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An efficient numerical approach based on weighted-average finite differences is used to solve the Newtonian plane Couette flow with wall slip, obeying a dynamic slip law that generalizes the Navier slip law with the inclusion of a relaxation term. Slip is exhibited only along the fixed lower plate, and the motion is triggered by the motion of the upper plate. Three different cases are considered for the motion of the moving plate, i.e., constant speed, oscillating speed, and a single-period sinusoidal speed. The velocity and the volumetric flow rate are calculated in all cases and comparisons are made with the results of other methods and available results in the literature. The numerical outcomes confirm the damping with time and the lagging effects arising from the Navier and dynamic wall slip conditions and demonstrate the hysteretic behavior of the slip velocity in following the harmonic boundary motion. [ABSTRACT FROM AUTHOR]

An exact analytical solution in closed form is obtained for a two-dimensional initial-boundary-value problem of heat wave propagation in a thick slab of an anisotropic rigid thermal conductor within the dual-phase-lag model. One-sided Fourier transform technique is used to obtain a formal solution. The method requires an essential change of the dependent variable in order to guarantee a suitable asymptotic time behavior of the unknown function. The solution satisfies prescribed boundary temperatures and zero initial conditions. Numerical results are presented to put in evidence the effect of the two thermal relaxation times on the behavior of the heat conduction process. In particular, it is shown that the governing equation for temperature includes both characters of wave propagation and diffusion due to the interplay between relaxation times. The influence of anisotropy is investigated. The present results confirm previous findings about heat propagation within dual-phase-lag. The proposed method can treat other geometries, viz. the half-space, quarter-space and the rectangular domain with arbitrary boundary and initial conditions. The obtained exact solution can be used to check approximate solutions arising from other techniques. [ABSTRACT FROM AUTHOR]