A Theoretical Model of Transient Heat Transfer in a Firestopped CableBundle

In this paper a mathematical model of heat transfer in the cable bundle of a firestopped vertical cable assembly is developed to assist in planning experiments and to evaluate the relative influence of the geometrical and thermophysical properties of this portion of the firestopped configuration. A representation of this complex cable bundle geometry in terms of an approximate transient one-dimensional, lumped parameter model is obtained through heuristic arguments. This is accomplished in a systematic way by first deriving a simplified model for a single conductor wire and progressing up in scale, by averaging and lumping parameters, to arrive at a heat transfer model of a single cable. The heat transfer in a cable bundle is then treated using the single-cable model. Cable-to-cable heat transfer is handled through boundary conditions at the contact surfaces of the individual cables. A set of coupled transient one-dimensional equations results, with as many equations as cables in the array. The model is then exercised to compute transient temperature distributions within a 2313