Conjugate heat transfer (CHT) is the simultaneous simulation of heat conduction in solid parts and heat transfer in a fluid flowing around or through them. The solid and fluid regions are solved together, and at every surface they share, temperature and heat flux are matched: the fluid sees the wall at the temperature the solid actually reaches, and the heat leaving the solid is the heat the fluid picks up. A CHT simulation therefore predicts the temperature of every part, the velocity and temperature of the fluid, and how the heat divides between the paths available to it.
The reason to use it is the heat transfer coefficient. A conventional thermal model replaces the fluid with an assumed coefficient h and a reference temperature on each cooled surface. That coefficient is not a property of the material or the fluid. It depends on the flow, the flow depends on the geometry, and in natural convection it depends on the temperatures as well. CHT simulation calculates it instead of assuming it, which matters most when the flow is restricted, when hot spots are local, or when the fluid warms noticeably on its way through the product.
How conjugate heat transfer works
A CHT model contains two kinds of region. In the solids, heat moves by conduction, governed by Fourier’s law:
q = −k ∇T
where q is the heat flux, k the thermal conductivity and ∇T the temperature gradient. Heat sources, such as the power dissipated by a component, resistive losses in a busbar or a heater element, are applied to the solids that produce them.
In the fluid, the solver handles conservation of mass, momentum and energy. Heat moves by conduction within the fluid and by advection, carried along with the flow. Where the flow is turbulent, a turbulence model represents the extra mixing that eddies produce, which raises heat transfer at the walls considerably.
At each solid-fluid interface, two conditions tie the regions together: the temperature is continuous across the interface, and the heat flux normal to the surface is the same on both sides. Nothing about surface heat transfer is specified in advance. It emerges from the thin thermal boundary layer that forms in the fluid next to each wall.
Why a fixed heat transfer coefficient falls short
The conventional approach applies Newton’s law of cooling at each surface:
q = h (Ts − T∞)
Here Ts is the surface temperature and T∞ a reference fluid temperature. The approach works well when h comes from a correlation that matches the geometry, such as flow along a flat plate or through a long round pipe. Real products rarely match those cases, and the commonly quoted ranges show how wide the uncertainty is: roughly 2 to 25 W/(m² K) for natural convection in gases, 25 to 250 W/(m² K) for forced convection in gases, and 100 to 20,000 W/(m² K) for forced convection in liquids. Choosing a value within one of those bands is often the largest single assumption in a thermal model.
Four effects make a single coefficient misleading:
- Local variation. The coefficient is highest where the thermal boundary layer is thin, at the leading edge of a fin or where flow strikes a surface, and it falls further downstream. An average value hides the hottest point.
- Geometry-driven flow. A tall capacitor shadows the components behind it. Air takes the easy path around a heat sink when the fin gaps are tight. A fixed coefficient knows nothing of either.
- Fluid heating. Coolant in a cold plate and air in a duct warm up as they absorb heat, so the last component in line sees warmer fluid than the first. A fixed reference temperature misses this.
- Coupling in natural convection. Buoyant flow is driven by the very temperature differences it then reduces, so flow and temperature cannot be found separately.
| Aspect | Fixed coefficient model | CHT simulation |
|---|---|---|
| Fluid | Replaced by h and a reference temperature | Solved for velocity, pressure and temperature |
| Heat transfer coefficient | An input, assumed or taken from a correlation | A result, calculated over every surface |
| Fluid temperature rise | Ignored, or estimated separately | Predicted along the whole flow path |
| Local hot spots | Smoothed out by averaged values | Shown where shadowing or bypass flow causes them |
| Pressure drop | Not available | Predicted, for fan or pump selection |
| Set-up effort | Lower | Higher: needs a fluid region and flow boundary conditions |
| Best suited to | Early estimates and well-characterised flows | Enclosures, finned parts, liquid cooling and design comparisons |
Natural and forced convection
Natural convection
In natural convection the flow is driven by buoyancy: fluid warmed by a surface becomes less dense and rises, drawing cooler fluid in behind it. Velocities in air are low, often a few tenths of a metre per second, and heat transfer coefficients are correspondingly small, so passive designs depend heavily on surface area, fin spacing, orientation and the free space around hot parts. Since the flow exists only because of the temperature field, CHT is the natural way to model it. In passively cooled products, radiation is often of similar size to convection, so it belongs in the same model.
