An equation for nonlinear wave propagation in thermoviscous fluids with an application to pistondriven flow
Abstract
A single equation for two and three dimensional potential flow in a viscous, heatconducting fluid is derived. An ordinary differential equation is obtained by grouptheoretic methods and is applied to the problem of fluid flow ahead of a cylindrically or spherically symmetric piston, with the piston radius proportional to the square root of the time. A closed form solution is obtained for the cylindrical case when the effect of the initial equilibrium pressure is neglected. A solution in series form which takes into account the initial pressure is also obtained. Corresponding numerical solutions for the case of spherical symmetry are presented. While direct numerical integration of the equation for the spherical piston is quite difficult, the cylindrical solution can be used as a first approximation. Further approximations are then obtained by a rapidly converging iterative scheme involving numerical integration of only a first order equation.
 Publication:

Ph.D. Thesis
 Pub Date:
 December 1976
 Bibcode:
 1976PhDT.......100M
 Keywords:

 Approximation;
 Conductive Heat Transfer;
 Nonlinear Equations;
 Piston Theory;
 Viscous Fluids;
 Wave Propagation;
 Cylindrical Waves;
 Differential Equations;
 Flow Equations;
 Spherical Waves;
 Three Dimensional Flow;
 Fluid Mechanics and Heat Transfer