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API · /prandtl-api

Heat Transfer Numbers API

healthy 3,766 Subscribers

Convective heat-transfer dimensionless numbers as an API, computed locally and deterministically. The prandtl endpoint computes the Prandtl number Pr = μ·cp/k (or ν/α), the ratio of momentum to thermal diffusivity that sets the relative thickness of the velocity and thermal boundary layers — air is about 0.71 and water about 7 at 20 °C. The grashof endpoint computes the Grashof number Gr = g·β·|ΔT|·L³/ν², buoyancy versus viscous forces in natural convection (for an ideal gas the thermal-expansion coefficient β ≈ 1/T). The rayleigh endpoint gives the Rayleigh number Ra = Gr·Pr, either from Gr and Pr or from the full natural-convection inputs, which governs the onset of convection (critical ≈ 1708 for a heated horizontal layer). The peclet endpoint computes the Péclet number Pe = Re·Pr = v·L/α, advection versus diffusion of heat. The biot endpoint computes the Biot number Bi = h·L/k and flags whether the lumped-capacitance transient model applies (Bi < 0.1). All inputs are SI. Everything is computed locally and deterministically, so it is instant and private. Ideal for thermal-engineering, HVAC, electronics-cooling, CFD, process-engineering and heat-transfer-education app developers, natural-convection and transient-conduction tools, and simulation software. Pure local computation — no key, no third-party service, instant. Live, nothing stored. 5 endpoints. These are convective heat-transfer groups; for the Reynolds number alone use a Reynolds API and for surface-tension numbers a Weber API.

#prandtl #heat-transfer #grashof #rayleigh #biot #developer-tools
api.oanor.com/prandtl-api
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Machine-readable spec so AI agents can integrate this API.

/api/prandtl-api/openapi.json
/api/prandtl-api/llms.txt

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API health

healthy
Uptime
100.00%
Server probes · 24h
Avg latency
84 ms
Server probes · 24h
Subscribers
3,766
active
Total calls
24
last 7 days
status Full status page → · 30 probes/24h

Pricing

Pick a tier — billed monthly, cancel anytime.

Free

Free

  • 3,700 calls / month
  • 2 requests / second
  • Hard cap (429 above quota, no overage)
  • 3,700 calls/month
  • 2 req/sec
  • Prandtl + Grashof + Rayleigh + Péclet + Biot
  • No credit card
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Starter

€6.80 /month

  • 35,000 calls / month
  • 6 requests / second
  • Hard cap (429 above quota, no overage)
  • 35,000 calls/month
  • 6 req/sec
  • Natural convection, lumped-capacitance
  • Email support
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Pro

€20.50 /month

  • 172,000 calls / month
  • 15 requests / second
  • Hard cap (429 above quota, no overage)
  • 172,000 calls/month
  • 15 req/sec
  • CFD & electronics-cooling pipelines
  • Priority support
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Mega

€63.00 /month

  • 1,040,000 calls / month
  • 40 requests / second
  • Hard cap (429 above quota, no overage)
  • 1,040,000 calls/month
  • 40 req/sec
  • Platform scale
  • Dedicated SLA
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Newton Cooling & Convection API

Newton's law of cooling and convective heat transfer as an API, computed locally and deterministically. The convection endpoint applies the convective-heat-transfer rate Q = h·A·ΔT — the heat carried away from a surface equals the convection coefficient times the area times the temperature difference between the surface and the fluid — and solves for whichever of the heat rate, the coefficient, the area or the temperature difference you leave out, with typical coefficients for natural and forced air, water, boiling and condensing built in. The cooling endpoint applies Newton's law of cooling, T(t) = T_env + (T0 − T_env)·e^(−k·t): from an initial temperature, the ambient temperature and a cooling constant (or time constant τ = 1/k) it gives the temperature after a time, or the time to reach a target temperature, or it solves the cooling constant from a measured temperature at a known time — the maths behind how a hot drink, a forensic body or a cooling casting approaches room temperature. The coefficient endpoint links the cooling constant to the physical properties, k = h·A/(m·c), and the thermal time constant. Everything is computed locally and deterministically, so it is instant and private. Ideal for thermal-engineering and HVAC tools, food-safety and forensic cooling apps, electronics-cooling and process-control software, and physics education. Pure local computation — no key, no third-party service, instant. Live, nothing stored. 3 endpoints. This is convection and transient cooling; for steady conduction through walls use a U-value API and for thermal radiation use a Stefan-Boltzmann API.

