The investigations on direct reduced iron (DRI) have commonly been made at two different scales: the pellet scale and the macroscopic or reactor scale. The reduction of a single pellet is typically investigated for developing kinetics of chemical reactions accompanied by heat and mass transport, whereas in the macroscopic view, the reduction process is investigated in the reactor scale. However, these two aspects are not independent of each other and usually the kinetic parameters that are used in the reactor modeling come from the single pellet study. This article reviews the most relevant models in the literature with regard to direct reduction reactions in the pellet scale together with more recently developed new approaches. This review also presents a critical assessment of the previously proposed models in terms of which models are applicable under what conditions and to what types of the solid structure. The flaws and pitfalls in some of these models are also pointed out with cautions. The present article is broadly divided into experimental and mathematical sections.

In the present paper, free heat convection and entropy generation of Newtonian and two types of non-Newtonian fluids, shear-thickening and shear-thinning, inside an Lshaped cavity subjected to a magnetic field have been investigated by the finite difference lattice Boltzmann method. The power-law model was used for modeling the rheology of the fluids. The bottom and left walls of the cavity have been kept at a uniform high temperature. Internal walls are also kept cold. The remaining walls have been insulated against heat and mass transfer. The Boussinesq approximation is used to take the temperature dependency of density into account. The distribution functions of energy and density are modeled through the use of the nine-velocity two-dimensional scheme. The effects of Hartmann number (Ha), aspect ratio, power-law index, and Rayleigh number (Ra), on the flow field, temperature distribution, and entropy distributions are studied. The results show that the magnetic field and the power-law index have an ever-decreasing effect on the heat transfer rate and the entropy generation, while the Ra number has an ever-increasing effect. The maximum heat transfer enhancement of 71% happens at the lowest and the highest values of power-law index and Ra number, respectively, for the case with no magnetic field. The maximum heat transfer deterioration of 77% happens at the highest and lowest values of power-law index and Ra number, respectively, in the presence of the highest magnetic field strength. It is interesting that the sensitivities of heat transfer rate and the entropy generation to the Ha number become significant for shear-thinning fluids. It is found that there is an everlasting interplay between conduction and convection contributions to the irreversibilities, so that, for the Newtonian and

In this study MHD flow around and through porous cylinder is numerically investigated. The governing equations are developed in polar coordinate arrangement in both porous and non-porous media on the basis of single-domain technique. The equations are solved numerically based on finite volume method over staggered grid structure. Nusselt number and drag coefficient are selected as two key parameters describing performance of this system. By applying response surface methodology the sensitivity of these parameters to main factors of the problem, including Stuart number, Darcy number and Reynolds number are quantified. RSM is also utilized to perform an optimization process to find the best condition in which the lowest drag force and highest heat transfer rate occur simultaneously. The CFD analysis is carried out for variant Reynolds numbers (10 ≤ Re ≤ 40), Darcy numbers (10-6 ≤ Da ≤ 10-2) and Stuart numbers (2 ≤ N ≤ 10). Streamlines and isotherms are presented to indicate the impacts of such parameters on heat and fluid flow. It can be seen that, Drag coefficient and Nusselt number increase by augmenting magnetic field strength. Beside, Darcy number and Reynolds numbers have a direct and inverse effect on Nuave and Cd, respectively. Results of optimization process show that Nuave and Cd are more sensitive to Reynolds and Stuart numbers, respectively, while they less sensitive to Darcy number. Moreover, it is revealed that the optimum condition occurs at Da = 10-2, Re = 38.1 and N = 4.49.

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