The Rayleigh number, which combines buoyancy, viscosity and thermal diffusivity over a characteristic length, indicates whether buoyant flow is laminar or turbulent. For a heated vertical plate, transition is commonly placed near Ra ≈ 10⁹, so the buoyant flow over small electronic assemblies is usually laminar.
Forced convection
In forced convection a fan, pump, blower or the motion of a vehicle drives the flow. The flow rate is not a free choice: it settles where the fan or pump curve meets the pressure drop of the system it pushes through, so a forced convection CHT model usually includes the fan curve rather than an assumed velocity. Flows are often turbulent, and heat transfer coefficients are typically several times to an order of magnitude higher than in natural convection in the same fluid.
Between the two lies mixed convection, where a weak forced flow and buoyancy are of similar strength. The Richardson number, the Grashof number divided by the square of the Reynolds number, indicates which dominates: well below 1, forced convection governs; well above 1, buoyancy does. Low-speed ventilation and slowly circulating coolant often fall in between, and CHT handles them without having to choose.
Where conjugate heat transfer is used
Electronics enclosures and heat sinks
This is the most common use. Components, circuit board, heat sink, enclosure and air are modelled together to predict case and junction temperatures at the worst-case ambient. The board itself is often an important heat path: its copper layers give it an in-plane conductivity many times its through-thickness value, which a CHT model represents with direction-dependent properties. The heat sink simulation page covers fin design in detail, and electronics thermal management covers complete enclosures.
Cold plates and liquid cooling
Power modules, battery packs, motor drives and laser sources are often cooled by liquid flowing through machined, brazed or tubed channels. CHT shows the trade-off that matters: more channels or narrower passages lower the peak temperature and even out the plate, but raise the pressure drop and the pump duty. It also shows the coolant temperature rise from inlet to outlet, which decides how hot the last module in line runs.
Heat exchangers
In a heat exchanger the wall between the hot and cold streams is a solid region, and fins or plates extend it. CHT captures conduction through those walls and fins together with the flow on both sides, including uneven distribution between passages, which methods based on a single overall coefficient treat as uniform.
Motors, lighting and process equipment
Motor frames and end caps, LED luminaires, and process equipment such as heated rollers, moulds and ovens all combine internal heat sources, conduction paths and a cooling flow. In each case the useful output is the same: the temperature of the critical part at the operating condition that governs.
What a CHT model needs
- Geometry of solids and fluid. CAD of the parts, plus the enclosure, ducts or channels that bound the flow. For internal flow, the fluid volume is extracted from the CAD.
- Heat sources. Power dissipation per component or region, at normal and worst-case load.
- Material properties. Thermal conductivity for each solid, direction-dependent where relevant, plus density and specific heat for a transient study.
- Flow conditions. Fan or pump curves, inlet flow rates or velocities, outlet pressures, coolant type and inlet temperature.
- Ambient conditions. Maximum ambient temperature, the direction of gravity for natural convection, and altitude where air density matters.
- Interfaces. Thermal interface materials and contact resistances between parts, which can account for a large share of the temperature rise from a component to its heat sink.
- Surfaces. Emissivity where radiation is included, which differs greatly between bare metal and painted or anodised finishes.
- Time dependence. Whether steady state answers the question, or whether warm-up, duty cycles or short overloads call for a transient study.
The level of detail in the CAD should match the question. Fins, gaps and vents that shape the flow need to be represented faithfully; screw threads, logos and small internal features usually do not. Our guide to preparing CAD for simulation covers this in more depth.
What CHT results tell you
A CHT study answers practical questions: whether every component stays below its limit with margin, which heat path carries most of the load, whether natural convection is enough or a fan is needed, which channel layout gives the most even plate temperature, and what pressure drop the fan or pump has to overcome. Because the temperature field is complete, it can also be passed to a structural model to predict thermal expansion and stress, as described in our guide to thermal stress.
When to bring in a specialist
A CHT model takes more care to set up than a fixed-coefficient one, and its value depends on framing the right question. SixGate™’s thermal simulation work includes conjugate heat transfer, with layouts, materials and cooling options compared side by side. The outcome is a design decision, such as which heat sink, channel layout or fan to use, with the predicted temperatures and margins behind it. From there the same team can take the chosen layout through detail design, draw it for its suppliers and put it into production.