Tyumen State University Herald. Physical and Mathematical Modeling. Oil, Gas, Energy


Releases Archive. Вестник ТюмГУ. Физико-математические науки. Информатика (№7, 2013)

Temperature waves in the ground near the base of heat construction

About the authors:

Maria B. Atmanskikh, Postgraduate Student of Mathematical Modeling Department, Tyumen State University
Ilya P. Rilo, Head of Research Department of Scientific and Production Association «Fundamentstroyarkos», Public Joint Stock Company
Alexey V. Tatosov, Dr. Sci. (Phys.-Math.), Professor, Department of Fundamental Mathematics and Mechanics, University of Tyumen; atatosov@utmn.ru


Numerical investigation of nonstationary conductivity in the ground near the pile is presented in this paper. The ground and the pile are exposed to temperature waves – seasonal variations of air temperature. The process of heat conduction in the ground is described by a two-dimensional nonstationary heat conduction equation with a variable conductivity coefficient, without the source term in the axisymmetric coordinate system. Algorithm CONDUCT is used for numerical solution of the problem. “Stationary periodic” mode is achieved during five periods in the present problem. Heat exchange with the environment is more intensive in the pile near the surface than on the surface of the ground. Penetration depth of temperature waves decreases exponentially with the depth of the construction, therefore their greatest influence on temperature distribution is found near the upper boundary. Thermal inertia demonstrates hyperbolic properties of solution for heat conduction equation with time-periodic boundary conditions. It contributes to phase difference between temperature oscillations at different depths.


1. Lykov, A.V. Teorija teploprovodnosti [Theory of Heat Conductivity] M.: Vysshaja shkola, 1967. 599 p. (in Russian).

2. Sivuhin D.V. Obshhij kurs fiziki: V 3 tt. T. 2. Termodinamika i molekuljarnaja fizika [Guidelines to Physics. In 3 vol. Vol. 2. Thermodynamics and Molecular Physics]. M.: Nauka, 1975. 519 p. (in Russian).

3. Tihonov, A.N. Samarskij, A.A. Uravnenija matematicheskoj fiziki [Equations of Mathematical Physics]. M.: Nauka, 1972. 736 p. (in Russian).

4. Kutateladze, S.S. Osnovy teorii teploobmena [Fundamentals of Heat Exchange Theory]. M.: Atomizdat, 1979. 416 p. (in Russian).

5. Eger, D., Karslou, G. Teploprovodnost' tverdyh tel [Thermal Conductivity of Solids]. M.: Nauka, 1964. 488 p. (in Russian).

6. Atmanskih, M.B., Zubkov, P.T. The Influence of Temperature and Thermoacoustic Waves on Heat Transmission in a Layer of Perfect Viscous Gas. Dinamika sploshnoj sredy — Continuous-Medium Dynamics. 2010. №. 126. Pp. 37-41. (in Russian).

7. Kalitkin, N.N. Chislennye metody [Numerical Techniques]. M.: Nauka, 1978. 512 p.

8. Fletcher, K. Vychislitel'nye metody v dinamike zhidkostej. T. 1. [Computational Techniques for Fluid Dynamics. Vol. 1]. M.: Mir, 1991. 504 p. (in Russian).

9. Patankar, S.V. Computation of Conduction and Duct Flow Heat Transfer. New York: Hemisphere, 1990. 250 p.

10. Patankar, S.V. Numerical Heat Transfer and Fluid Flow. New York: Hemisphere, 1980. 200 p.