Conjugate Heat Transfer & CFD Coupling

What Is It?

Conjugate Heat Transfer (CHT) in thermal analysis is the simultaneous solution of fluid flow (convection) and solid conduction, coupled at the fluid-solid interface. The fluid flow is solved with CFD — the Navier–Stokes and energy equations give the velocity, pressure and temperature in the fluid. The solid conduction is solved with the heat conduction equation. At the interface, the temperature and heat flux are continuous — the heat leaving the solid enters the fluid and vice versa. CHT resolves the convective heat transfer from the flow field rather than prescribing it as an assumed convection coefficient.

Why It Matters

In many thermal problems, the convection coefficient is the most uncertain input. It depends on the flow — the velocity, the turbulence, the geometry, the fluid properties — which may be complex and difficult to predict with correlations. Using an assumed convection coefficient introduces uncertainty that can dominate the analysis. CHT removes this uncertainty by computing the convection from the actual flow field. The heat transfer coefficient becomes an output of the analysis, not an input. This is particularly valuable for complex geometries (cooling channels, electronics, heat exchangers) where correlations are unreliable or unavailable.

CFD can resolve the fluid-side heat transfer when a single assumed convection coefficient is not sufficient. The convection coefficient emerges from the computed flow field — it varies along the surface and captures the effect of separation, recirculation and local flow features.

Why Prescribing a Guessed h May Be Insufficient

For simple geometries — a flat plate, a straight pipe — the convection coefficient can be obtained from well-established correlations. The flow is well-characterised, the geometry is simple and the correlation is reliable. For complex geometries — a manifold, a heat sink with fins, a duct with bends and obstructions — the flow is complex (separation, recirculation, secondary flow) and the correlations may not apply. Prescribing a guessed convection coefficient for these cases can produce errors of 50% or more in the heat transfer, leading to significant errors in the predicted temperature. CHT resolves the actual flow and the actual heat transfer, avoiding the guesswork.

Interface Conservation

At the fluid-solid interface, two conditions must be satisfied: temperature continuity (the fluid temperature at the wall equals the solid temperature at the wall) and heat flux continuity (the heat flux leaving the solid equals the heat flux entering the fluid). These conditions couple the fluid and solid domains. The wall temperature is not assumed — it is computed from the coupled solution. The heat transfer coefficient is not assumed — it emerges from the flow field. The interface conservation is enforced by the CHT solver, allowing heat to flow naturally between the domains.

• Temperature continuity: T_fluid(wall) = T_solid(wall)
• Heat flux continuity: q_fluid(wall) = q_solid(wall)
• Wall temperature is computed, not assumed
• Heat transfer coefficient is an output, not an input

Applications

When CHT Is Justified vs Assumed h

CHT is computationally expensive — it requires solving the full fluid flow in addition to the solid conduction. For simple geometries where correlations are reliable, an assumed convection coefficient is adequate and CHT is unnecessary. CHT is justified when the geometry is complex, when the flow features (separation, recirculation) affect the heat transfer, when the convection coefficient is spatially varying, when the wall temperature is unknown, or when the accuracy requirement justifies the computational cost. The engineer should start with an assumed h and a sensitivity study; if the results are highly sensitive to h, or if the assumed h is unreliable, CHT is justified.

BOUNDARY-CONDITION CONSIDERATION: Before running CHT, assess whether an assumed convection coefficient with a sensitivity study would be adequate. CHT is justified when the geometry is complex, the correlations are unreliable, or the results are highly sensitive to the convection coefficient.

Computational Cost

CHT is significantly more expensive than a solid-only thermal analysis. The CFD solution requires a fluid mesh, a flow solver, turbulence modelling and convergence of the flow field — all in addition to the solid conduction. The cost depends on the flow complexity, the mesh size and whether the analysis is steady or transient. For steady CHT, the cost is several times that of a solid-only analysis. For transient CHT, the cost is higher still — the fluid flow must be solved at each time step. The cost should be justified by the engineering value — the improved accuracy of the convection prediction and the elimination of the h uncertainty.

Steady vs Transient CHT

Steady CHT solves the steady fluid flow and the steady solid conduction simultaneously — it gives the equilibrium temperature distribution. Transient CHT solves the time-dependent fluid flow and the time-dependent solid conduction — it captures the thermal history and the fluid-flow response to changing conditions. Transient CHT is needed when the flow changes with time (start-up, shut-down, pulsed flow) or when the thermal history matters (peak temperature timing, thermal cycling). The time step for transient CHT must be appropriate for both the fluid (fast) and the solid (slow) — the fluid time scale may be much shorter than the solid time scale, requiring careful time-step selection or sub-cycling.

Key Takeaways

• CHT solves fluid convection and solid conduction simultaneously with interface continuity
• The convection coefficient is an output of CHT, not an assumed input — it varies along the surface
• CHT is justified when geometry is complex, correlations are unreliable or results are sensitive to h
• CHT is computationally expensive — the fluid flow must be solved in addition to the solid conduction
• Steady CHT gives equilibrium; transient CHT captures the thermal and flow history