An analysis is presented for the steady, two-dimensional, free convection around line
sources of heat and heated cylinders in unbounded saturated porous media. It is
extended to account also for the effects of forced convection. The study is based on
the Boussinesq equations, with the velocities calculated using Darcy's law.The analysis begins with the non-dimensional formulation and numerical solution
of the problem of pure free convection around a line source of heat. When this
analysis is extended to include the effects of forced convection, two parameters
appear in the non-dimensional formulation: the non-dimensional value, V∞, of the
free-stream velocity and its angle γ of inclination with respect to the vertical. We
first describe the asymptotic form 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 heated cylinders, is needed to facilitate the numerical solution of the problem.
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 temperature distribution near
the source involves a constant A0(V∞, γ), to be calculated with
the numerical solution of the complete problem, which is used in the evaluation of the heat transfer from
heated cylinders when the Rayleigh and Péclet numbers are small compared with
unity. In this case 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 problem for
circular cylinders with a wide range of Rayleigh numbers and some representative
values of V∞ and γ. We give correlations for the Nusselt number in the limiting cases
of pure free convection and pure forced convection.
Free and forced convection around line sources of heat and heated cylinders in porous media
