Heat conduction problem in hollow cylinder
There are a lot of researches for calculating the temperature field in various shapes using different boundary and initial conditions. Some researchers have used analytical approaches to solve the periodic heat conduction problems. In 1947,Hesser obtained unstable temperature field in a long solid cylinder, solid sphere and infinite flat plate, with homogeneous boundary condition. Also, Ozisik(1993) determined the unstable temperature field in solid cylinder under the periodic boundary condition. Trosel(1956) gained stresses field created by different temperature distribution.VDI(2003) presented the calculation of periodic boundary condition which is simulated by harmonic oscillation of ambient temperature.
Earlier work in this field focused on one-dimensional heat conduction in solid and hollow cylinders. Carslaw and Jaeger(1957) discussed the general heat conduction problem with emphasis on solid cylinders. Analytical solutions to unsteady heat conduction problems relied on the use of Green’s function but still proved extremely difficult.
The determination of temperature distribution in a medium (solid, liquid, gas or combination of phases) is the main objective of a conduction analysis, that is, to know the temperature in the medium as a function of space at steady state and as a function of time during the transient state. Once this temperature distribution is known, the heat flux at any point within the medium, or on its surface, may be computed from Fourier’s law.