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The inadequacy of Fick’s law to incorporate causality can be overcome by replacing it with the Green–Naghdi type II (GNII) flux relation. Combining the GNII assumption and conservation of mass leads to [see document for equation] where r (x, t) is the density function, S(p) is a source term and c¥ is a positive constant which carries (SI) units of m/sec. A general source term given by [see document for equation] is proposed. Here, the constants y and ps are the rate coefficient and saturation density respectively. The travelling wave solutions and numerical analysis of four special cases of equation (2), namely: Pearl-Verhulst Growth law, Zel’dovich Law, Newmann Law and Stefan- Boltzmann Law are investigated. For both analysis, results are compared with the available literature and extended for other cases. The numerical analysis is carried out by imposing well-studied Initial Boundary Value Problem and implementing a built-in method in the software package Mathematica 9. For Pearl-Verhulst source type, the results are compared to those found in literature . Confirming the validity of built-in method for Pearl-Verhulst law, the generic built-in method is extended to study the transient signal response for similar initial boundary value problems when the source terms are Zel’dovich law, Newmann law and Stefan-Boltzmann law.
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Tiwari, Ganesh, "Numerical Analysis of Non-Fickian Diffusion with a General Source" (2013). Senior Honors Theses. 49.