Coupled radiation and conduction in free mixing.

Abstract

Abstract : Heat transfer by both grey radiation and conduction is examined in the case of Oseen-like free-mixing flow which is formally analogous to a one-dimensional unsteady transfer problem. The equation describing the transport of energy by non-convective means is obtained by linearization of the conservation of energy relation. The geometry of the time-dependent problem may be envisaged as a slab of finite width separating two infinite half-spaces; this configuration is analogous to the steady, free-mixing flow of a two-dimensional jet or wake. The initial temperature profile of the jet with respect to the surrounding gas is taken to be a step function. By means of the transform calculus the determination of the temperature for the entire region of the jet and the fluid adjacent to it may be given as an inversion integral. This approach does not require a kernel substitution in the solution of the integro-differential equation for the temperature and thus avoids some of the limitations imposed thereby. Analytic solutions in the limiting cases of 'thin' and 'thick' gas behavior are readily recovered from the general solution. From the bounded variation of the integrand the temperature distribution may be computed for all possible combinations of the heat conduction and radiation parameters. Exact numerical evaluation of the inversion integral is employed to provide a complete description of the temperature variations in the flow. (Author)