Thermal convection in a horizontal, eccentric annulus containing a saturated porous medium—an extended perturbation expansion

Abstract

Thermal convection in a saturated porous medium confined between two horizontal, isothermal, eccentric cylinders is studied through the use of a regular perturbation expansion in terms of the Darcy-Rayleigh number ( R). Terms up to O( R 30) are computed. In particular, the Nusselt number ( Nu) is expressed as a power series of R for various eccentricities. The above power series has, however, a limited radius of convergence. Various non-linear transformations are employed in order to extend the range of utility of the series. The results are used to demonstrate that the heat transfer in the annulus can be optimized by a proper choice of eccentricity. These results have a bearing on the design of thermal insulators.