Second Law Analysis for Extended Graetz Problem Including Viscous Dissipation in Microtubes

The entropy generation rate has become a useful tool for evaluating the intrinsic irreversibilities associated with a given process or device. This work presents an analytical solution for entropy generation in hydrodynamically fully developed thermally developing laminar flow in a microtube. The rarefaction effects as well as viscous heating effects are taken into consideration, but axial conduction is neglected. Using fully developed velocity profile, the energy equation is solved by means of integral transform. The solution is validated by comparing the local Nusselt numbers against existing literature data. From the results it is realized that the entropy generation decreases as Knudsen number increases, while the effect of increasing values of Brinkman number and the ratio of Brinkman number to dimensionless temperature difference is to increase entropy generation. The average entropy generation number over the cross section of channel increases with increasing values of axial coordinate, until it reaches a constant value at fully developed conditions.