The similarity solutions of concentration dependent diffusion equation. (English) Zbl 1360.76219

Summary: This paper deals with the similarity solution of concentration dependent diffusion equation. A fundamental transport process in environmental fluid mechanics is diffusion. A well-known example is the diffusion of perfume in an empty room. The physical phenomenon of the solute transport due to combined effect of diffusion and convection in a medium is represented by the partial differential equation. It is a diffusion equation with constant diffusion coefficient. It is a parabolic type partial differential equation. It is based on the principle of conservation of mass. It is derived using Fick’s law. The solution is obtained by using the method of group invariance under an infinitesimal transformation. The solution is represented in the form of Hermite polynomial which is well suited for meaningful interpretation of the response of the physical phenomenon. It is found in good agreement with results of earlier researchers. It is more classical than other results obtained by earlier researchers. It has wide applications in sold physic, petroleum engineering, chemical engineering and bioscience.


76M55 Dimensional analysis and similarity applied to problems in fluid mechanics
76R50 Diffusion
35K57 Reaction-diffusion equations
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