Unsteady Natural Convection Fluid Flow in a Vertical Microchannel under the Effect of the Dual-Phase-Lag Heat-Conduction Model

The unsteady hydrodynamics and thermal behavior of fluid flow in an open-ended vertical parallel-plate microchannel are investigated semi-analytically under the effect of the dual-phase-lag heat conduction model. The model that combines both the continuum approach and the possibility of slip at the boundary is adopted in the study. The effects of the Knudsen number Kn, the thermal relaxation time τ _q , and the thermal retardation time τ _T on the microchannel hydrodynamics and thermal behavior are investigated using the dual-phase-lag and hyperbolic-heat-conduction models. It is found that as Kn increases the slip in the hydrodynamic and thermal boundary condition increases. Also, the slip in the hydrodynamic behavior increases as τ _T and τ _q decrease, but the effect of τ _T and τ _q on the slip of the thermal behavior is insignificant.