Dissipation and entropy generation in fully developed forced and mixed laminar convection

A power series expansion of the axial velocity has been used to solve the coupled partial differential equations for fully-developed mixed convection in a vertical tube with uniform heat flux at the wall, uniform internal volumetric heat source and viscous dissipation. Explicit analytical expressions have been obtained for the temperature and velocity profiles as well as for the axial pressure gradient. They were satisfactorily validated for the case of forced convection with both heat source and dissipation, and also for cases of mixed convection with heat source and with or without dissipation. The power series solution has been used to study the effect of viscous dissipation on mixed convection. A Brinkman number of 0.5 results in a significant decrease of both the pressure gradient and the Nusselt number with respect to their values for Br=0. The entropy generation rate has also been calculated for both forced and mixed convection; in both cases the contribution of internal friction is significantly higher than that of conduction.