Pressure increase in a flat fracture filled with freezing liquid
The paper considers the problem of pressure variations in circular and rectangular flat fractures filled with liquid as the liquid crystallises, taking into account rigidity of the solid phase forming. We suppose that as a liquid crystallises, the volume it occupies inside the fracture changes due to the difference in density of the solid and liquid phases, and the fracture walls deform due to the pressure difference between the environment and the internal zone. Assuming that the solid and liquid phases are incompressible, we may equate the change in the internal fracture volume caused by the deformation of the surrounding walls to that in the volume of the liquid undergoing a state transition. We presume that crystallisation occurs at the top of the fracture, the temperature of the liquid is constant and equals its crystallisation temperature, and the phase boundary between the liquid and solid phases is flat. We consider the side walls and the bottom to be thermally insulated and perfectly rigid. We derived analytical expressions for determining the pressure
 Duffie J.A., Beckman W.A. Solar energy thermal processes. Wiley, 1974, 386 p. [In Russ.: Duffie J.A., Beckman W.A. Teplovye protsessy s ispolzovaniem solnechnoy energii. Moscow, Mir Publ., 1977, 420 p.].
 Malozemov V.V., Kudryavtseva N.S. Sistemy termoregulirovaniya kosmicheskikh apparatov [Spacecraft thermal control systems]. Moscow, Mashinostroenie Publ., 1983, 112 p.
 Favorskiy O.N., Kadaner Ya.S. Voprosy teploobmena v kosmose [Problems of heat transfer in space]. Leningrad, Vysshaya Shkola Publ., 1972, 280 p.
 Kazakov V.A., Sigalaev S.K., Ermolaeva Yu.O. Raschet paneli trubchatogo kholodilnika-izluchatelya dlya resheniya zadachi minimizatsii ego massy [Computing parameters of a tubular cooling radiator panel to solve the problem of minimising its mass]. Nauchnye trudy Mezhdunarodnoy molodezhnoy nauchnoy konferentsii “XLI Gagarinskie chteniya” [Proc. of the International young scientist conference 41st Gagarin Readings]. Moscow, INFRA-M Publ., 2015, pp. 143–145.
 Tovarnykh G.N. Inzhenerny vestnik — Engineering Bulletin, 2014, no. 11. Available at: http://engbul.bmstu.ru/doc/738625.html
 Tovarnykh G.N. Inzhenernyy zhurnal: nauka i innovatsii — Engineering Journal: Science and Innovation, 2015, issue 5 (41). DOI: 10.18698/2308-6033-2015-5-1396
 Tovarnykh G.N. Mashinostroenie i inzhenernoe obrazovanie — Mechanical Engineering and Engineering Education, 2016, no. 4, pp. 15–18.
 Feodosev V.I. Soprotivlenie materialov [Strength of materials]. 14th ed. Moscow, BMSTU Publ., 2007, 389 p.
 Vasilev V.V. Mekhanika konstruktsiy iz kompozitsionnykh materialov [Mechanics of composite material structures]. Moscow, Mashinostroenie Publ., 1988, 272 p.
 Bychkovskiy N.N. Ledovye stroitelnye ploshchadki, dorogi i perepravy [Construction on ice covers, ice roads and ice bridges]. Saratov, Yuri Gagarin State Technical University of Saratov Publ., 2005, 260 p.