Free convection in a square porous cavity filled with a nanofluid using thermal non equilibrium and Buongiorno models

Abstract

Purpose

The purpose of this paper is to theoretically analysis the steady-state natural convection flow and heat transfer of nanofluids in a square enclosure filled with a porous medium saturated with a nanofluid considering local thermal non-equilibrium (LTNE) effects. Different local temperatures for the solid phase of the nanoparticles, the solid phase of porous matrix and the liquid phase of the base fluid are taken into account.

Design/methodology/approach

The Buongiorno’s model, incorporating the Brownian motion and thermophoresis effects, is utilized to take into account the migration of nanoparticles. Using appropriate non-dimensional variables, the governing equations are transformed into the non-dimensional form, and the finite element method is utilized to solve the governing equations.

Findings

The results show that the increase of buoyancy ratio parameter (Nr) decreases the magnitude of average Nusselt number. The increase of the nanoparticles-fluid interface heat transfer parameter (Nhp) increases the average Nusselt number for nanoparticles and decreases the average Nusselt number for the base fluid. The nanofluid and porous matrix with large values of modified thermal capacity ratios (γ _p and γ _s ) are of interest for heat transfer applications.

Originality/value

The three phases of nanoparticles, base fluid and the porous matrix are in the LTNE. The effect of mass transfer of nanoparticles due to the Brownian motion and thermophoresis effects are also taken into account.

Citation

Pop, I., Ghalambaz, M. and Sheremet, M. (2016), "Free convection in a square porous cavity filled with a nanofluid using thermal non equilibrium and Buongiorno models", International Journal of Numerical Methods for Heat & Fluid Flow, Vol. 26 No. 3/4, pp. 671-693. https://doi.org/10.1108/HFF-04-2015-0133