Effects of Brownian and thermophoretic diffusions on nonequilibrium heat conduction in a nanofluid layer with periodic heat flux on one side and specified temperature on the other side are investigated numerically. The problem are described by eight dimensionless parameters: density ratio, heat capacity ratio, Lewis number, Soret coefficient, initial volume fraction of nanoparticles, initial temperature, Sparrow number, and period of the surface heat flux. Effects of Brownian and thermophoretic diffusions of nanoparticles on nonequilibrium heat conduction in nanofluid obtained by dispersing copper nanoparticles into ethylene glycol are investigated. The results showed that the Brownian and thermophoretic diffusions only affect the nanoparticle temperature but their effect on the heat transfer enhancement is negligible.

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