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In this paper, the problem of unsteady natural convective heat transfer flow of nanofluids having various sizes of nanoparticles inside an inclined square enclosure in the presence of oriented magnetic field is investigated numerically. The Brownian motion of nanoparticles is taken into consideration in the thermal conductivity model construction. Two opposite walls of the enclosure are insulated and the other two walls are kept at different temperatures. Galerkin weighted residual finite element technique has been employed to solve the governing nonlinear dimensionless equations. In order to ensure the accuracy of the present numerical code, comparisons with previously published works are performed and excellent agreement is obtained. The effects of model parameters such as Rayleigh number, Hartmann number, nanoparticles volume fraction, inclination angle of magnetic field, inclination angle of the geometry, diameter and Brownian motion of the nanoparticles on the fluid flow and heat transfer are investigated. The results indicate that an increment in Rayleigh number and nanoparticle volume fraction increases the heat transfer rate in a significant way, whereas, an increment in Hartmann number decreases the overall heat transfer rate. It is also observed that the heat transfer enhancement strongly depends on the diameter of the nanoparticles as well as the types of the nanofluids. It is observed that the time taken to reach the steady state is controlled by the different model parameters and in particular, it is longer for low Rayleigh number and shorter for high Rayleigh number. A comparison between the two studies of with and without Brownian motion shows that when Brownian motion is considered, the solid volume fraction has more significant effects on the heat transfer rate at all Rayleigh numbers considered in the square cavity. Finally, the distribution of average heat transfer rate for different cavity inclination angle along with various model parameters has been found as almost parabolic shape.
Khamis S. Al Kalbani (Fri,) studied this question.