The effects of viscous dissipation and nanofluids as working fluid on the thermal development in an isothermal microchannel

Abstract

This study investigated the effects of viscous dissipation on the characteristics of thermal development in an isothermal-isothermal circular microchannel, also known as Graetz Brinkman problem, analytically and highlighted a critical Brinkman number of approximately 1.12 that delineates Nusselt number trends across Brinkman numbers ranging from 0.5 to 1.2. The findings revealed instances where the heat transfer direction changes, and the mean fluid temperature exceeds the wall temperature, leading to thermal development characterisation when the Brinkman number is lower than the critical value. The heat transfer coefficient beyond the axial distance where the bulk mean temperature equals the wall temperature marks the overriding effect of viscous dissipation over convection heat transfer. Additionally, local heat transfer coefficients across 30-μm, 50-μm, and 100-μm circular microchannels cooled by two types of working fluids: water and a 5 vol% Al₂O₃-water nanofluids are compared. Results suggested that nanofluid outperforms water near the entrance of the microtube but starts to deteriorate further from the entrance owing to viscous dissipation effects and is exacerbated with an increasing Reynolds number. A more significant viscous dissipation effect in nanofluids tends to expedite the thermal development and renders its role as a coolant ineffective in an isothermal microchannels.