Heatline analysis on natural convection for nanofluids confined within square cavities with various thermal boundary conditions

Natural convection of nanofluids in presence of hot and cold side walls (case 1) or uniform or non-uniform heating of bottom wall with cold side walls (case 2) have been investigated based on visualization of heat flow via heatfunctions or heatlines. Galerkin finite element method has been employed to solve momentum and energy balance as well as post processing streamfunctions and heatfunctions. Various nanofluids are considered as Copper–Water, TiO2TiO2–Water and Alumina–Water. Enhancement of heat transfer with respect to base fluid (water) has been observed for all ranges of Rayleigh number (Ra)(Ra). Dominance of viscous force or buoyancy force are found to play significant roles to characterize the heat transfer rates and temperature patterns which are also established based on heatlines. In general, convective closed loop heatlines are present even at low Rayleigh number (Ra=103)(Ra=103) within base fluid, but all nanofluids exhibit dominant conductive heat transport as the flow is also found to be weak due to dominance of viscous force for case 1. On the other hand, convective heat transport at the core of a circulation cell, typically represented by closed loop heatlines, is more intense for nanofluids compared to base fluid (water) for case 2 at Ra = 105. It is also found that heatlines with larger heatfunctions values for nanofluids coincide with heatlines with smaller heatfunction values for water at walls. Consequently, Nusselt number which is also correlated with heatfunctions show larger values of nanofluids for all ranges of Ra  . Average Nusselt numbers show that larger enhancement of heat transfer rates for all nanofluids at Ra=105Ra=105 and Alumina–Water and Copper–Water exhibit larger enhancement of heat transfer rates.