Transient heat conduction introduction

The above phenomena me physically miomalous and can be remedied through the introduction of a hyperbolic equation based on a relaxation model for heat conduction, which accounts for a finite thermal propagation speed. Recently, considerable interest has been generated toward the hyperbolic heat conduction (HHC) equation and its potential applications in engineering and technology. A comprehensive survey of the relevant literature is available in reference [6]. Some researchers dealt with wave characteristics and finite propagation speed in transient heat transfer conduction [3], [7], [8], [9] and [10]. Several analytical and numerical solutions of the HHC equation have been presented in the literature. 

For the introduction and explanation of the method we will discuss the case of transient, geometric one-dimensional heat conduction with constant material properties. In the region x0 < x < xn the heat conduction equation... 

As discussed in the introduction, disruptions cause the most severe thermomechanical loading experienced in a tokamak. In each of the 500 or so disruptions expected in ITER, approximately 10-20 MJ/m will be deposited onto the first wall in 0.01 to 3 seconds. Such a disruption will cause very high thermal stresses and significant material erosion (Section 4). As these events are transient in nature, the ability of the PFC to withstand the disruption depends on the material s ability to both conduct and to absorb the deposited heat, before reaching a temperature or stress limit. For comparative purposes, a disruption figure of merit takes this into account ... 

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