Conjugate free convection in a vertical channel filled with nanofluid
Keywords:
Free convection, heat transfer, nanofluid, Brownian motion, thermophoresis, heat generation, thermal energy.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 equa- tions is written in terms of dimensionless velocity, temperature and concentra- tion 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.
Mathematics Subject Classification (2010): 76R10, 82D15, 82D80.
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