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TitleA finite difference program to solve the transient heat conduction equation involving latent heat in cylindrical symmetry
AuthorTaylor, A
SourceEarth Physics Branch, Open File 78-8, 1978, 180 pages,
PublisherEnergy, Mines and Resources Canada (Ottawa, Canada)
Documentopen file
Mediapaper; on-line; digital
File formatpdf
Subjectsgeophysics; heat conduction; heat flow
Released1978 01 01; 2018 11 13
AbstractA numerical model has been developed to simulate the transient thermal regime arising from a cylindrically symmetric disturbance in a semi-infinite medium. Heat transfer by radial conduction only is considered and provision is made for a phase change involving latent heat to occur within the medium. The numerical solution to the transient heat conduction equation using the explicit finite difference method is outlined in detail. Some aspects of the computer solution are described. The program has been used to produce a set of tables giving both temperatures at various distances from the source for a range of dimensionless times and the radial heat flow leaving the source region. Data are tabulated for cases with and without a phase change; in the case of a phase change, 3 tables are given for latent heat densities of 10 and 100 MJ/m and several source and initial temperatures. This is an extended data set, complementing that in Taylor (1978). In both cases, the source disturbance· is considered to be either sustained indefinitely or to last for a finite period, after which cooling occurs. The program finds application in such geophysical problems as the study of the disturbance to the geothermal regime resulting from the drilling of and production from petroleum wells, from buried pipelines and power cables and from underground tunnels. Using the tables gives an "off-the-shelf" solution to the transient thermal regime in many of these applications. As an example, the program is used to calculate theoretical temperature profiles for a Mackenzie Delta well and to point out the thermal advantage of using an insulating annulus through the permafrost.