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Analytical solution for single phase microtube heat transfer including axial conduction and viscous dissipation

Barışık, Murat
Heat transfer of two-dimensional, hydrodynamically developed, thermally developing, single phase, laminar flow inside a microtube is studied analytically with constant wall temperature thermal boundary condition. The flow is assumed to be incompressible and thermo-physical properties of the fluid are assumed to be constant. Viscous dissipation and the axial conduction are included in the analysis. Rarefaction effect is imposed to the problem via velocity slip and temperature jump boundary conditions for the slip flow regime. The temperature distribution is determined by solving the energy equation together with the fully developed velocity profile. Analytical solutions are obtained for the temperature distribution and local and fully developed Nusselt number in terms of dimensionless parameters; Peclet number, Knudsen number, Brinkman number, and the parameter κ. The results are verified with the well-known ones from literature