Thermal Behavior of a Stagnant Gas Confined in a Horizontal Microchannel as Described by the Dual-Phase-Lag Heat Conduction Model

Abstract

The transient thermal behavior of a stagnant gas confined in a horizontal microchannel is investigated analytically under the effect of the dual-phase-lag heat conduction model. The microchannel is formed from two infinite horizontal parallel plates where the upper plate is heated isothermally and the lower one is kept adiabatic. The model that combines both the continuum approach and the possibility of slip at the boundary is adopted in this study. The effects of the Knudsen number Kn, the thermal relaxation time τ _q , and the thermal retardation time τ _T on the microchannel thermal behavior are investigated using three heat conduction models. It is found that the deviations between the predictions of the parabolic and the hyperbolic models are insignificant. On the other hand, the deviations between the parabolic and dual-phase-lag models are significant under the same operating conditions.