Analysis of Conjugate Mixed Convection Flow of a Nanofluid Over a Vertical Fin in Porous Media

This paper presents a detailed study of the interaction between conduction through a vertical fin and conjugate mixed convection of a nanofluid flowing in a porous medium. The fin model and the primitive partial differential equations governing the nanofluid with boundary conditions are transformed into dimensionless forms. For the nanofluid, fin, and fin-nanofluid interface equations, a second-level nonsimilarity transformation is obtained and solved by the bvp4c solver. A validation of the computational code is ensured by comparing the results to a conventional fluid. It was found that the fin temperature is strongly controllable by the geometrical parameters and thermal conductivity of the fin, while Brownian motion and thermophoresis have a moderate effect on it. In addition, low values of Nr and Ω favor the fin efficiency. An analysis on very different values of the Pr number reveals that the use of nanofluids with a suitable base fluid allows high fin dissipations. A more advantageous thermal design can be achieved by combining a nanofluid in a porous medium with a fin in specific applications. These main results provide valuable information on the necessary optimization of the fin efficiency.