Analytical Solution of the Graetz Problem Extended to Slip-Flow in Microtube

Abstract

The original Graetz problem is extended to slip-flow in microtube. The extended Graetz problem in slip-flow with the isothermal boundary condition on the wall was solved using conventional energy equation with both the velocity slip and the temperature jump condition of slip-flow. The analytical solution was obtained by solving the energy equation with the method of separation of variables. The accurate eigenvalues were obtained by solving the eigenfunction with the method of power series expansion. In the end, temperature distributions, local Nusselt number Nux , and dimensionless temperature jump θs were obtained. In addition, the influences of Knudsen number Kn on Nux , Nu∞ , and θs were discussed.