Applying a constant or transient heat flux on a plane slab is a common technique in microelectronics technology and material processing, including laser patterning, micromachining, and laser surface treatment processes. Although Fourier's law is typically very precise for evaluating temperatures in solids, a number of experimental observations suggest the existence of non-Fourier transient conduction in these applications. Since the dual-phase-lag (DPL) model of heat conduction can be compatible with the hypothesis of local equilibrium thermodynamics (as shown here), the effects of temperature gradient relaxation time on the non-Fourier hyperbolic conduction in a finite slab subjected to an arbitrary time-dependent surface heat flux is examined by this model. The combination of diffusion- and wave-like features in heat conduction process is properly monitored by the DPL model for two types of heat flow regimes, namely, gradient precedence and flux precedence. The results indicate considerable deviations between the predictions of these regimes.