Two phase numerical simulation of natural convection of nanofluid considering thermophoresis and brownian motion effects

Abstract

Natural convection heat transfer in cavities is of great interest because of its wide applications in different areas in engineering and technology. Nanofluids are widely used in the heat removal industry as they are more effective in heat transfer enhancement due to their higher thermal conductivity than that of conventional fluids. In this thesis heat transfer by natural convection considering thermophoresis and Brownian motion effects in a square cavity with an obstacle using nanofluid has been studied numerically. A Cartesian co-ordinate system is used with the origin at the lower left corner of the computational domain. The system consists of a square enclosure with sides of length L. A solid square obstacle is positioned at the center of the cavity. In addition, the cavity is saturated with Cu-water nanofluid. Moreover, the vertical walls of the cavity considered to be at a constant temperature Tc (left wall) and Th (right wall), concentration ∅_c(left wall) and ∅_h(right wall). Furthermore, both the top and bottom surfaces of the enclosure are kept adiabatic. The physical problem is represented mathematically by different sets of governing two-dimensional equations along with the corresponding boundary conditions. Using a class of appropriate transformations, the governing equations along with the boundary conditions are transformed into non-dimensional form, which are then solved by employing a finite-element method based on Galerkin weighted residuals approach. The investigations are conducted for different values of Rayleigh number Ra (= 103 – 106), buoyancy ratio number Nr (= 0.1 – 4), Lewis number Le (= 2 – 8), Brownian motion parameter Nb (= 0.1 – 5), thermophoretic parameter Nt (= 0.1 – 3) and Prandtl number Pr (= 4.2 – 10). Various characteristics such as streamlines, isotherms, iso-concentrations and heat transfer rate in terms of the local Nusselt number (Nu) and average Nusselt number (Nuav) are presented for the aforesaid parameters. The results indicate that the mentioned parameters strongly affect the flow phenomenon and temperature field inside the cavity. Suitable combination of parameters may be used from this study to achieve the optimum heat transfer for such physical model. Comparisons with previously published work are performed and the results are found to be in excellent agreement.