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Transient heat conduction in one-dimensional composite slab. A “natural” analytic approach. (English) Zbl 0964.80003

Summary: The transient response of one-dimensional multilayered composite conducting slabs to sudden variations of the temperature of the surrounding fluid is analysed. The solution is obtained applying the method of separation of variables to the heat conduction partial differential equation. In separating the variables, the thermal diffusivity is retained on the side of the modified heat equation where the time-dependent function is collected. This choice is the essence of composite medium analysis itself. In fact, it ‘naturally’ gives the relationship between the eigenvalues for the different regions and then yields a transcendental equation for the determination of the eigenvalues in a less complex form than the ones resulting from the application of traditional techniques. A new type of orthogonality relationship is developed by the author and used to obtain the final complete series solution. The errors, which develop when the higher terms in the series solution are neglected, are also investigated. Some calculated results of a numerical example are shown in a graphical form, by using dimensionless groups, and therefore discussed.

MSC:

80A17 Thermodynamics of continua
74A15 Thermodynamics in solid mechanics
80A20 Heat and mass transfer, heat flow (MSC2010)
35K05 Heat equation
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