Conjugate Heat Transfer (CHT) — CFD Overview
Real thermal problems involve heat moving across solid-fluid boundaries simultaneously. CHT couples convective heat transfer in the fluid with conduction in the solid, giving you the complete thermal picture in a single simulation.
By NovaSolver Contributors (Anonymous Engineers & AI) | CFD / Fluid Analysis | 日本語版 →
1. What is Conjugate Heat Transfer?
I know that CFD handles fluid flow and FEA handles heat conduction in solids. What does "conjugate heat transfer" mean — is it just combining both?
Exactly. In real engineering, heat doesn't just stay in the fluid or just in the solid — it crosses the interface continuously. In an electronics cooling problem, your processor generates heat in silicon, that heat conducts through the chip, crosses the thermal interface into a heatsink, and then is carried away by forced air convection. If you separate these into independent simulations, you have to guess the wall temperature or heat flux at the boundary — which introduces a major error. CHT solves the fluid and solid energy equations simultaneously, with automatic matching of temperature and heat flux at every interface cell. No guessing required.
So the solver needs to handle both the fluid Navier-Stokes equations and the solid heat conduction equation at the same time?
Right. The domain is divided into regions — fluid regions where the full N-S + energy equations are solved, and solid regions where only the Fourier heat conduction equation is solved (no momentum equation needed). OpenFOAM's chtMultiRegionFoam handles an arbitrary number of such regions. The regions are coupled at shared interfaces where temperature and heat flux are matched. The critical constraint is that the mesh must be conforming at those interfaces — face-to-face matching — or you need interpolation, which adds complexity.
2. Governing Equations
In the fluid region, the energy equation (for incompressible flow, in terms of static temperature $T$):
$$\rho c_p \left(\frac{\partial T}{\partial t} + \mathbf{u} \cdot \nabla T\right) = \nabla \cdot (\lambda_f \nabla T) + \nabla \cdot (\lambda_t \nabla T) + S_h$$where $\lambda_f$ is the fluid thermal conductivity, $\lambda_t = \mu_t c_p / Pr_t$ is the turbulent thermal conductivity (with turbulent Prandtl number $Pr_t \approx 0.85$ for air), and $S_h$ is a volumetric heat source.
In the solid region, only the Fourier conduction equation:
$$\rho_s c_{p,s} \frac{\partial T}{\partial t} = \nabla \cdot (\lambda_s \nabla T) + S_h$$There is no velocity — no convection in the solid, only diffusion.
The interface conditions enforcing physical continuity:
$$T_{fluid}^{interface} = T_{solid}^{interface} \quad \text{(temperature continuity)}$$ $$\lambda_f \frac{\partial T_f}{\partial n} = \lambda_s \frac{\partial T_s}{\partial n} \quad \text{(heat flux continuity)}$$3. Applications
| Application | Fluid Region | Solid Region | Key Challenge |
|---|---|---|---|
| Electronics cooling (PCB/chip) | Forced air or liquid coolant | Si chip, PCB, heatsink (Al/Cu) | Junction temperature prediction; contact resistance |
| Heat exchanger | Hot and cold fluid streams | Metal tube walls, fins | Overall heat transfer coefficient U; fouling effects |
| Turbine blade cooling | Hot combustion gas (outer), cooling air (inner channels) | Nickel superalloy blade | Film cooling effectiveness; thermal fatigue at leading edge |
| Brake disc thermal analysis | Ambient air (convective cooling) | Cast iron or carbon disc | Frictional heat generation; hot spot formation |
| Cold plate (EV battery cooling) | Water-glycol coolant in channels | Aluminum cold plate + battery cells | Uniform temperature distribution across cells |
4. Turbulence Effects on Heat Transfer — Nusselt Number
How does turbulence affect heat transfer? Is a turbulent flow always better for cooling than a laminar flow?
Yes — turbulence dramatically enhances heat transfer because turbulent eddies constantly sweep hot fluid away from the wall and bring cool fluid in. The heat transfer enhancement is captured by the Nusselt number Nu = hL/λ, which represents the ratio of convective to conductive heat transfer. For laminar pipe flow, Nu = 3.66 (constant wall temperature). For turbulent pipe flow, the Dittus-Boelter correlation gives Nu = 0.023 Re^0.8 Pr^0.4 — at Re = 10,000 that's Nu ≈ 60, roughly 16 times higher than laminar. That's why all industrial heat exchangers are designed to run in turbulent flow.
Dittus-Boelter correlation for turbulent pipe flow (Re > 10,000, 0.7 < Pr < 160):
$$Nu = 0.023 \, Re^{0.8} \, Pr^{0.4} \quad \text{(heating)}, \quad Nu = 0.023 \, Re^{0.8} \, Pr^{0.3} \quad \text{(cooling)}$$In CFD, the turbulent contribution to wall heat transfer is through the turbulent thermal conductivity:
$$\lambda_{eff} = \lambda_f + \lambda_t = \lambda_f + \frac{\mu_t c_p}{Pr_t}$$Accurate prediction of wall heat transfer therefore requires accurate prediction of $\mu_t$ right at the wall — which is why y+ requirements are strict for CHT.
5. Mesh Requirements and y+ for CHT
I've heard y+ requirements are even stricter for heat transfer than for pure flow. Why?
Exactly right. The thermal boundary layer can be thinner than the velocity boundary layer — the ratio depends on the Prandtl number: $\delta_T / \delta_v \approx Pr^{-1/3}$. For water, Pr ≈ 7, so the thermal layer is about half the thickness of the velocity layer. If your first cell y+ is too large, you miss the steep temperature gradient right at the wall, and your computed heat flux (proportional to ∂T/∂n) is wrong. As a rule of thumb: for resolved wall treatment (no wall functions), aim for y+ ≈ 1. For wall functions, y+ = 30–300 is acceptable but heat transfer accuracy degrades — avoid wall functions for CHT where hot spot accuracy is critical.
| Flow Type | Fluid | Prandtl Number | y+ Requirement | Note |
|---|---|---|---|---|
| Forced air convection (electronics) | Air | Pr ≈ 0.71 | y+ ≤ 1 | Thermal and velocity BL similar thickness |
| Liquid water cooling | Water at 20°C | Pr ≈ 7 | y+ ≤ 1 | Thin thermal BL; strict near-wall resolution needed |
| Oil cooling | Engine oil | Pr ≈ 100–1000 | y+ ≤ 0.5 | Very thin thermal BL; demand very fine first cell |
| Hot gas (turbine) | Combustion products | Pr ≈ 0.7 | y+ ≤ 1 | High temperature gradients near blade surface |