| Abstract |
The heat transfer mechanism in the rock mass around a borehole is an axisymmetric heat conduction process. Earlier works considered this phenomenon to be a two-dimensional radial heat flow, which is congruent in any horizontal plane. The solution is obtained by solving the differential equation of the heat conduction, applying a cylindrical coordinate system. Accordingly a cylindrical interface is the boundary between the heated and the undisturbed rock mass. Now a new method will be applied in which the heat flux field is the function determined primarily, instead of the temperature field. The axisymmetric heat flux field can be described by complex-variable analytic functions. Because of the validity of the Cauchy-Riemann equations the particular solutions of them can be superimposed. In our model the terrestrial heat flux is a homogeneous component, to which a line-source of variable intensity is placed as a singularity, distorting the homogeneous heat flux field. The heat flux field can be determined analogously to an axisymmetric perfect fluid flow. The isotherms of the temperature filed forms a set of axisymmetric surfaces, analogously to the velocity potential, orthogonally to the stream surfaces which are tangential to the heat flux vectors. The thermal potential function and the heat-stream function are determined by potential-theory method. The stream surface determined by the zero constant, divides the heated region from the intact rock mass. This domain is a paraboloid-like body of revolution around the well axis. Its equation is obtained by analytic method. The equation of the bounding surface is a complex transcendent expression, can be determined numerically only. This method is more accurate to describe and calculate the borehole heat transfer. |