Natural convection of nanofluids in a square enclosure with protruding heater

This paper reports a numerical study on natural convection from a protruding heater located at the bottom of a square cavity filled with a copper-water nanofluid. The vertical walls of the cavity are cooled isothermally; the horizontal ones are adiabatic, and the heater is attached to the bottom wall. The heat source is assumed either to be isothermal or to have a constant heat flux. The effective viscosity and thermal conductivity of the nanofluid are modeled according to Brinkman and Patel, respectively. Numerical solutions of the full-governing equations, based on the lattice Boltzmann method, are obtained for a wide range of the governing parameters: the Rayleigh number, Ra; the Prandtl number, Pr; the geometrical parameters specifying the heater; the volume fraction of nanoparticles, Φ. For a particular geometry, it has been found that, for a given Ra, heat transfer is enhanced with increasing Φ, independently of the thermal boundary condition applied on the heater.