Validation of the local thermal equilibrium assumption for free convection boundary layer flow over a horizontal cylinder embedded in an infinite saturated porous medium

Abstract

This study numerically investigated the validity of the local thermal equilibrium model for free convection over a horizontal cylinder embedded in an infinitely packed bed of spherical particles saturated with Newtonian fluid. The local thermal non-equilibrium and Forchhemimer-Brinkman extended Darcy model were used by considering the boundary-layer theory assumptions and were solved with the implicit Keller box finite difference scheme. The governing parameters considered are the porosity, thermal conductivity ratio, Rayleigh number, Prandtl number, the ratio of cylinder diameter to spherical particle diameter and Biot number. The results showed the two parameters of conductivity ratio and Biot number can significantly affect the other parameters. For low Biot number and conduction coefficient ratio, the local thermal non-equilibrium assumption was inapplicable in almost all cases. Significantly, for high values of the conductivity ratio and Biot number, the assumption that the fluid and solid matrix are isothermal, could be used in almost all cases studied. Furthermore, increasing the amount of Rayleigh number, Porosity and Prandtl increased the temperature difference between the solid and fluid phases. In addition, increasing the ratio of cylinder diameter to particle diameter reduced the temperature difference between the two phases. The average temperature difference between fluid and solid can have the most changes as follows: It can experience 200% growth when the Prandtl number changes from 2 to 7. Also, it can reduce by 33% by increasing the Bio number from 0.01 to 10. In addition, the temperature difference of two phases can be increased by 7 and 0.5 times by increasing the porosity from 0.25 to 0.85 and increasing the ratio of cylinder diameter to particle diameter from 20 to 100, respectively.