Temperature distribution in an array of moving cracks acting as heat sinks

The temperature distribution in a periodic array of parallel cracks acting as heat sinks is studied for the case of stationary crack motion by use of the Wiener–Hopf method. The problem arises in the investigation of cracks propagating into solid material, where the stresses driving crack motion are caused by heat transfer from the solid through the crack surfaces. The solution is given in terms of Fourier integrals involving infinite products. The heat-flux distribution in the vicinity of the crack tips is computed analytically from the high wavenumber asymptotics. Numerical solutions of the temperature distribution are presented for several values of the Biot and Péclet number, and the effect of varying these parameters is discussed qualitatively.

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