Numerical Simulation of steady and unsteady natural convection heat transfer of nanofluids in eccentric and concentric porous annuluses

This paper is devoted to numerical simulation of steady and unsteady natural heat transfer convection of nanofluids in an eccentric porous annulus. Governing equations including mass, momentum, and energy conservation are discretized by means of finite difference methods and they are solved by Alternating Direction Implicit (ADI) method and Successive over Relaxation (SOR) method. In the present study, the effect of Rayleigh number, nanoparticle volume fraction (in the range of 0 to 4 percent), Darcy number, porosity coefficient, and eccentricity ratio on average Nusselt number, local Nusselt number, streamlines, and isothermal lines are investigated. The results show that by increasing Rayleigh number, the porosity coefficient, and the nanoparticle volume fraction, the heat transfer rate increases. Reducing the Darcy number reduces the permeability of the porous medium and therefore reduces the heat transfer. In unsteady conditions, by increasing the amplitude of the inner wall temperature fluctuation, (due to the increase of the temperature gradient between the two walls), the average Nusselt number increases, and the frequency of the variation of the average Nusselt number is consistent with the inner wall temperature variation frequency.