Showing papers on "Shell balance published in 1995"

Plane surface suddenly set in motion in a non-Newtonian fluid

Abstract: The flow field of a fluid being called “the third order fluid” or the “fluid of grade three” is considered for a non-Newtonian flow in the vicinity of a plane wall, suddenly set in motion. The velocity field of the flow is described by a fourth order, non-linear partial differential equation. The solution of this differential equation shows that for short time a strong non-Newtonian effect is present in the velocity field. However, for long time the velocity field becomes a Newtonian one.

Evolution of the balance equations in saturated thermoelastic porous media following abrupt simultaneous changes in pressure and temperature

Abstract: A mathematical model is developed for saturated flow of a Newtonian fluid in a thermoelastic, homogeneous, isotropic porous medium domain under nonisothermal conditions. The model contains mass, momentum and energy balance equations. Both the momentum and energy balance equations have been developed to include a Forchheimer term which represents the interaction at the solid-fluid interface at high Reynolds numbers. The evolution of these equations, following an abrupt change in both fluid pressure and temperature, is presented. Using a dimensional analysis, four evolution periods are distinguished. At the very first instant, pressure, effective stress, and matrix temperature are found to be disturbed with no attenuation. During this stage, the temporal rate of pressure change is linearly proportional to that of the fluid temperature. In the second time period, nonlinear waves are formed in terms of solid deformation, fluid density, and velocities of phases. The equation describing heat transfer becomes parabolic. During the third evolution stage, the inertial and the dissipative terms are of equal order of magnitude. However, during the fourth time period, the fluid's inertial terms subside, reducing the fluid's momentum balance equation to the form of Darcy's law. During this period, we note that the body and surface forces on the solid phase are balanced, while mechanical work and heat conduction of the phases are reduced.