An exact formulation of simultaneous radiation, conduction, and convection heat transfer for steady-state conditions in a one-dimensional, semi-infinite, isotropic, homogeneous, absorbing, and scattering porous bed is presented. Both diffuse and collimated radiant fluxes are incident on the bed causing absorption, scattering, emission, and heating of the bed which in turn heats a transparent, constant-property fluid flowing normal to the surface. Spectral selectivity is allowed for when the source energy is of shorter wavelength than the emitted energy. Exact and approximate numerical solutions and a linearized closed-form solution are given for inflow, as in a solar heat collector, and outflow, as with a heat shield.