## 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, Romanian Academy)

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.

## About this paper

##### Publisher Name

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

##### Paper on journal website

##### Print ISSN

0252-1938

##### Online ISSN

2065-961X

## MR

3437423

## ZBL

1389.76049

## Google Scholar

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