# Conjugate free convection in a vertical channel filled with nanofluid

## Abstract

The steady natural conjugate convection in a long vertical channel filled with a nanofluid and including internal heat generation is presented in this paper. A new mathematical model is proposed for the momentum, energy and nanoparticles’ concentration equations. The system of partial differential equations is written in terms of dimensionless velocity, temperature and concentration of the nanoparticles and is solved analytically. The effects of the governing parameters, such as the ratio between the thermophoresis parameter and the Brownian motion parameter, R, and the buoyancy ratio parameter, Nr, on the velocity, temperature and nanoparticles’ concentration are studied. It is found that the addition of the nanoparticles into the fluid reduces the temperature and enhances the heat transfer. A limit case when the thermal conductivity of the nanoparticles is much larger than the thermal conductivity of the base fluid has been also studied

## Authors

Flavius Patrulescu
(Tiberiu Popoviciu Institute of Numerical Analysis,

Teodor Groşan
(Babeş-Bolyai University Faculty of Mathematics and Computer Sciences)

## Keywords

free convection, heat transfer, nanofluid, Brownian motion, thermophoresis, heat generation, thermal energy

## Cite this paper as

F. Pătrulescu, T. Groşan, Conjugate free convection in a vertical channel filled with nanofluid, Stud. Univ. Babeș-Bolyai Math. vol. 60 no. 4 (2015), pp. 611–621.

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##### Publisher Name

Universitatea Babeş-Bolyai, Cluj-Napoca; Cluj University Press, Cluj-Napoca

0252-1938

2065-961X

3437423

1389.76049