Abstract
Analytical and numerical solutions are presented for steady-state, thermal convection induced by hot/cold pipes buried in a saturated, semi-infinite, permeable medium, the surface of which is horizontal, impermeable and subject to Robin's (convective) boundary condition. The pipe's surface is impermeable and isothermal. The analytical solution consists of the construction of a double expansion in terms of the Rayleigh and the inverse Biot numbers. Computer algebra (MACSYMA) is used to carry out the more tedious mathematical manipulations. The numerical approach involves both the construction of a regular perturbation expansion in terms of the Rayleigh number and the solution of the full nonlinear governing equations. The results of the perturbative analysis and the numerical calculations, which include descriptions of the flow and temperature fields as well as correlations for the Nusselt number, are compared and found to agree favorably.
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