Abstract:
In theclassicalframework,theNavier–Stokes–Fourier
equations areobtainedthroughthelinearuncoupled
thermodynamic force-fluxrelationswhichguarantee
the non-negativityoftheentropyproduction.
However,theconventionalthermodynamicdescrip-
tion isonlyvalidwhentheKnudsennumberis
sufficientlysmall.Here,itisshownthattherangeof
validity oftheNavier–Stokes–Fourierequationscan
be extendedbyincorporatingthenonlinearcoupling
among thethermodynamicforcesandfluxes.The
resultingsystemofconservationlawsclosedwith
the coupledconstitutiverelationsisabletodescribe
many interestingrarefactioneffects,suchasKnudsen
paradox, transpirationflows,thermalstress,heat
flux withouttemperaturegradients,etc.,which
cannot bepredictedbytheclassicalNavier–Stokes–
Fourier equations.Forthissystemofequations,
a setofphenomenologicalboundaryconditions,
which respectthesecondlawofthermodynamics,
is alsoderived.Someofthebenchmarkproblems
in fluidmechanicsarestudiedtoshowthe
applicability ofthederivedequationsandboundary
conditions.