Significance of Upstream Wall Conditions in Characterizing the Heat Transfer Phenomena of Rarefied Flows

Abstract Slip flows in small-scale flow networks involve simultaneous presence of multiple factors governing the flow field. In addition, conditions of upstream wall need to be clearly defined. The present work addresses these aspects by analyzing the heat transfer aspects of slip flows. The complete form of the governing equations are solved. The fully developed Nusselt number (Nufd) is found to rise first, before dropping continuously with rise in Knudsen number (Kn). The pair of Kn and maximum Nufd is found to be dependent on Peclet number (Pe) of the system. Local Nu is found to drop to a minimum, lower than Nufd for Kn ~ O(10-3) due to a significant radial advection. The presence of an adiabatic upstream wall reveals that heat may propagate up to the inlet for Kn ≳ 0.015. An analytical solution is developed to approximate this limiting value of Kn and it agrees well with the numerical results. The observed flow behavior leads to the categorization of flow regime into three types: (i) Kn < 0.001, possessing dependence on change in Pe only, (ii) 0.001 ≤ Kn < 0.01, possessing concurrence of effects due to change in Pe and Kn, and (iii) 0.01 ≤ Kn < 0.1, possessing dependence on change in Kn only. Further, Pe is shown to represent Nubulk for the flow, where in the range 0.01 ≤ Kn < 0.1, Nutot ≈ Nubulk as Kn approaches 0.01 and Nutot ≈ Nuin as Kn approaches 0.1.