THE CARTESIAN COLLAPSED-DIMENSION METHOD FOR USE IN NUMERICAL 2-D RADIATION CALCULATIONS IN ABSORBING-EMITTING MEDIA

A new numerical approach has been devised for performing accurate absorbing-emitting non-scattering radiation calculations for Cartesian co-ordinate based problems with one ordinate symmetry using only the solution plane formed by the other two ordinates. To accomplish this, the method makes use of 'effective intensity rays' which only exist and have meaning in the solution plane of the problem but which are made, through a special procedure, to contain the information of the third dimension. This novel procedure thus eliminates the problem of solid angles and greatly reduces both the complexity and computational expense involved in the solution of such problems. Yet it can do this without producing loss in accuracy. The approach is ultimately intended for use in combustion problems involving high temperatures and optically thin media. For verification purposes the method is applied to the problem of heat exchange in infinitely long rectangular enclosures and is found to give excellent results over a optical thickness range that includes the optically very thin case.