Computational Methods in Engineering

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One of the great enemies of rubber compounds is heat. Heat will cause chemical and physical degradation of vulcanized rubber as well as a considerable loss in its strength. A major source of heat generation in a tire is due to internal friction resulting from the viscoelastic deformation of the tire as it rolls along the road. Another source of heat generation in a tire is due to its contact friction with the road. Prediction of the temperature rise at different parts of the tire will help to detect the behavior of the tire as regards its strength and its failure. In the present work, initially the data required for the thermal analysis of the tire are determined which include: the thermal conductivity of rubber compounds, the tire rolling resistance and its heat build-up rate. The thermomechanical analysis of a typical tire then follows based on the thermodynamics of an irriversible process. The mechanical dissipatives, i.e. the hystersis losses are assummed to be the major source of heat in the mathematical formulation. A finite element code is developed for two-dimensional heat transfer analysis of the tire. The results obtained show that the highest temperature rise will occur on the carcass-tread interface in a tire specially at heavy loading and under high speed conditions. Keywords: Heat Generation, Rubber, Contact Friction, Design, Finite Element, Viscoelastic Deformation

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A two-phase lattice Boltzmann model considering the interaction forces of nanofluid has been developed in this paper. It is applied to investigate the flow and natural convection heat transfer of Al₂O₃–H₂O nanofluid in an enclosure containing internal heat generation. To understand the heat transfer enhancement mechanism of the nanofluid flow from the particle level, the lattice Boltzmann method is used because of its mesoscopic feature and numerical advantages. By using a two-component lattice Boltzmann model, the heat transfer enhancement of the nanofluid is analyzed through incorporating the different forces acting on the nanoparticles and the base fluid . The effects of interaction forces, nanoparticle volume fractions (0.0-0.05), and internal and external Rayleigh numbers (10³-10⁶) on the nanoparticle distributions and heat transfer characteristics are investigated. The average Nusselt number increases with the increase of nanoparticle volume fraction and Rayleigh number. We also compared and analyzed adding internal heat generation on the nanoparticles and the base fluid separately, and it was found that by considering heat generation on the base fluid, it mostly affects the temperature field, and by considering that on nanoparticles, it mostly affects the stream field.

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In the present work, the effect of magnetic field, changes in the angle of inclination of the cavity and the shape of nanoparticles on the flow field and heat transfer of water-alumina with uniform heat generation/absorption is investigated by Lattice Boltzmann method (LBM). The curved wall and the diagonal walls of the cavity are at a constant temperature of hot and cold, respectively. Nanoparticle volume fraction  of 0, 0.02 and 0.04, Hartmann number of 0, 15, 30, 45 and 60, heat generation/absorption coefficient of -5, 0 and +5 and inclination angle of 45, 135 and 225 degrees are studied. The high accuracy of the results compared to previous studies confirmed the correctness of the code written in Fortran language. The results shows that in all cases, increasing the Hartmann number leads to a decrease in the maximum value of the streamlines and the average Nusselt number, with the lowest effect at 225 degrees. Also increasing the strength of the magnetic field leads to an average decrease of 28, 23 and 7% of the average Nusselt number for angles of 45, 135 and 225 degrees, respectively. Increasing the heat generation/absorption coefficient is a determining factor in the effectiveness of the magnetic field and adding nanoparticles, and increasing it reduces the amount of heat transfer. On average, heat generation reduces the average Nusselt number by 71, 98, and 145 percent for the angles of 45, 135, and 225 degrees, respectively. In general, the lowest value of the average Nusselt number is related to the angle of 225 degrees, but the effect of adding nanoparticles in increasing the average Nusselt number is the highest at this angle. Generally, an increase in the percentage of nanoparticles leads to an average increase of 12% in the average Nusselt number. The effect of nanoparticle shape is more apparent with increasing their volume fraction. The highest amount of heat transfer is related to the cylindrical nanoparticles, in which the average Nusselt number is on average about 6% higher than the spherical state.