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Wave Heat and Mass Transferin Nonlinear Anisotropic Space


E.L. Kuznetcova, V.F. Formalev

It’s well known that heat transfer defined by parabolic linear equation has infinite process velocity. That can be shown using each fundamental solution, for example, of the heat transfer equation with constant transfer factors. This paradox was eliminated by Maxwell by supposing the wave type of heat transfer, so that guide to wave-type heat transfer equation with finite relaxation time for heat flow from temperature gradient. For the heat transfer with nonlinear temperature dependence of heat transmission factor the wave type of solution is proved. In anisotropic bodies this process has different velocities in different directions. Some different aspects of heat and mass transfer in nonlinear anisotropic space are considered in the presented work based on the new analytical solution of nonlinear problem of anisotropic heat conduction, where nonlinearity is characterized by power dependence from temperature of components of heat conductivity with arbitrary power. The solution has been carried out using four transforms of independent variables and unknown function to derive the Cauchy’s problem for second-order nonlinear differential equation. The solution analysis has shown that the isotherms motion has wave type, isotherms have ellipsoidal (or elliptic in two-dimensional subcase) definitional domains. Wave process is characterized by isotherm motion over the cold space with continuous heat flows and temperatures and discontinuous on the heat wave fronts second derivatives. A heat wave velocity is defined for elliptic heat wave in nonlinear anisotropic space. A heat wave analysis in anisotropic spaces with discontinuous transfer properties can be used as a basis of non-destructive testing in defectoscopy.

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