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The classical fencing problem occurs in radiant heat-transfer computations when a surface extends from one compartment to another, with the two compartments otherwise exchanging little heat. The surface that separates the two compartments is called a “fence.” If the gap between the bottom of the fence and the surface that extends under the fence is small, the potential for a large fencing error is evident from an examination of the drawings. In large models, with many surfaces forming many compartments, the fencing error is less evident. In this paper we examine the fencing errors in two prototype geometries. If the fenced surface is adiabatic, the error is found to be significant for surprisingly large gaps. A surface can be adiabatic due either to a high reflectance or a layer of insulation. The error is found to become insignificant when there is no reflectance.

Simulation of radiant heat transfer in large systems results in perhaps millions of radiant-interchange factors. In the interest of reducing computation times, some engineers frequently omit the smallest factors. Others combine the smallest factors into effective radiation nodes. Still others reduce the number of radiation factors by introducing fictitious partitions, known as multiple enclosure simplification shields that divide the large system into smaller systems. In this paper we examine the errors introduced by these various techniques and offer a new method that has the same accuracy as incorporating all of the radiation factors but requires little increase in computation time. The methods are compared by application to three simple models that clearly illustrate how significant errors can be generated if the methods are incorrectly applied.