Investigation of Numerical Evaluation Improvement for Three-Dimensional Infinite Cylindrical Heat Conduction Problems

Abstract

To estimate the thermal properties from transient data, a model is needed to produce numerical values with sufficient precision. Iterative regression or other estimation procedures must be applied to evaluate the model again and again. From this perspective, infinite or semi-infinite heat conduction problems are a challenge. Since the analytical solution usually contains improper integrals that need to be computed numerically, computer-evaluation speed is a serious issue. To improve the computation speed with precision maintained, an analytical method has been applied to three-dimensional (3D) cylindrical geometries. In this method, the numerical evaluation time is improved by replacing the integral-containing solution by a suitable finite body series solution. The precision of the series solution may be controlled to a high level and the required computer time may be minimized by a suitable choice of the extent of the finite body. The practical applications for 3D geometries include the line-source method for obtaining thermal properties, the estimation of thermal properties by the laser-flash method, and the estimation of aquifer properties or petroleum-field properties from well-test measurements. This paper is an extension of earlier works on one-dimensional (1D) and two-dimensional (2D) cylindrical geometries. In this paper, the computer-evaluation time for the finite geometry 3D solutions is shown to be hundreds of times faster than the infinite or semi-infinite solution with the precision maintained.