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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Summary In a comprehensive study, the thermal conductivity, dynamic viscosity, and the rheological behavior of a SiO2/water nanofluid are investigated experimentally at the temperatures, solid concentrations, and the shear rates of 25°C to 50°C, 0% to 1.5%, and 400 to 1400(s−1), respectively. The Response Surface Methodology (RSM) is utilized to obtain regression models for the thermal conductivity and the dynamic viscosity. Subsequently, the sensitivity of the aforementioned models to 10% changes in the temperature, and the nanofluid concentration is analyzed. Afterward, Nondominated Sorting Genetic Algorithm II (NSGA‐II) is utilized to find the maximum thermal conductivity and the minimum viscosity. The nondominated optimal points are presented through a fitted correlation on a Pareto front to make the results more practical. The measurements of the investigated nanofluid could be summarized as a paper of a handbook. The workability of the investigated nanofluid is also examined in both laminar and turbulent flow regimes through analysis of the heat transfer merit graphs. To this end, the ratio of the dynamic viscosity enhancement to the thermal conductivity enhancement and the Mouromtseff number are chosen as two criteria of the laminar and turbulent flow regimes, respectively. Finally, the results are compared with those for SiO2/glycerin and SiO2/ethylene glycol nanofluids to check the workability in different base fluids. From a thermal‐efficiency point of view, the SiO2/water nanofluid is not suggested for use in both laminar and turbulent pipe flows, except in temperatures higher than 30°C and volume concentrations lower than 1% for the case of laminar flow. This is because the favorable heat transfer enhancement of the nanofluid is more than the unfavorable increase of the pumping power. From the rheological point of view, though, a SiO2/water nanofluid would be a good choice in lubricating moving surfaces for both laminar and turbulent flow regimes. It is found that in higher nanofluid concentrations, the thermal conductivity of a SiO2/water nanofluid is highly influenced by temperature. Moreover, adding nanoparticles at temperatures of 35°C to 40°C would have the highest increasing effect on the thermal conductivity. It is also revealed that increasing the temperature does not significantly affect the viscosity when 1% SiO2 nanoparticles are suspended within the water.

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This article studies buoyancy-driven natural convection of a nanofluid affected by a magnetic field within a square enclosure with an individual conductive pin fin. The effects of electromagnetic forces, thermal conductivity, and inclination angle of pin fin were investigated using non-dimensional parameters. An extensive sensitivity analysis was conducted seeking an optimal heat transfer setting. The novelty of this work lies in including different contributing factors in heat transfer analysis, rigorous analysis of design parameters, and comprehensive mathematical analysis of solution domain for optimization. Results showed that magnetic strength diminished the heat transfer efficacy, while higher relative thermal conductivity of pin fin improved it.Based on the problem settings, we also obtained the relative conductivity value in which the heat transfer is optimal. Higher sensitivity of heat transfer was, though, noticed for both magnetic strength and fin thermal conductivity in comparison to fin inclination angle. Further studies, specifically with realistic geometrical configurations and heat transfer settings, are urged to translate current findings to industrial applications.