Non-Darcy Assisted Flow along a Channel with an Open Cavity Filled with Water–TiO 2 Nanofluid Rehena Nasrin and M.A. Alim Department of Mathematics, Bangladesh University of Engineering and Technology, Dhaka, Bangladesh Numerical investigation on forced (assisted) convection heat transfer in a two-dimensional horizontal porous channel with an open cavity is studied in this article. A non-uniform heat flux is considered to be located on the bottom surface of the cavity. The rest of the surfaces are taken to be perfectly insulated. The physical domain is filled with a water-based nanofluid containing TiO 2 nanoparticles. The fluid enters from the left and exits from the right with initial velocity U i and temperature T i . Governing equations are discretized using the penalty finite element method. The simulation is carried out for a wide range of Reynolds number Re (= 10–500) and Darcy number Da (= 10 –5 –∞). Results are presented in the form of streamlines, isothermal lines, local and average Nusselt numbers, average temperatures of the fluid, horizontal and vertical velocities at mid-height of the channel and mean velocity fields for various Re and Da. The enhancement of heat transfer rate is caused by the increasing Re and falling Da. © 2013 Wiley Periodicals, Inc. Heat Trans Asian Res, 42(4), 300–318, 2013; Published online 26 March 2013 in Wiley Online Library (wileyonlinelibrary.com/journal/htj). DOI 10.1002/htj.21046 Key words: water–TiO2 nanofluid, non-Darcy assisted flow, channel with open cavity, porous medium, penalty finite element method 1. Introduction Nanofluid technology has emerged as a new enhanced heat transfer technique in recent years. A nanofluid is made by adding nanoparticles and a surfactant into a base fluid and can greatly enhance thermal conductivity and convective heat transfer. The diameters of nanoparticles are usually less than 100 nm which improves their suspension properties. The knowledge of forced convection heat transfer inside geometries of irregular shape (for example, channel, pipe bend, channel with cavity) for porous media has many significant engineering applications; for example, geothermal engineering, solar-collectors, cold storage performance, and thermal insulation of buildings. Some published articles are available that deal with flow characteristics, heat transfer, flow and heat transfer instability, transition to turbulence, design aspects, etc. Many researchers [1–6] have considered different physical situations which can be classified into two broad groups. The first group of problems covers a wide range of applications; for example, flow through blood vessels, food © 2013 Wiley Periodicals, Inc. Heat Transfer—Asian Research, 42 (4), 2013 300