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In this paper, the fully-developed temperature profile and corresponding  Nusselt value is determined analytically for a gaseous flow in a microtube  with a thermal boundary condition of constant wall heat flux. The flow  assumed to be laminar, and hydrodynamically and thermally fully developed.  The fluid is assumed to be constant property and incompressible. The effect  of rarefaction, viscous dissipation and axial conduction, which are  important at the microscale, are included in the analysis. Second-order slip  model is used for the slip-flow and temperature jump boundary conditions for  the implementation of the rarefaction effect. Closed form solutions for the  temperature field and the fully-developed Nusselt number is derived as a  function of Knudsen number, Brinkman number and Peclet number.

Evaluation of Nusselt number for a flow in a microtube using second-order slip model