THE GRAETZ PROBLEM EXTENDED TO SLIP-FLOW

The original problem for thermally developing heat transfer in laminar flow through a circular tube, as formulated by Graetz, did not consid er the 'slip-flow' condition. This paper extends the original work of Graetz to include the effect of slip-flow, which occurs in gases at lo w pressures or in microtubes at ordinary pressures. A special techniqu e was developed to evaluate the eigenvalues for the problem. Eigenvalu es were evaluated for Knudsen numbers ranging between 0 and 0.12. Simp lified relationships were developed to describe the effect of slip-flo w on the convection heat transfer coefficient. (C) 1997 Elsevier Scien ce Ltd.