Free Convection in a Carbon Nanotube-Water Nanofluid Filled Enclosure with Power-Law Variation Wall Temperature

A numerical study has been done in this work to study the flow and heat transfer characteristics of CNT-water nanofluid in a cavity with power-law variation wall temperature. The square enclosure used has been bounded by adiabatic top wall and isotherm temperature cold vertical walls. The bottom wall temperature varies as the power of the axial coordinate. For the thermophysical properties of CNTs, empirical correlations are used in terms of the volume concentration of CNT nanoparticles. For the effective thermal conductivity of CNTs, a new model has been used. Steady governing equations of heat and fluid flow are solved via finite volume method. Calculations were performed for Rayleigh number (10(3) <= Ra <= 10(5)), volume fraction of nanoparticles (0 <= phi <= 0.09) and exponent in the power-law variation (0 <= n <= 2). Results are presented in terms of isotherms, fluid flow patterns, graphs of local and average Nusselt numbers. It has been found that for a given Rayleigh number and a given exponent n an increase of volume fraction of nanoparticles causes an increase of the mean Nusselt number. The heat transfer rate increase as the Rayleigh number increases or as the exponent n decreases for a given volume fraction of nanoparticles.