Abstract
The objective of this study is to derive an analytical solution of one dimensional heat conduction equation applied in a hollow cylinder, which is subjected to a periodic boundary condition at the outer surface while the inner surface is insulated. The material is assumed to be homogenous and isotropic with time-independent thermal properties. Because of the time-dependent term in the boundary condition, Duhamel's theorem is used to solve the problem for a periodic boundary condition. The periodic boundary condition is decomposed by Fourier series. The obtained temperature distribution contains two characteristics, the dimensionless amplitude and the dimensionless phase difference. These results were plotted with respect to Biot and Fourier numbers. The agreement between our results and the former work that was related to one dimensional solution of infinite, solid cylinder, under simple harmonic condition was realized to be very good.
Highlights
There were a lot of researches for calculating the temperature field in various shapes using different boundary and initial conditions
Trostel[3] gained stresses field created by different temperature distribution
The temperature distribution field in hollow cylinder recognized with two characteristics
Summary
There were a lot of researches for calculating the temperature field in various shapes using different boundary and initial conditions. Obtained unstable temperature field in a long solid cylinder, solid sphere and infinite flat plate, with homogenous boundary condition. Determined the unstable temperature field in hollow and solid cylinder under the periodic boundary condition. Trostel[3] gained stresses field created by different temperature distribution. VDI[4] presented the calculation of periodic boundary condition which is simulated by harmonic oscillation of ambient temperature
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