Cooling of a composite slab. (English) Zbl 0598.73119

A mixed boundary value problem associated with the diffusion equation, that involves the physical problem of cooling of an infinite parallel- sided composite slab, is solved completely by using the Wiener-Hopf technique. An analytical expression is derived for the sputtering temperature at the quench front being created by a cold fluid moving on the upper surface of the slab at a constant speed v. The dependence of the various configurational parameters of the problem under consideration, on the sputtering temperature, is rather complicated and representative tables of numerical values of this important physical quantity are prepared for certain typical values of these parameters. Asymptotic results in their most simplified forms are also obtained when (i) the ratio of the thicknesses of the two materials comprising the slab is very much smaller than unity, and (ii) the quench-front speed v is very large, keeping the other parameters fixed, in both the cases.


74A15 Thermodynamics in solid mechanics
74B99 Elastic materials
74H99 Dynamical problems in solid mechanics
74E30 Composite and mixture properties
35K05 Heat equation
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