Numerical analysis of natural convective flow and heat transfer of nanofluids in a vertical rectangular duct using Darcy-Forchheimer-Brinkman model

In this paper, natural convective flow and heat transfer of nanofluids in a vertical rectangular duct filled with porous matrix is investigated. The Darcy-Forchheimer-Brinkman model is used to represent the fluid transport within the porous medium covering the parametric ranges of 1 ≤ Gr ≤ 25,0 ≤ Br ≤ 8, and 0.0001 ≤ Da≤ 100. Also, pure water and five different types of nanofluids (Cu, diamond, TiO2, Ag and SiO2) are used with a volume fraction range of 0% ≤ Ø ≤0.2%. The governing nonlinear, coupled partial differential equations for the two-dimensional laminar, steady flow and heat transfer are solved numerically by a finite difference method with second order accuracy. It is found that the heat transfer is enhanced due to the use of a nanofluid. Further, it is noticed that an increase in the Darcy or Grashof or Brinkman numbers, or the aspect ratio parameter increase the flow and heat transfer characteristics; whereas the inertial or the viscosity ratio parameters reduce the flow and heat transfer characteristics. It is observed from 2-D graphs that the fluid rise up from the middle portion of the vertical wall and flow down along the two horizontal walls forming symmetric rolls with clockwise and counter-clockwise rotation inside the cavity. The temperature contours in 2-D are smooth curves which span the entire enclosure, and they are generally symmetry with respect to the horizontal symmetric line. The results obtained reveal many interesting behaviors that warrant further study on the heat transfer enhancement due to the nanofluids.