfer might not be well-resolved.
• Ensure that the thermal contact conductance is realistic and not too low. If it's too low, Fluent and Thermal might not exchange heat effectively.

4. Solver Settings in ANSYS Steady-State Thermal

• Try changing the solver type to Full Newton-Raphson instead of automatic or iterative methods.
• In the solver control options, increase the stabilization settings to avoid small pivot terms.