Sharif Digital Repository

The objective of this paper is to derive the mathematical model of two-dimensional heat conduction at the inner and outer surfaces of a hollow cylinder which are subjected to a time-dependent periodic boundary condition. The substance is assumed to be homogenous and isotropic with time-independent thermal properties. Duhamel's theorem is used to solve the problem for the periodic boundary condition which is decomposed by Fourier series. In this paper, the effects of the temperature oscillation frequency on the boundaries, the variation of the hollow cylinder thickness, the length of the cylinder, the thermophysical properties at ambient conditions, and the cylinder involved in some... 

To ensure an optimized borehole in terms of heat capacity and cost-effectiveness, it is necessary to predict the heating performance of underground U-tube heat exchangers (boreholes) so that proper parameters such as length, diameter, material, etc. can be designed and selected. To this end, employing reliable equations is essential to predicting the heating performance of a borehole and also, to resolving the design issues. In this study, a single vertical U-tube borehole with a constant wall temperature is considered and analytical equations for temperature distribution in the surrounding ground around the borehole are evaluated based on one- and two-dimensional heat conduction,...