Analysis of heat transfer and entropy generation for a low-Peclet-number microtube flow using a second-order slip model: an extended-Graetz problem

Abstract

The classical Graetz problem, which is the problem of the hydrodynamically developed, thermally developing laminar flow of an incompressible fluid inside a tube neglecting axial conduction and viscous dissipation, is one of the fundamental problems of internal-flow studies. This study is an extension of the Graetz problem to include the rarefaction effect, viscous dissipation term and axial conduction with a constant wall temperature thermal boundary condition. The energy equation is solved to determine the temperature field analytically using general eigenfunction expansion with a fully developed velocity profile. To analyze the low-Peclet-number nature of the flow, the flow domain is extended from $$-\infty $$ to $$+\infty $$ . To model the rarefaction effect, a second-order slip model is implemented. The temperature distribution, local Nusselt number, and local entropy generation are determined in terms of confluent hypergeometric functions. This kind of theoretical study is important for a fundamental understanding of the convective heat transfer characteristics of flows at the microscale and for the optimum design of thermal systems, which includes convective heat transfer at the microscale, especially operating at low Reynolds numbers.