Gaseous slip flow forced convection in a micropipe and parallel-plate microchannel with a piecewise uniform wall heat flux and axial heat conduction

A forced convective heat transfer problem inside a micropipe as well as inside a microchannel with parallel walls in the laminar gaseous slip flow regime, a with finite heating region and a prescribed wall heat flux, including the axial heat conduction effect, is analytically investigated. The temperature field and Nusselt number are derived under the assumption that the flow is hydrodynamically fully developed in the finite-length heating region. The solution is found by applying the functional analysis method, by decomposing the energy equation into a pair of first-order partial differential equations. The first-order slip boundary conditions are imposed at the gas-wall interface. The analytical solution is compared with available calculations. The results show that the thermal characteristics in the heating region are significantly affected by the axial heat conduction, rarefaction effects, and finite length of the heating region.