Laws of unsteady-state heat transfer with the radiative heating of the laminar flow of a liquid in long channels

An analytical study of the transient cooling of a fluid flowing with a parabolic velocity distribution through a plane or round channel, subject to a uniform heat-flux boundary condition consisting of radiative and convective contributions, is reported. A general solution is obtained by joining the unsteady and steady-state partial solutions along a characteristic curve in the plane. The influence of the radiative boundary condition upon the Nusselt number and streamwise surface temperature is presented. Radiative transfer is found to reduce the surface temperatures. At early times, the Nusselt number is reduced by the radiative boundary condition.