Exact solutions to differential-difference heat and mass transfer equations with a finite relaxation timeстатья
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Аннотация:Certain exact solutions to the linear differential-difference heat and mass transfer equations with a finite relaxation time are specified. The exact solution to the one-dimensional Stokes problem with the periodic boundary condition when a first-order volume chemical reaction occurs is given. A wide class of exact solutions to the nonlinear differential-difference heat-conduction equation with the following source is described: Theta(t) = div[f(T)del T]+ g(Theta), Theta = T(r, t + tau), where T = T(r, t) is temperature and tau is the relaxation time. Certain more complex heat conduction models with a variable relaxation time that can depend on time and a temperature gradient are also considered.