TEMPERATURE FIELD OF TURBULENT FLOW IN A WELL WITH ACCOUNT FOR THE DEPENDENCE OF THERMAL CONDUCTIVITY COEFFICIENT ON TEMPERATURE

A method of solving the problem on nonstationary heat transfer of turbulent fl ow with variable coeffi cients and nonlinearity caused by the dependence of the thermal conductivity of oil on temperature is considered. The method consists of the joint application of the asymptotic methods of small and formal parameters. Based on the analysis of experimental data on the dependence of the thermal conductivity coeffi cient on temperature, it is shown that this dependence can be presented by a linear function in the form of the Taylor series containing the small parameter. The expansion of the problem in the small parameter leads to a linear problem in zero approximation that can be solved by using the asymptotic method of formal parameter. To determine the fi rst coeffi cient of the expansion in the small parameter, a unique procedure of uncoupling has been developed. Analytical dependences of temperature in a well and in the surrounding rocks on time and spatial coordinates have been found that account for the orthotropy of the thermophysical properties of the media.
A method of solving the problem on nonstationary heat transfer of turbulent fl ow with variable coeffi cients and nonlinearity caused by the dependence of the thermal conductivity of oil on temperature is considered. The method consists of the joint application of the asymptotic methods of small and formal parameters. Based on the analysis of experimental data on the dependence of the thermal conductivity coeffi cient on temperature, it is shown that this dependence can be presented by a linear function in the form of the Taylor series containing the small parameter. The expansion of the problem in the small parameter leads to a linear problem in zero approximation that can be solved by using the asymptotic method of formal parameter. To determine the fi rst coeffi cient of the expansion in the small parameter, a unique procedure of uncoupling has been developed. Analytical dependences of temperature in a well and in the surrounding rocks on time and spatial coordinates have been found that account for the orthotropy of the thermophysical properties of the media.
Author:  A. I. Filippov, A. B. Shabarov, and O. V. Akhmetova
Keywords:  heat transfer, temperature field, turbulent fl ow, asymptotic method, variable coefficients
Page:  9