Conjugate Heat Transfer (CHT)

Category: Fluid Analysis (CFD) | Integrated 2026-04-06
CAE visualization for conjugate ht theory - technical simulation diagram
Conjugate Heat Transfer (CHT) โ€” Fundamental Theory of Solid-Fluid Coupling

Conjugate Heat Transfer (CHT): Theoretical Foundations

What is Conjugate Heat Transfer?

๐Ÿง‘โ€๐ŸŽ“

Professor, conjugate heat transfer is about "solving for the solid and fluid simultaneously," right? Is there really a point to coupling them?


๐ŸŽ“

Absolutely. For example, in turbine blade cooling design, the cooling air flowing through internal cooling passages and the high-temperature combustion gas passing over the external blade surface are thermally coupled through the blade metal. To accurately obtain the temperature distribution on the solid side, it's necessary to solve the fluid temperature field and solid heat conduction simultaneously, rather than assuming a heat transfer coefficient $h$ on the fluid side.


๐Ÿง‘โ€๐ŸŽ“

Not having to assume a heat transfer coefficient is certainly a big advantage. Is it also used in electronics cooling and such?


๐ŸŽ“

Of course. Any problem where solid heat conduction and fluid convective heat transfer are tightly coupled is a candidate for CHT: combinations of heat sinks and fan cooling, cold plate design for power semiconductor modules, heat dissipation design for LED packages, etc.


Governing Equations

๐Ÿง‘โ€๐ŸŽ“

Specifically, what equations are solved?


๐ŸŽ“

In the fluid domain, the Navier-Stokes equations and the energy equation are solved. In the solid domain, the heat conduction equation is solved. Then, continuity conditions for temperature and heat flux are imposed at the interface between these two domains.


๐ŸŽ“

The interface conditions can be written mathematically as follows.


$$ T_f\big|_{\text{interface}} = T_s\big|_{\text{interface}} $$
$$ \left.k_f\frac{\partial T}{\partial n}\right|_f = \left.k_s\frac{\partial T}{\partial n}\right|_s $$

๐Ÿง‘โ€๐ŸŽ“

Temperature is continuous, and heat flux is also continuous. Essentially, energy is conserved across the interface, right?


๐ŸŽ“

Exactly. The steady-state heat conduction equation for the solid side is


$$ \nabla \cdot (k_s \nabla T_s) + \dot{q}_v = 0 $$

where $\dot{q}_v$ is volumetric heat generation (like Joule heating). The energy equation on the fluid side includes the convection term. The essence of CHT is that these two are coupled through the interface conditions.


๐Ÿง‘โ€๐ŸŽ“

Can we ignore interface thermal resistance (contact thermal resistance)?


๐ŸŽ“

The above is fine for an ideal interface. For actual TIMs (Thermal Interface Materials) or bolted joint surfaces, contact thermal resistance needs to be added to the interface conditions. In Ansys Fluent or STAR-CCM+, this can be set as a thin wall or contact resistance.

Coffee Break Yomoyama Talk

Pentium 4's Thermal Runaway Made CHT Analysis an Industry Standard

In the early 2000s, Intel's Pentium 4 saw a rapid increase in heat density due to higher clock speeds, leading to frequent problems where CPUs would experience thermal throttling (performance reduction due to heat) due to cooling design failures. Until then, cooling design was often based on the rule of thumb "just attach a heat sink and it's fine," but this incident suddenly made the necessity of CHT analysis, which solves for the CPU (solid) and cooling airflow (fluid) simultaneously, widely recognized. It's no exaggeration to say that the Pentium 4's failure was the starting point for modern thermal design CAE.

Computational Methods for Conjugate Heat Transfer (CHT)

Classification of Coupling Approaches

๐Ÿง‘โ€๐ŸŽ“

Are there different ways to solve CHT?


๐ŸŽ“

There are two main types: monolithic and partitioned. Monolithic solves the solid and fluid simultaneously with a single solver. Ansys Fluent, STAR-CCM+, and OpenFOAM's chtMultiRegionFoam use this approach.


๐Ÿง‘โ€๐ŸŽ“

What about partitioned?


๐ŸŽ“

Partitioned runs separate solid and fluid solvers and exchanges interface data. For example, co-simulation between Ansys Mechanical and Fluent, or between Abaqus and STAR-CCM+, falls into this category. It's also a method used in FSI (Fluid-Structure Interaction).


๐ŸŽ“

Monolithic offers high interface consistency and faster convergence. Partitioned provides flexibility to combine existing solvers, but requires attention to interface interpolation accuracy and convergence stability.


Interface Mesh Design

๐Ÿง‘โ€๐ŸŽ“

Does it cause problems if the mesh size is completely different between solid and fluid?


๐ŸŽ“

It certainly can. The solid side can often be relatively coarse, but the fluid side needs to resolve the wall boundary layer. In Ansys Fluent, you choose to set the wall first layer $y^+$ to around 1 and not use wall functions (low-Re turbulence model), or use $y^+ \approx 30$ with wall functions.


๐Ÿง‘โ€๐ŸŽ“

For CHT, you want to accurately capture the temperature gradient at the wall, so $y^+ \approx 1$ is better, right?


๐ŸŽ“

Exactly. Especially if discussing local heat transfer coefficient or Nu number distribution, you should place a sufficient number of prism layers (inflation layer). In STAR-CCM+, you can specify total thickness from the wall and number of layers for automatic generation. In OpenFOAM, you set it in snappyHexMesh's addLayersControl.


Convergence Judgment Notes

๐Ÿง‘โ€๐ŸŽ“

Since both solid and fluid are solved simultaneously, convergence judgment seems tricky.


๐ŸŽ“

Monitoring temperature and heat flux at the interface is crucial, not just residuals. You need to confirm that the average or maximum temperature at the interface stops fluctuating between iterations. In Fluent, a standard practice is to track the area-weighted average temperature of the interface using a surface monitor.


๐Ÿง‘โ€๐ŸŽ“

Is there a guideline for the number of iterations?


๐ŸŽ“

For monolithic, it's similar to regular CFD calculations. For partitioned co-simulation, set the number of sub-iterations per step to around 3โ€“10 and confirm that interface value fluctuations become sufficiently small. Adjusting the relaxation factor (under-relaxation) is also key.

Coffee Break Yomoyama Talk

"Interface Continuity Conditions"โ€”The Simple Equations at the Core of CHT Coupling Methods

The most important aspect of conjugate heat transfer (CHT) coupling methods is matching both temperature and heat flux at the solid-fluid interface. Implementing these "two simple equations" is actually difficult; in segregated (partitioned) solutions, adjusting relaxation factors is necessary for convergence, and without using iterative methods, heat balance at the interface won't match. If you analyze with the misunderstanding that "matching temperature alone is enough," you'll get incorrect results where the heat balance is off between the solid and fluid sides. Understanding interface conditions is the starting point for CHT.

Conjugate Heat Transfer (CHT) in Practice

Analysis Workflow

๐Ÿง‘โ€๐ŸŽ“

What's the typical procedure for a CHT analysis?


๐ŸŽ“

A typical procedure is as follows. (1) Define solid and fluid domains from CAD. (2) Generate mesh for the fluid domain, resolving the wall boundary layer with prism layers. (3) Generate mesh for the solid domain. (4) Connect the interface conformally (node-matched) or non-conformally. (5) Set material property values. (6) Set boundary and initial conditions and execute the calculation.


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