Burnett equations

History

The Burnett equations were derived by the English mathematician D. Burnett.

Continuum mechanics
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Solid mechanics Deformation Elasticity (linear) Plasticity Hooke's law Stress Finite strain Infinitesimal strain Compatibility Bending Contact mechanics (frictional) Material failure theory Fracture mechanics
Fluid mechanics Fluids Statics⧼dot-separator⧽Dynamics Archimedes' principle⧼dot-separator⧽Bernoulli's principle Navier–Stokes equations Poiseuille equation⧼dot-separator⧽Pascal's law Viscosity (Newtonian⧼dot-separator⧽non-Newtonian) Buoyancy⧼dot-separator⧽Mixing⧼dot-separator⧽Pressure Liquids Surface tension Capillary action Gases Atmosphere Boyle's law Charles's law Gay-Lussac's law Combined gas law Plasma
Rheology Viscoelasticity Rheometry Rheometer Smart fluids Electrorheological Magnetorheological Ferrofluids
Scientists Bernoulli Boyle Cauchy Charles Euler Gay-Lussac Hooke Pascal Newton Navier Stokes

Series expansion

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Extensions

The Onsager-Burnett Equations, commonly referred to as OBurnett, which form a superset of the Navier-Stokes equations and are second-order accurate for Knudsen number.

Eq. (1) $\sqrt{\tau }\frac{d{u}^s}{ds}-\frac{9}{8}{\alpha }_1{u}^{*}(\frac{d{u}^{*}}{ds}{)}^2=\frac{\tau }{u^{*}}-{\tau }_0-1+u^{*}$

Eq. (2) $\frac{45}{16}\sqrt{\tau }\frac{d\tau }{ds}+\frac{9}{4}{\gamma }_1\tau (\frac{d{u}^{*}}{ds}{)}^2-\frac{9}{4}\mathrm{\Psi }{u}^{*}\frac{d\tau }{ds}\frac{d{u}^{*}}{ds}=\frac{3}{2}(\tau -{\tau }_0)-\frac{1}{2}(1-u^{*}{)}^2-{\tau }_0(1-u^{*})$

Derivation

Starting with the Boltzmann equation $\frac{\partial f}{\partial t}+c_k\frac{\partial f}{\partial x_k}+F_k\frac{\partial f}{\partial c_k}=J(f,f_1)$

See also

• Fluid dynamics
• Lars Onsager
• Non-dimensionalization and scaling of the Navier–Stokes equations
• Stokes equations
• Chapman–Enskog theory
• Navier-Stokes equations

Further reading

• García-Colín, L.S.; Velasco, R.M.; Uribe, F.J. (August 2008). "Beyond the Navier–Stokes equations: Burnett hydrodynamics". Physics Reports. 465 (4): 149–189. Bibcode:2008PhR...465..149G. doi:10.1016/j.physrep.2008.04.010.

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