Free and forced convection around line sources of heat and heated cylinders in porous media

An analysis is presented for the steady, two-dimensional, free convection a round line sources of heat and heated cylinders in unbounded saturated poro us media. It is extended to account also for the effects of forced convecti on. The study is based on the Boussinesq equations, with the velocities cal culated using Darcy's law. The analysis begins with the non-dimensional formulation and numerical solu tion of the problem of pure free convection around a line source of heat. W hen this analysis is extended to include the effects of forced convection, two parameters appear in the non-dimensional formulation: the non-dimension al value, V-infinity, of the free-stream velocity and its angle gamma of in clination with respect to the vertical. We first describe the asymptotic fo rm of the solution for large and small values of the distance to the source . The far-field description, which is also applicable to the flow around he ated cylinders, is needed to facilitate the numerical solution of the probl em. It includes a thermal wake, aligned with the free stream, and an outer irrotational flow with a sink and a vortex at the line source. The temperat ure distribution near the source involves a constant A(0)(V-infinity, gamma ), to be calculated with the numerical solution of the complete problem, wh ich is used in the evaluation of the heat transfer from heated cylinders wh en the Rayleigh and Peclet numbers are small compared with unity. In this c ase we find an inner region where heat conduction is dominant, and an outer region where the cylinder appears as a line source of heat. The asymptotic analysis is complemented with the numerical solution of the general proble m for circular cylinders with a wide range of Rayleigh numbers and some rep resentative values of V-infinity and gamma. We give correlations for the Nu sselt number in the limiting cases of pure free convection and pure forced convection.