Mixed Convection

Exactly. When external flow (from fans or pumps) and buoyancy-driven flow coexist with comparable strength, it is called mixed convection. For example, in upward flow inside a vertical pipe with heated walls, the forced flow from the pump and the upward flow due to buoyancy superimpose.

It is judged by the Richardson number $Ri$.

If $Ri \ll 1$, forced convection is dominant; if $Ri \gg 1$, natural convection is dominant; if $Ri \sim O(1)$, it is mixed convection. Practically, the range $0.1 < Ri < 10$ can be considered the mixed convection region.

It is very important. In upward flow in a heated vertical pipe, buoyancy acts in a direction that aids the flow (aiding flow). Conversely, in downward flow, buoyancy and flow are in opposite directions (opposing flow).

In aiding flow, the Nusselt number increases compared to pure forced convection. In opposing flow, flow deceleration, reverse flow, and relaminarization can occur, causing the Nusselt number to change complexly. Particularly, the relaminarization phenomenon in opposing flow is known to be difficult to predict accurately with CFD.

In horizontal pipes, buoyancy generates secondary flow (longitudinal vortices). High-temperature fluid accumulates in the upper part of the pipe cross-section, and low-temperature fluid pools in the lower part. To accurately predict this asymmetric temperature distribution, 3D calculation is essential; 2D axisymmetric approximation cannot be used.

To correctly handle the buoyancy term, how to model the temperature dependence of density is key. The simplest is the Boussinesq approximation, which linearly approximates density as

and reflects this variation only in the buoyancy term. Density is treated as constant in other terms of the momentum equation. In Ansys Fluent, set Gravity in Operating Conditions and set Material Density to Boussinesq.

Accuracy degrades when the temperature difference is large, around $\beta \Delta T > 0.1$~$0.2$. For air, caution is needed for $\Delta T > 30$°C or so. In such cases, the nonlinear temperature dependence of density should be handled directly using ideal gas or polynomial density. Fluent's Incompressible Ideal Gas setting is convenient.

The buoyancy-induced turbulence generation/damping effect becomes important. In k-ε type models, the buoyancy production term $G_b = -g_i \frac{\mu_t}{\rho Pr_t} \frac{\partial \rho}{\partial x_i}$ is added. In Fluent, it is strongly recommended to turn ON "Full Buoyancy Effects" in the Viscous Model Options.

Also, the Transition SST model is effective for predicting relaminarization phenomena in opposing flow. Standard turbulence models cannot predict laminarization and overestimate the Nusselt number.

Wall-normal mesh requirements are similar (recommended $y^+ \approx 1$), but the mesh in the pipe cross-sectional direction must also be sufficiently fine to resolve secondary flow due to buoyancy. For horizontal pipes, at least 40~60 divisions in the cross-sectional direction are necessary. If too coarse, secondary flow cannot be resolved, and the asymmetry of the Nusselt number will be underestimated.

Extremely important. In office air conditioning, supply air from the ceiling (forced convection) coexists with buoyancy from heat sources inside the room (PCs, people, lighting). If the cold air from ceiling diffusers does not have sufficient momentum, a warm air layer (warm layer) stagnates in the upper part of the room, causing thermal stratification.

Exactly. In Fluent, for steady RANS, Realizable k-ε + Enhanced Wall Treatment is the standard choice for indoor environment CFD. In OpenFOAM, combine buoyantSimpleFoam with kOmegaSST. Human body heat generation is modeled as a heat source of about 80~120W, and a practical workflow includes comfort evaluation via PMV-PPD.

In enclosures with fans, forced convection is dominant, but in fanless (natural air cooling) or fan failure scenarios, it becomes buoyancy-driven. Design-wise, both cases need to be evaluated, which is precisely a mixed convection problem.

In practice, a 3D enclosure model is created, and components are modeled as volume heat sources. Circuit boards are modeled as orthotropic (anisotropic) thermal conductors, with in-plane and out-of-plane thermal conductivities input separately. Solving solid-fluid simultaneously using STAR-CCM+ or Fluent's CHT function is standard.

Sharp observation. Natural convection in sealed enclosures may not have a steady-state solution (at high Ra numbers, it becomes unsteady oscillatory flow). If residuals oscillate in steady-state calculations, you should switch to unsteady calculation and take a time average. In Fluent, using adaptive time stepping in Transient settings is practical.