%0 Report %1 citeulike:3754070 %A Austin, Stephen A. %C Newport, Rhode Island %D 1995 %K 76a05-non-newtonian-fluids %T An Analytical Solution for the Unsteady Flow of a Bingham Plastic Fluid in a Circular Tube %X The solution of unsteady, non-Newtonian fluid velocity profiles is developed using numerical approximations as found in Edwards et al. (1972), Lipscomb and Denn (1984), Duggins (1972), Atkin et al. (1991), and Walton and Bittleston (1991). The closed form solution of unsteady velocity profiles in circular tubes has been accomplished by Szymanksi (1932) for Newtonian fluids. An attempt to provide a closed form solution of the unsteady flow in circular tubes was made by Atabek (1964) for a non-Newtonian Bingham plastic fluid. The predominant method of solution for a Bingham plastic fluid in a circular tube has been to assume the form of the velocity profile in the boundary layer region, which was done by Chen et al. (1970) with an integral equation-based solution and by Duggins (1972) with a numerical solution. In this report, the solution of the start up of a Bingham flow in a long circular tube is presented in an analytical closed form. This non-Newtonian fluid model will be compared with Newtonian fluid models in order to determine the rheological influence for such borderline fluids as blood, which exhibit characteristics of both fluid classifications.

@techreport{citeulike:3754070, abstract = {{The solution of unsteady, non-Newtonian fluid velocity profiles is developed using numerical approximations as found in Edwards et al. (1972), Lipscomb and Denn (1984), Duggins (1972), Atkin et al. (1991), and Walton and Bittleston (1991). The closed form solution of unsteady velocity profiles in circular tubes has been accomplished by Szymanksi (1932) for Newtonian fluids. An attempt to provide a closed form solution of the unsteady flow in circular tubes was made by Atabek (1964) for a non-Newtonian Bingham plastic fluid. The predominant method of solution for a Bingham plastic fluid in a circular tube has been to assume the form of the velocity profile in the boundary layer region, which was done by Chen et al. (1970) with an integral equation-based solution and by Duggins (1972) with a numerical solution. In this report, the solution of the start up of a Bingham flow in a long circular tube is presented in an analytical closed form. This non-Newtonian fluid model will be compared with Newtonian fluid models in order to determine the rheological influence for such borderline fluids as blood, which exhibit characteristics of both fluid classifications.}}, added-at = {2017-06-29T07:13:07.000+0200}, address = {Newport, Rhode Island}, author = {Austin, Stephen A.}, biburl = {https://www.bibsonomy.org/bibtex/221db04f590b139ebaca153e625c75c09/gdmcbain}, citeulike-article-id = {3754070}, citeulike-attachment-1 = {austin_95_analytical_33838.pdf; /pdf/user/gdmcbain/article/3754070/33838/austin_95_analytical_33838.pdf; c351ce288bca741057481908c1ffcf43ac18961d}, comment = {(private-note)Cites Szymanski (1932) but with a second initial in the author's name.}, day = 17, file = {austin_95_analytical_33838.pdf}, howpublished = {NUWC-NPT Technical Report 11,011}, institution = {Naval Undersea Warfare Center Division}, interhash = {59f91ef20424ac1268ff9d1b7df8d144}, intrahash = {21db04f590b139ebaca153e625c75c09}, keywords = {76a05-non-newtonian-fluids}, month = oct, posted-at = {2008-12-08 03:48:17}, priority = {1}, timestamp = {2017-06-29T07:13:07.000+0200}, title = {{An Analytical Solution for the Unsteady Flow of a Bingham Plastic Fluid in a Circular Tube}}, year = 1995 }