Laminar Forced Convection in a Circular Tube With Constant Heat Flux and Slip Flow

An analytical solution to the problem of laminar gas flow in microtubes with a constant heat flux boundary condition at the wall is presented. The microtube diameter is small enough that the Knudsen number becomes an important parameter; thus, both a slip flow hydrodynamic condition and a temperature jump thermal condition are assumed at the wall. The fluid is assumed to be hydrodynamically fully developed at the tube entrance. An indirect solution method utilizes the solution for a previously reported isothermal wall problem. The results indicate that the fully developed Nusselt number decreases with Knudsen number. For instance, with a Knudsen number of 0.04, the Nusselt number for fully developed flow is reduced 14 % over that obtained for a nonslip boundary condition.The reduction is strongly influenced by the increased temperature jump as Knudsen number increases.