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A numerical study is presented for forced convection of an incompressible oscillating flow in a two-dimensional channel at constant wall temperature using the lattice Boltzmann method. The oscillatory motion of the fluid in the channel is driven by a periodic pressure gradient. The model adopted in this study is the coupled lattice Bhatnagar-Gross-Krook model. Pressure boundary condition is used in the inlet and outlet boundaries, and extrapolation scheme is used in the solid boundaries. The dependence of the flow and heat transfer characteristics on different Womersley numbers and the amplitudes of the pressure gradient are presented. Results are consistent with those from previous numerical simulations and theoretical analyses.

Recent rapid advances in microelectromechanical system have facilitated the applications of various oscillating microstructures, where fluid damping plays a critical role and becomes a main cause of energy dissipation. In the present study, we have used lattice Boltzmann method to investigate the Stokes' second problem for non-equilibrium effect.

In this study, the mathematical model of oscillating flow in an annular straight pipe due to an imposed oscillating pressure gradient and with harmonic boundary motion is established. So far, no literature is devoted to investigate the effect of harmonic boundary motion on the velocity profile and shear stress. The Navier–Stokes Equation in the cylindrical coordinate is the governing equation of fluid motion. The exact solution of this system in terms of real function only is presented. This method is more understood and helpful for deeply investigating the internal oscillating flow than the conventional complex method presented by Womersley. It is found that the effects of the boundary motion, the wave frequency, the Womersley number, and the radius ratio on the velocity profile and shear stress distribution are significant.