Molecular gas radiation and laminar or turbulent heat diffusion in a cylinder with internal heat generation

Simultaneous nongray radiation and thermal diffusion in a thermally and hydrodynamically established laminar or turbulent pipe flow with uniform internal heat generation is treated. The governing integrodifferential thermal energy equation is solved using the Galerkin technique for the laminar case and finite difference as well as numerical iteration techniques for turbulent flow. Solutions are presented for radiative and convective Nusselt numbers as a function of the radiation-to-molecular conductance ratio, the optical depth along the radius at a photon wavenumber spectrally located at the head of an exponential-tailed absorption band, and a turbulent Reynolds number. The radiative Nusselt number is found to increase almost linearly with the radiance-conductance ratio, linearly with turbulent Reynolds number at small values of this number, and approximately logarithmically at large values of this number. The radiative transfer also increases with increasing turbulence since the turbulence improves the effective wall-layer gas transmissivity.