The stresses and displacements in the initial phase of applying a thermal load on the bounding surfaces of an orthotropic hollow circular cylinder are obtained using the Hankel asymptotic expansions for the Bessel functions of the first and second kind. Such a load may be constant temperature, constant heat flux, zero heat flux, or heat convection to a different medium at either surface. The material properties are assumed to be independent of temperature. A constant applied temperature at the one surface and convection into a medium at a different temperature at the other surface is used to illustrate the variation of stresses with time and through the thickness in the initial transient phase.

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