Green’s Function Solution for the Dual-Phase-Lag Heat Equation

Dual-phase-lag heat equation of fractional order of heat transfer within microscale region

In this article, the author has used fractional calculus to explain the wave nature of heat propagation as well as heat conduction at molecular level with dual phase lag; in this row he proposed dual phase lag heat equation of fractional order. Modified Adomian Decomposition Method and New Iterative Method are applied to obtain the approximate analytical solutions of the proposed model. Numeric...

An alternative discretization and solution procedure for the dual phase-lag equation

Alternative discretization and solution procedures are developed for the 1-D dual phase-lag (DPL) equation, a partial differential equation for very short time, microscale heat transfer obtained from a delay partial differential equation that is transformed to the usual non-delay form via Taylor expansions with respect to each of the two time delays. Then in contrast to the usual practice of de...

Analytical Analysis of The Dual-phase-lag Heat Transfer Equation in a Finite Slab with Periodic Surface Heat Flux (RESEARCH NOTE)

This work uses the dual-phase-lag (DPL) model of heat conduction to demonstrate the effect of temperature gradient relaxation time on the result of non-Fourier hyperbolic conduction in a finite slab subjected to a periodic thermal disturbance. DPL model combines the wave features of hyperbolic conduction with a diffusion-like feature of the evidence not captured by the hyperbolic case. For the ...

Qualitative Aspects in Dual-Phase-Lag Heat Conduction

We consider the system of dual-phase-lag heat conduction proposed by Tzou [21]. First, we prove that the solutions of the problem are generated by a semigroup of quasicontractions. Thus, the problem of third-order in time is well-posed. Then the exponential stability is investigated. Finally the spatial behavior of solutions is analyzed in a semi-infinite cylinder.

Solution for the Heat Equation