Theoretical investigation of scaling effects from macro-to-microscale convection due to variations in incompressible fluid properties

Abstract

We re-examine the governing continuum-based conservation equations for single-phase laminar forced convection of liquids, incorporating temperature dependence of fluid viscosity and thermal conductivity. The effects of property variations become highly significant from macro-to-microscale convection. Further, the effects of property variations along the flow become more significant relative to property variations over the cross section; thereby necessitating consideration of additional convection mechanisms at the microscale, in addition to mechanisms known at the macroscale. The same Brinkman number that determines convection with viscous dissipation, also determines convection with variations in fluid properties; but now the significance in convection increases with decreasing Brinkman number.