Heat exchange between adjacent streams

Two channels running close together exchange heat through the resin between them. At microfluidic scale this happens fast — the surface-to-volume ratio is high and the wall is thin — which makes an on-chip heat exchanger practical in a few square centimetres.

Why it works at this scale

Three things line up:

Short conduction path. A 0.4–2 mm wall of resin between two channels.
Large surface relative to volume. Every millilitre of fluid is in contact with a lot of wall.
Laminar flow. Predictable, so the coefficient can actually be estimated.

The counterweight is that resin is a poor conductor — around 0.2 W/m·K, against ~400 for copper and ~15 for stainless steel. The wall is usually the dominant resistance in the whole chain, which is why wall thickness matters more here than fluid velocity does.

The chain of resistances

Heat crosses in three steps, in series:

Convection from the hot fluid to the wall.
Conduction through the resin.
Convection from the wall into the cold fluid.

Combined into an overall coefficient U:

1/U = 1/h_hot + t_wall/k_resin + 1/h_cold

The convection coefficients come from the Nusselt number:

h = Nu · k_fluid / Dₕ

For laminar duct flow, Nu is a constant that depends only on the cross-section shape and the wall condition — 3.66 for a circular duct at constant wall temperature, and roughly 3.4–4.4 across rectangular aspect ratios. OpenChip uses a single laminar value, because the difference across that range is well inside the uncertainty of everything else in the estimate.

Above the laminar threshold it switches to the Dittus–Boelter correlation, which is where the Prandtl number starts to matter. In practice you will never see that branch in a microchannel.

Counter-flow

Run the two streams in opposite directions and the temperature difference stays roughly constant along the whole exchanger. Run them in the same direction and it collapses towards the middle, where both streams approach the same temperature and heat stops crossing.

For the same area and the same flows, counter-flow transfers substantially more heat, and it can bring the cold outlet above the hot outlet — which co-flow can never do.

This is what the counter-flow exchanger example is: two channels 1.2 mm apart, water entering at 60 °C against a 50 % glycerol blend at 20 °C, 10 µL/min each.

Reading the numbers

The heat-exchange table under the per-segment results, for each qualifying pair:

Column	Is
Pair	Which two segments.
Wall	Resin thickness between them, mm.
Contact	How much of their length runs alongside, mm.
U	Overall coefficient, W/m²·K.
Flux	Heat crossing, W/m².
Heat	Total transferred, mW.
NTU	Number of transfer units — `UA/(ṁcₚ)`, the dimensionless size of the exchanger.
ε	Effectiveness — actual heat transferred over the thermodynamic maximum.
Approach	How close the outlets get to each other, K.

NTU and ε are the pair to look at when comparing designs. NTU below ~1 means a short exchanger with room to improve; above ~3, you are close to the limit and more length buys little. ε is the fraction of the theoretical maximum you are actually getting.

What to change

Want	Do
More heat transfer	Thinner wall (the dominant resistance), more contact length
A closer approach	Lower flow rate, or more length
Less transfer	Move the channels apart

Thinning the wall is the highest-leverage change and the one with a floor: channels-too-close will tell you when you are below what resin can hold, and 0.4 mm is about the practical limit.

Assumptions, stated

The estimate treats each pair as a one-dimensional exchanger through the resin between them. Specifically it assumes:

A single bulk temperature per stream at each station. No temperature field across the channel cross-section, so a thermal entrance region is not resolved.
Constant fluid properties. Water’s viscosity nearly halves between 20 °C and 60 °C, and the model does not update it as the stream heats.
The rest of the chip is adiabatic. No loss to the air, the build plate, the tubing or the fittings. On a real bench this is optimistic — a thin chip in moving air loses meaningfully to its surroundings.
Only channel pairs that run alongside each other. Heat crossing diagonally through the block, or between three channels sharing a region, is not accounted for.
A constant resin conductivity of 0.2 W/m·K by default. Real photopolymers vary, and yours is probably not exactly this. It is editable.

Treat the result as the right order of magnitude and the right direction, not as a design margin. If a device depends on hitting a temperature within a degree, measure it.