Enhancement of heat transfer: Combined convection and radiation in the entrance region of circular ducts with porous inserts

Using porous ceramic inserts in high temperature equipment has been proven to be an effective means to enhance combined convective–radiative heat transfer. The porous ceramic insert was referred to as a convection-to-radiation converter (CRC) by previous investigators. We consider a novel application of CRC cores in a partial by pass flow system for heat transfer enhancement. Both hydrodynamically and thermally developing laminar flow is considered in the entrance region of a circular pipe with a porous insert located at the center. The momentum and Darcy–Brinkman equations are applied to the flow field in the annular gas layer and central porous layer respectively. The energy equation is coupled with the radiative transfer equation by the radiation source term. The radiative transfer is simulated by the newly developed integral equations [X.L. Chen, W. Sutton, Radiative transfer in finite cylindrical media using transformed integral equations, J. Quant. Spectrosc. Radiat. Transfer 77 (3) (2003) 233–271; W. Sutton, X.L. Chen, A general integration method for radiative transfer in 3-D non-homogeneous cylindrical media with anisotropic scattering, J. Quant. Spectrosc. Radiat. Transfer 84 (2004) 65–103] to avoid singularity problem and give high accuracy. The working fluid and porous medium are both considered as participating media. Finally, this highly non-linear system of equations is solved by a mixed iteration method. The results are compared between the cases with and without the porous insert. The porous insert enhances both convective and radiative transfer by about 35% and 105% respectively at the most. The effects of important parameters on this enhancement are discussed in detail.