api.oanor.com/cooling-api

Optical Resolution API

Optical resolution by the Rayleigh criterion as an API, computed locally and deterministically. The angular endpoint gives the smallest angle two points can be apart and still be told apart through a circular aperture, θ = 1.22·λ/D — the diffraction limit set by the wavelength and the aperture diameter — in radians, degrees, arcminutes and arcseconds (a 100 mm telescope resolves about 1.4 arcseconds in green light), and solves the aperture needed for a target resolution. The distance endpoint turns that angle into a real separation at a distance, s = θ·L = 1.22·λ·L/D — how far apart two objects must be to be resolved at a given range. The microscope endpoint computes resolving power from the numerical aperture: the Rayleigh limit d = 0.61·λ/NA and the Abbe limit d = λ/(2·NA), with NA = n·sin(θ) from a refractive index and half-angle, and the maximum useful magnification. Wavelength defaults to 550 nm (visible) and can be set in metres, nanometres or micrometres. Everything is computed locally and deterministically, so it is instant and private. Ideal for astronomy, telescope and binocular tools, microscopy and imaging-system design, camera and optics apps, and physics education. Pure local computation — no key, no third-party service, instant. Live, nothing stored. 3 endpoints. This is the diffraction-limited resolving power; for thin-lens imaging use a lens API and for slit and grating diffraction use a diffraction API.

api.oanor.com/resolution-api

Tennis Score API

Tennis scoring maths as an API, computed locally and deterministically — the game, set and match logic a scoring app, umpire tool or tennis league runs on. The game endpoint plays a game from a sequence of who won each point and returns the proper tennis score: points run 0, 15, 30, 40 and then game, but at 40-40 it is Deuce and a player must lead by two — Advantage, then game — so a,a,a,a is 40-0 and a win, while three-all is Deuce; a tiebreak flag scores to seven by two instead (and keeps going at 7-7). The set endpoint reads a set from the games each player has won: a set is taken at six games with a two-game lead, 6-6 triggers a tiebreak that ends it 7-6, and 7-5 wins if a player pulls ahead first. The match endpoint settles the match from the sets won — best-of-three is decided by two sets, best-of-five by three — and tells you the winner the moment it is reached. Everything is computed locally and deterministically, so it is instant and private. Ideal for tennis, racket-sport, scoring, umpiring and league app developers, scoreboard and live-scoring tools, and club software. Pure local computation — no key, no third-party service, instant. Scoring logic, not analytics. Live, nothing stored. 3 compute endpoints.

api.oanor.com/tennis-api

Bowling Score API

Ten-pin bowling maths as an API, computed locally and deterministically — the scoring, handicap and average numbers a bowler, league or scoring app runs on. The score endpoint plays a full game from a comma list of the pins knocked down on each roll and applies the real rules: a strike scores 10 plus your next two rolls, a spare 10 plus the next one, an open frame just the pins, with the 10th frame’s bonus rolls handled — so twelve strikes is a perfect 300, twenty 9-then-miss frames are 90, and all spares with a 5 bonus is 150, returned frame by frame with the running total. The handicap endpoint levels a league: handicap per game = ⌊(basis − average) × percent⌋, never below zero, so a 150 average on the common 90 %-of-220 setup earns 63 pins a game and 189 over a three-game series. The average endpoint divides total pins by games (dropping the fraction, as leagues do), rolls in a new series to update it, and works out the pins you need over the next games to reach a target average. Everything is computed locally and deterministically, so it is instant and private. Ideal for bowling-league, scoring, sports and recreation app developers, scorekeeping and handicap tools, and centre-management software. Pure local computation — no key, no third-party service, instant. Live, nothing stored. 3 compute endpoints.

api.oanor.com/bowling-api

Frequently asked questions

Quick answers about pricing, quotas, and integration.

How do I get an API key for Heat Transfer Numbers API?
Sign up for free at oanor.com, generate an API key from the developer dashboard, and call Heat Transfer Numbers API with the x-oanor-key header. No credit card needed for the free tier.
What's the rate limit for Heat Transfer Numbers API?
Free tier allows 1 request per second. Paid plans scale up to 50 requests per second on the Mega tier. Hard limits return HTTP 429 above the quota — no surprise overage charges.
How much does Heat Transfer Numbers API cost?
Heat Transfer Numbers API has a free tier with 100 calls / month. Paid plans start at €6.80 / month with higher quotas and faster rate limits.
Can I cancel my subscription anytime?
Yes. Plans are billed monthly and you can cancel anytime from your billing dashboard. No long-term contracts and no cancellation fee.
Is Heat Transfer Numbers API GDPR-compliant?
All requests to Heat Transfer Numbers API go through our EU-based gateway. Your upstream API key never leaves our server and no personal data is shared with the upstream provider beyond the request you send.

Pick an endpoint from the list on the left to see its details and try it.

Code snippets

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curl https://api.oanor.com/prandtl-api/SOME_PATH \
  -H "x-oanor-key: oanor_test_..."
const res = await fetch("https://api.oanor.com/prandtl-api/SOME_PATH", {
  headers: { "x-oanor-key": "oanor_test_..." }
});
const data = await res.json();
$ch = curl_init("https://api.oanor.com/prandtl-api/SOME_PATH");
curl_setopt($ch, CURLOPT_RETURNTRANSFER, true);
curl_setopt($ch, CURLOPT_HTTPHEADER, ["x-oanor-key: oanor_test_..."]);
$response = curl_exec($ch);
import requests
r = requests.get(
    "https://api.oanor.com/prandtl-api/SOME_PATH",
    headers={"x-oanor-key": "oanor_test_..."},
)
print(r.json())

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