Solution for non-Fourier dual phase lag heat conduction in a semiinfinite slab with surface heat flux

This work derives a solution for transient temperature in a semi-infinite slab subjected to constant heat flux at its surface, while governed by the non-Fourier 'dual phase lag' (DPL) model [1, 2] of heat conduction developed recently. The solution shows temperatures predicted with the DPL model can differ significantly from predictions based on the classical model of Fourier's Law. Interest in the DPL model should grow in the near future because it shows good agreement with experiments across a wide range of length and time scale [3], including the 'microscale' range of increasing importance. Hence, the solution derived here will permit quick estimates of DPL behavior for practical situations, such as laser heating of semiconductors during fabrication of microscale electronic devices. Also, this solution will help test numerical solution methods likely to be developed for the model. The first part of this work uses the DPL model to derive a solution for transient temperature in a semi-infinite slab with constant surface temperature. In the second part, this solution serves as the starting point for deriving the desired solution for constant surface heat flux. Also, the solution for constant surface temperature derived in the first part is a convenient alternative to others published previously.; The non-Fourier dual phase lag (DPL) model is used to derive a solution for transient temperature in a semi-infinite slab with constant surface temperature. This solution serves as a starting point for deriving the desired solution for constant surface heat flux. The model accounts for the non-zero times required by heat flux and temperature gradient to gradually become established in response to thermal disturbances.