Forced Convection Coefficient Calculator
What a fan actually buys you. Enter the air velocity over the surface and the flow length, and this returns the average coefficient from the standard flat-plate correlations, switching from laminar to mixed flow at the transition Reynolds number.
Choosing something to solve for makes Convection coefficient an editable target and computes the chosen input from it.
Formula
| Re | Reynolds number, inertial over viscous forces |
| u | free-stream air velocity (m/s) |
| L | flow length along the surface (m) |
| nu | kinematic viscosity of air at the film temperature (m^2/s) |
| Nu | average Nusselt number over the plate |
What this model assumes, and where it stops
Assumptions
- Smooth flat plate in parallel flow, with the boundary layer starting at the leading edge.
- Uniform free-stream velocity and an isothermal surface.
- Air at one atmosphere, properties evaluated at the film temperature.
- Steady state, no radiation, no buoyancy contribution.
- The mixed correlation assumes transition at Re = 5e5.
Limitations
- The velocity that matters is the one actually at the surface, which inside a real enclosure is often a fraction of the fan rating. Getting this number wrong dominates every other error here.
- A fresh boundary layer at the leading edge is optimistic. Downstream of other components the air arrives already heated and disturbed, and both effects cut the coefficient.
- Transition depends on surface roughness and free-stream turbulence, so the fixed 5e5 threshold is nominal.
- This is a flat plate, not a duct or a fin channel. Channel flow between closely spaced fins follows different correlations and can be much worse.
- At low velocity, buoyancy still matters and the flow is mixed rather than purely forced; neither this page nor the natural convection page is right in that band.
- The average coefficient hides a strong gradient - the leading edge is far better cooled than the trailing edge.
When you need a 3D field solution instead
Closed-form models like the one above hold on idealised geometry. These are the cases where they stop being good enough and a full 3D electromagnetic and thermal solution is the only way to get a trustworthy answer:
- Working out the actual local air velocity in an enclosure, which is a flow problem this page simply takes as given.
- Fin channels and ducts, where the boundary layers from the two walls meet and the flat-plate result no longer holds.
- Components in the wake of other components, where the incoming air is preheated and turbulent.
- Mixed convection at low airflow, where buoyancy and forced flow are comparable.
- Any case where you need the local coefficient distribution to find the hot spot rather than a surface average.
Common questions
What does 1 m/s of airflow buy me over natural convection?
Roughly a factor of four: about 25 W/(m2.K) averaged over a 100 mm plate, against 5 to 6 in still air. It also decouples cooling from the temperature rise, which makes the thermal design linear and predictable. This is why even a small, slow fan transforms an enclosure design.
Is my flow laminar or turbulent?
Over a smooth flat plate the transition is around Re = 5e5, which at 1 m/s in room air is a plate about 7 m long - so an isolated PCB or heat sink fin at fan speeds is solidly laminar (the default case runs Re around 5800). Real electronics trip turbulence far earlier through grilles, component roughness and fan swirl, which raises h above the laminar prediction; treat the laminar answer as the conservative floor.
How does h scale with fan speed?
As the square root, in the laminar regime: doubling the velocity from 1 to 2 m/s takes the default plate from 25 to 35 W/(m2.K), not 50. Fan power grows as speed cubed, so the last decibels of fan noise buy very little cooling - a larger, slower fan on a bigger surface nearly always wins.
References
- Incropera & DeWitt - Fundamentals of Heat and Mass Transfer, 6th ed., ch. 7
- Whitaker - Forced convection heat transfer correlations, AIChE J. 18 (1972)