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Gaseous Flow in Microconduits with Viscous Dissipation
Barbaros Cetin, Hafit Yuncu and Sadik Kakac

Heat transfer analysis of two-dimensional, incompressible, constant property, hydrodynamically developed, thermally developing, single phase laminar flow in microtubes and microchannels between parallel plates with negligible axial conduction is performed for constant wall temperature and constant wall heat flux thermal boundary conditions for slip flow regime. Fully developed velocity profile is determined analytically, and energy equation is solved by transforming the steady-state problem into a transient problem then by the use of the finite difference scheme for both of the geometries. The rarefaction effect which is important for flow in low pressures or flow in microchannels is imposed to the boundary conditions of the momentum and energy equations. The viscous dissipation term which is important for high speed flows or flows in long pipelines is included in the energy equation. The effects of rarefaction and viscous heating on local Nusselt number are discussed. The results of the numerical method are verified with the exact solutions of the flow in macrochannels (i.e. Kn =0, Br =0) and with the available analytical results of flow in micro channels for simplified cases. The results show significant deviations from the flow in macrochannels.

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