Thesis (Ph.D) - Cairo University - Faculty of Science - Department of Mathematics

This thesis is concerned with the study of some phenomena occuring in deformable piezoelastic media subjected to various thermal,mechanical and electric influences, within Extended Thermodynamics.These media are characterized by a complex structure,thus requiring special attention to the continuum model describing them.We have chosen as our basic model the 2dual-phase-lag 3 model that has become increasingly popular in the past two decades or so.This model is characterized by two thermal relaxation times that describe lagging behavior. The problems tackled in this thesis illustrate the different behavioral faces of heat propagation under different conditions. We have produced both exact and approximate solutions to two-dimensional problems. Different proper mathematical techniques have been applied to resolve these problems:One-sided Fourier transform technique, normal mode analysis, and numerical method based on an explicit finite-difference scheme. We have illustrated our results graphically whenever possible, to show the behavior of the quantities of practical interest, and we have compared the results obtained by DPL model with those obtained by L-S theory in some cases. We have pointed out at the various applications involved in the obtained solutions,in the different fields of Technology and in Applied Sciences

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