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Abstract
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In this study, the local thermal non-equilibrium model (LTNE) and the parabolic boundary layer governing diferential equations were used to investigating the efect of the fow and solid matrix parameters on the Nusselt number for free convection over a horizontal cylinder embedded in a saturated infnite packed bed. The Forchheimer–Brinkman-extended Darcy and the local thermal non-equilibrium scheme were solved by the Keller box numerical method. Using the variables of the boundary layer, the physical environment is transferred to a rectangular computational domain; then with the new variables, one order of the derivatives of the equations is reduced and the three-diagonal matrix of the coefcients is calculated. The impacts of the porosity, thermal conductivity ratio, Rayleigh number, the ratio of cylinder diameter to spherical particle diameter and Biot number parameters on the local and average Nusselt number have been studied. The obtained results showed that, the increasing Rayleigh number and porosity increase the mean Nusselt number of two phases. In such a way that increasing the porosity from 0.2 to 0.85 can increase the Nusselt of fuid by 8 times. Also, increasing the ratio of cylinder diameter to spherical particle diameter from 20 to 100 causes the mean fuid Nusselt to decrease by 64%. In addition, increasing the ratio of solid to fuid conductivity and Biot number reduces the average Nusselt of the fuid. Except for the Rayleigh number, the changes of other fuid and solid parameters did not have a signifcant efect on the amount of solid Nusselt.
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