caa a22 4500 46908135X CHVBK 20180323132951.0 cr unu---uuuuu 170328e19920901xx s 000 0 eng 10.1007/BF01194109 doi (NATIONALLICENCE)springer-10.1007/BF01194109 Utilization of nonlinear diffusion solutions for n -diffusion and power-law materials [Elektronische Daten] [D. Hill, J. Hill] Summary: The equation ofn-diffusion, as originally formulated by J. R. Philip for various problems involving unsteady turbulent flows, applies directly to the one-dimensional flow of a non-Newtonian power-law fluid as well as indirectly to the laminar boundary layer flow of such fluids over a flat plate. The purpose of this note is to utilize a simple relation between one-dimensionaln-diffusion and nonlinear diffusion with power-law diffusivity such that ifp(x, t) denotes ann-diffusion pressure thenc(x, t)=|ϖp/ϖx| satisfies the nonlinear diffusion equation with power law diffusivity. This means in particular that the large number of solutions presently known for nonlinear diffusion can be utilized in the context ofn-diffusion. Known solutions ofn-diffusion are obtained via this procedure as well as newn-diffusion solutions, including the source solution and a solution of the problem of fluid withdrawal at a constant flow rate for a non-Newtonian fluid in a porous medium of infinite extent. Solutions arising from other exact nonlinear diffusion profiles are also investigated as well as the limiting case ofn-diffusion forn tending to infinity and the results are displayed graphically. Springer-Verlag, 1992 Hill D. Department of Mathematics, University of Wollongong, Wollongong, New South Wales, Australia aut Hill J. Department of Mathematics, University of Wollongong, Wollongong, New South Wales, Australia aut Acta Mechanica Springer-Verlag 91/3-4(1992-09-01), 193-208 0001-5970 91:3-4<193 1992 91 707 https://doi.org/10.1007/BF01194109 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/BF01194109 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Hill D. Department of Mathematics, University of Wollongong, Wollongong, New South Wales, Australia aut NATIONALLICENCE 700 1- Hill J. Department of Mathematics, University of Wollongong, Wollongong, New South Wales, Australia aut NATIONALLICENCE 773 0- Acta Mechanica Springer-Verlag 91/3-4(1992-09-01), 193-208 0001-5970 91:3-4<193 1992 91 707 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer