Transient heat conduction in one-dimensional composite slab. A ‘natural’ analytic approach

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 conduction 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.