Engineering task and calculation objective
This module calculates the heat transfer of impinging jets according to the VDI Heat Atlas (VDI-Wärmeatlas, 12th edition 2019, section G10). In jet impingement, a fluid jet from a nozzle strikes a surface perpendicularly or nearly perpendicularly. In the stagnation region, very thin boundary layers form — and with them exceptionally high local heat transfer coefficients. This is why impinging jets are used wherever large heat flux densities must be transferred in a confined space: cooling of sheet metal and glass, drying of paper and film webs, temperature control of tooling, or cooling of electronics and gas turbine blades.
The calculation according to the correlations of Martin distinguishes the nozzle type: single round nozzle, single slot nozzle, and arrays of round nozzles or slot nozzles. The governing parameters are the nozzle diameter or slot width, the distance between nozzle and target plate, additionally the relative nozzle area for nozzle arrays, and the Reynolds number of the jet. The result is the heat transfer coefficient averaged over the impingement surface.
If you want to calculate the heat transfer of impingement cooling or impingement drying, this module provides the method validated in the VDI Heat Atlas, including the limits of validity for distances, pitches, and Reynolds numbers.
Standard and calculation basis: VDI-Wärmeatlas, 12. Auflage 2019
Calculation workflow
- Select the nozzle type: First, the nozzle configuration is defined: single round nozzle, single slot nozzle, array of round nozzles, or array of slot nozzles. Each configuration has its own correlation with its own geometry parameters.
- Capture geometry and operating data: The inputs are the nozzle diameter or hydraulic slot width, the distance between nozzle exit and target surface, and, for arrays, the nozzle pitch; from these, the relative distance H/D and the relative nozzle area follow. The Reynolds number of the jet is formed from the exit velocity and the fluid properties.
- Check the range of validity: The correlations are valid only within defined ranges of Reynolds number, relative distance, and relative nozzle area. The module checks these limits, because outside them — for example at very small nozzle-to-plate distances — transferring the correlations to other geometries is not permissible.
- Calculate the mean Nusselt number: For the selected nozzle type, the Nusselt number averaged over the associated impingement area is calculated from the Reynolds number, the Prandtl number, the relative distance, and the geometry function. The Prandtl number dependence is captured with the exponent 0.42.
- Evaluate the heat transfer coefficient: The Nusselt number, the thermal conductivity of the fluid, and the nozzle diameter or characteristic length give the mean heat transfer coefficient of the impingement surface; together with the area and the temperature difference, the transferred heat flow follows.
Input quantities
| Quantity | Symbol | Unit |
|---|---|---|
| Fluid temperature, nozzle outlet | TD | °C |
| Fluid temperature, product track | TO | °C |
| Mean fluid temperature (TD + TO)/2 | Tm | °C |
| Thermal conductivity | λ | W/(m·K) |
| Kinematic viscosity | ν | m²/s |
| Prandtl number | Pr | - |
| Reynolds number | Re | - |
| Hydraulic diameter, corrected | D′ | m |
| Slot width, corrected | B′ | m |
| Distance nozzle - product track | H | m |
| Surface of product track | A | m² |
| Velocity at nozzle outlet | w | m/s |
| Nusselt-number of nozzle | NuERD | - |
| Parameter of single, circular nozzle | F(Re) | - |
| Radius | Radius r | m |
| Ratio | r/D r* = r/D′ | - |
| Ratio | H/D h* = H/D | - |
| Shape factor of nozzle | x | m |
| Ratio | x/D x* = x/D | - |
| Nusselt number slot nozzle | NuESD | - |
| Parameter,single slot nozzle | m | - |
| Nusselt number arrays of round nozzles | NuRDF | - |
| Parameter arrays of round nozzles | G | - |
| Parameter arrays of slot nozzles | d* | - |
Calculation options
Nozzle arrangement
square · triangular
Nozzle Type
Single, round nozzle · Single, slot nozzle · Arrays of round nozzles · Arrays of slot nozzles
Frequently asked questions
Which nozzle-to-surface distance gives the best heat transfer?
The local heat transfer at the stagnation point reaches its maximum when the target surface lies roughly at the end of the jet core — typically at relative distances H/D of about 5 to 7. At smaller distances the jet core has not yet fully covered the surface; at larger distances the jet velocity is already decaying due to mixing with the surroundings. For the area-averaged heat transfer of nozzle arrays, the optimum shifts depending on the pitch.
Why are nozzle arrays not simply the sum of many single nozzles?
In nozzle arrays the jets interact with each other: the outflowing cross flow from neighboring jets deflects the jets and weakens the impingement, and the spent air must be removed between the nozzles. With too dense a nozzle arrangement or poor exhaust routing, the heat transfer drops markedly. The array correlations therefore include the relative nozzle area as a separate parameter, and the design of the spent-air removal is a key engineering issue.
What is the advantage of jet impingement over parallel flow?
With perpendicular jet impingement, the boundary layer in the stagnation region is extremely thin, so heat transfer coefficients are achieved there that exceed those of parallel flow at the same fan power by a factor of several. Jet impingement therefore pays off when high heat flux densities are required on a limited area. The drawback is the non-uniform local distribution — considerable differences can exist between the stagnation point and the outer region, which must be taken into account for temperature-sensitive products.
Does the calculation also apply to liquid jets?
The correlations of section G10 were validated predominantly with gas jets (air); the Prandtl number function Pr^0.42 allows a limited transfer to liquids. For liquid jets with a free surface (impingement in an ambient gas), however, additional effects such as film spreading and the hydraulic jump occur, which require dedicated approaches.