Some new thermo-elastic solutions for cylindrical and spherical composites

In modern engineering applications, multilayered structures are extensively used due to the added advantage of combining physical, mechanical, and thermal properties of different materials. Many of these applications require a detailed knowledge of transient temperature and heat-flux distribution within the component layers. Both analytical and numerical techniques may be used to solve such problems. Nonetheless, numerical solutions are preferred and prevalent in practice, due to either unavailability or higher mathematical complexity of the corresponding exact solutions. Rather limited use of analytical solutions should not diminish their merit over numerical ones; since exact solutions, if available, provide an insight into the governing physics of the problem, which is typically missing in any numerical solution. Moreover, analyzing closed-form solutions to obtain optimal design options for any particular application of interest is relatively simpler. In addition, exact solutions find their applications in validating and comparing various numerical algorithms to help improve computational efficiency of computer codes that currently rely on numerical techniques. Although multilayer heat conduction problems have been studied in great detail and various solution methods including orthogonal and quasi-orthogonal expansion technique, Laplace transform method, Green’s function approach, finite integral transform technique are readily available; there is a continued need to develop and explore novel methods to solve problems for which exact solutions still do not exist. One such problem is to determine exact unsteady temperature distribution in polar coordinates with multiple layers in the radial direction. Numerous applications involving multilayer cylindrical geometry require evaluation of temperature distribution in complete disk-type. One typical example is a nuclear fuel rod, which consists of concentric layers of different materials and often subjected to asymmetric boundary conditions. Moreover, several other ...