Heat transfer characteristics of mildly rarefied gaseous flows in the slip regime

The present numerical work aims to delineate the heat transfer characteristics present in mildly rarefied gaseous Nitrogen flows with comparable Knudsen number throughout the flow domain. The principal objective is to analyze the behavior of the resulting thermal flow field with an increasing degree of rarefaction and to establish the dependence of Nusselt number on Knudsen number and Reynolds number. The current analysis deals with the flow through an isothermally heated circular pipe with a temperature of 350 K at the heating wall. The ranges of mean Knudsen numbers and Reynolds numbers considered in the analysis are (0.0009 - 0.09) and (20 - 0.004), respectively. These correspond to a pressure ratio less than 1.03 in all the test cases. The coupled set of governing equations are solved using the finite volume method algorithm SIMPLEC in FLUENT 2020-R2. The results are validated with the experimental results from Hemadri et al. [1] to authenticate the adopted solution methodology. Notably, with increasing Knudsen number, the fully developed Nusselt number is found to attain a maximum value of about 4.022 corresponding to Knudsen number approximate to 0.006 and Reynolds number approximate to 0.468. The fully developed Nusselt number starts dropping monotonically with a further rise in Knudsen number. The axial span of the thermally fully developed region is also observed to follow this pattern qualitatively with rising degree of rarefaction. Importantly, Brinkman number is seen to increase from about0 to 1 for each test case. All the same, the strength of viscous dissipation remains negligible in the complete flow domain. The rate of increase in the kinetic energy due to expansion work is observed to become marginally small with increasing rarefaction. These findings confirm that the rate of pressure work, viscous stress work at the wall, and viscous dissipation need not be considered for such practical situations. The defining factors that govern the overall heat transfer phenomena are advection, conduction, and the amount of non-equilibrium of the fluid parcels near the wall. These findings also defend the argument that the heat transfer correlations cannot be generalized in terms of Brinkman number or Peclet number only. Instead, they need to be formulated separately depending on the operating conditions of the problem.

Automated summary

The present numerical work investigates the heat transfer characteristics in mildly rarefied gaseous Nitrogen flows. The study analyzes the behavior of thermal flow field with increasing rarefaction and establishes the dependence of Nusselt number on Knudsen number and Reynolds number. The findings show that the fully developed Nusselt number reaches a maximum value at a certain Knudsen number and Reynolds number, and then decreases with further increase in Knudsen number. The axial span of the thermally fully developed region also decreases with rising degree of rarefaction. The strength of viscous dissipation remains negligible, and the increase in kinetic energy due to expansion work becomes smaller as rarefaction increases.