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An Exact Solution on Compression of a Cavity in a Viscous Heat-Conducting Compressible Medium


A partially spherically symmetric exact solution of dynamics of a heat-conducting medium with the thermodynamic equations of state of a perfect gas for which the viscous stress tensor depends on the strain-rate tensor in an arbitrary way is given. It is assumed that the strain rates and the pressure are homogeneous and there is no acceleration; in this case, the equations of motion are identically satisfied. As a result of separation of variables in the energy equation, the three-dimensional Poisson equation is obtained for the density as a function of the Lagrangian coordinates. Its solution simulates compression of a domain of significantly variable density in the medium considered, for example, in the case of full spherical symmetry of a buble or a drop. Non-spherical constant-density surfaces are also possible. Flow can occur from the state of rest with a finite mass of the medium due to the motion of the compressing spherical piston. The power-law non-Newtonian liquids are investigated. The energy of medium is calculated and its behavior is presented in the neighborhood of the instant of compression to a point.

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Correspondence to D. V. Ukrainskii.

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Translated by E.A. Pushkar

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Golubyatnikov, A.N., Ukrainskii, D.V. An Exact Solution on Compression of a Cavity in a Viscous Heat-Conducting Compressible Medium. Fluid Dyn 57, 494–502 (2022).

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  • bubble compression
  • compressible medium
  • viscosity
  • heat conduction
  • exact solution
  • energy concentration