Analysis of Herchel-Bulkley fluid flows in planar and circular microducts with constant heat flux and slip boundary condition

Abstract

The hydrodynamically and thermally fully developed Herchel-Bulkley fluids flows in circular and planar microducts with constant heat flux at the wall was investigated by applying second law analysis while imposing slip boundary condition and including viscous dissipation. To determine tendencies of effects of Brinkman number, slip boundary condition, flow behavior index, cross sectional ratio and heat flux on the Nusselt number, entropy generation rate and thus, irreversibility distribution ratio were investigated. One-dimensional momentum and energy equations with viscous dissipation term were analytically solved to obtain equations for the velocity, temperature distribution, Nusselt number, entropy generation and irreversibility distribution ratio. It was observed that the slip coefficient and the Brinkman number and thus viscous dissipation affecting the Nusselt number, entropy generation and thus, irreversibility distribution ratio cannot be ignored in the analysis. This research illustrates that the Nu increases with increasing the slip coefficient and decreases with increasing the Br and n. The entropy generation rate and thus, the irreversibility distribution ratio increases with increasing the n and Br and decreases with increasing the beta. The obtained results from this study are compared with those obtained from the related experimental and theoretical studies and reasonable agreement is achieved.