#rayleigh

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.

api.oanor.com/prandtl-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