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Fire stop systems prevent the passage of fire, gas and heat between compartments, so that they reduce the damage and save lives, which are deeply associated with the products assembled in the field or pre-manufactured. Silicone and Latex sealant fire stop systems are usually employed in sealing around pipes, cables, joints and gaps. All fire stop systems are tested under the same ASTM standard to ensure repeatability and suitability for the specific application. The fire stop systems have a major responsibility in defense-in-depth. Because of a great number of fire stop systems constructed under the old standard of ASTM E-119, safety of all the systems did not verify with the new test method of ASTM E-814 up to now. Ratings are established on account of the resistance time to the fire exposure, the development time of first through opening, flaming on the unexposed surface, limiting thermal transmission criterion, and acceptable performance under application of the cable stream. Corresponding to ASTM E-814, not only the F-rating test but also the T-rating test should be carried out to verify the fire stop system. For that purpose, the complementary use of a test-simulator is suitable. Especially, dynamic heat conduction in a cable through the fire stop system should be investigated to develop the test-simulator that the T-rating test of the fire stop system can be carried out with. Dynamic heat conduction occurring in the cable through the fire stop system is formulated in a parabolic partial differential equation subjected to a set of initial and boundary conditions. There are a few assumptions given in this work. There is no heat flow from the fire stop system to the tray of penetration cables and to the firewall. Fire tests are performed with the ASTM-119 standard temperature-time curve. The fire-side surface of the fire stop system is always at the temperature of the ASTM-119 standard temperature-time curve, and the fire-side surfaces of the tray and of the cable streams are also assumed to be at the same temperature. These assumptions are summarized as the boundary condition equations. First, the partial differential equation is converted to a series of ordinary differential equations at finite elements, where the time and spatial functions are assumed to be of orthogonal collocation state at each element. The heat fluxes are calculated by the Galerkin finite element method. This work was aimed to know how dynamic heat conduction came about in the penetration cable of the fire stop system between compartments of nuclear power plants. Therefore, the interest was concentrated on computing the thermal development around the penetration cables. The penetration cable was modeled, simulated and analyzed. Through the simulations it was shown clearly that the temperature distribution was influenced very much by the thickness of the cable and its covering. In addition, it was found that the feature of heat conduction could be understood as an unsteady-state process. These numerical results are useful for making a performance-based design for the cable penetration fire stop system.