Anisotropy Deviation from Stokes and Fourie Laws in Nanochannels
E.E. Son, K.E. Son
Joint Institute for High Temperature Rassian Academy of Sciences, RU
Keywords: Gas flow in nanochannels, heat exchange, pressure driven flow
Abstract:In the growing technology CMOS chip, the heat released from the chip is rapidly increa . If the cooling technology is not adequate to heat release, the operating temperature of the electronic micro chips could reach values where the components loose their physical properties and the related function would cease. Because of the large surface area to volume ratio, microchannels cooling with gas or liquid coolant have been shown to be strong prospects. Gas flows in micro- and nanochannels with nonsymmetrical heating essential for have to be described by different from Stokes law for stress - deformation rate and Fourie Laws. In consideration of three limiting cases of fluid flow - rarefied at small Knudsen number, dense gas with Navier-Stokes equations for laminar flows only NS case is bescribed by linear stress-deformation rate closure with viscosity depending only on local thermodynamical parameters. For the cases of turbulent flow and rarefied flow viscosity and other transort coefficients have size effects depending on flow geometry. The result is in the appearing fluxes in perpenicular to temperature gradients and skew stresses. The results follow from Kuette and Poiselle flows considered from the Boltzmann equation in BGK approximation with exact solution. The developed approach is the basis of closure for stress - deformation rate and temperature gradient to heat fkuxes closures. Results compared with other approximations and experiments.