Analysis of the local thermal non equilibrium ipothesis on the fully developed convection in a porous channel saturated by a nanofluid

The term “nanofluid,” suggested by Choi [1], refers to a liquid containing a suspension of metallic or nonmetallic nanometer- sized solid particles and fibers (nanoparticles). In the last decade, in the literature attention has been paid to the investigation of nanofluid saturated porous media, with special reference to the heat transfer phenomena. The interest in this subject is mainly due to the technological value of an improved design of heat exchangers with high thermal performances and a small size. Concerning this aim, an optimal fluid-to-solid heat exchange is devised through a metal foam, and the usual fluid is replaced by a nanofluid. The argument supporting the use of a nanofluid, instead of an ordinary fluid, is grounded on its enhanced features relative to the high thermal conductivity and to the high heat transfer rates. The present paper aims to investigate the behaviour of a nanofluid saturated porous medium. In the literature, two different approaches can be distinguished in order to model the nanofluid: one may consider the distribution of the nanoparticles inside the base fluid as homogeneous or may consider the distribution of nanoparticles inside the base fluid as non-homogeneous. A non- homogeneous model, on the other hand, adds one or more equations to the set of governing equations in order to describe the nanoparticle distribution and/or the nanoparticle velocity and the most widely employed is the model by [2], a model suitable for the heat transfer analysis and for the investigation of the non-homogeneous distributions of nanoparticles. Recently, Nield and Kuznetsov [3] introduced the LTNE model. According to this approach, the effect of local thermal non-equilibrium among the particle, fluid, and solid-matrix phases is investigated using a three-temperature model. In the present contribution, we aim to investigate the Darcy convection in a parallel-plane porous channel, saturated by a nanofluid. The non homogeneous Bongiorno model is employed. A boundary temperature varying with the longitudinal coordinate is prescribed, and the fully developed region is investigated with an analytical approach. For the nanoparticle concentration, an inlet condition given by a uniform distribution is assumed while the boundary walls are considered as impermeable. The nanoparticle concentration and the three temperature fields (particle, fluid and solid matrix) will be determined.