Modeling using conformal mapping of a temperature field around a hot-water system for channel-free laying

Abstract

The article deals with the development of methods for mathematical modeling of a temperature field around a hot-water system for channel-free laying by means of conformal mapping. A major disadvantage of the existing numerical methods for designing temperature fields around pipelines of heat supply systems is a high likelihood of errors due to instability of suggested solutions and convergence problems that still remained unaddressed. These solutions can be made more accurate by using analytical calculation methods, e.g., the conformal mapping method. An essential characteristic of a model in question is a possibly accurate analytical solution for designing temperature fields and streamlines. The implementation of various available functions in symbolic mathematical packages (in particular, linear-fractional ones) retains a high accuracy in numerical studies of the models. Using mathematical models for designing streamlines and temperature fields by means of the theory of conformal mappings, a solution can be obtained that is as identical as possible to the analytical one, which would ultimately enable us to improve the accuracy of the results. These results can be employed in design and reconstruction of heat supply systems.