Shell balance

About: Shell balance is a research topic. Over the lifetime, 154 publications have been published within this topic receiving 3691 citations.

Momentum Balance for Two-Phase Horizontal Pipe Flow Part 2: Testing of Models

Abstract: Momentum balance models were tested against reliable data for both holdup and pressure drop. The best prediction performance was achieved using a model that considered the actual shape of the liquid phase in the pipe. In such circumstances the momentum balance calculation tended to under predict both the holdup and pressure drop for some of the annular and stratified regimes. Suggestions are made for improvements in the momentum balance approach.

Study of the Effects of Pressure-Induced Viscmity Changes on the Fluid Flow Characteristics in a Circular Tube

Abstract: 6 = fj. = v = p = Nomenclature fluid compressibility factor, in./lb length of pressure release tube, in. fluid pressure, lb/in. pressure in pressure pot at time equal to zero, lb/in. atmospheric pressure, lb/in. volume rate of fluid flow, in./sec radial and longitudinal coordinates, in. internal radius of the pressure release tube, in. event time, msec volume of fluid in reservoir, in. volume of fluid that exits the reservoir during depressurization, in. longitudinal velocity of fluid within bore of pressure release tube, in./sec time constant, msec coefficient of viscosity of fluid, lb-sec/in. kinematic viscosity of fluid, in./sec mass density of fluid, slugs/in.

Approximate Solutions of Differential Equations of Non-Newtonian Fluids Flow Arising in the Study of Helical Screw Rheometer

Abstract: The thesis presents the theoretical analyses of extrusion process inside Helical Screw Rheometer (HSR).Efforts to obtain better insight into the process must be mainly theoretical rather than experimental. But the hope, of course, is that better insight than experimental so gained will provide practical benefits such as better control of the processing, optimize the processing process and improve the quality of production. The main objective of the study is to develop mathematical models in order to evaluate the velocity profiles, shear stresses and volume flow rates for isothermal flow of incompressible non-Newtonian fluids in HSR.The calculations of these values are of great importance during the production process.In this thesis, two types of geometries are considered. ² In first geometry the Cartesian co-ordinates system is used to study the flow of third-grade fluid, co-rotational Maxwell fluid, Eyring fluid, Eyring-Powell fluid and Oldroyd 8-constant fluid models in HSR.The geometry of the HSR is simplified by unwrapping or flattening the channel, lands and the outside rotating barrel.A shallow infinite channel is considered by assuming the width of the channel large as compared to the depth.We also assumed that the screw surface, the lower plate, is stationary and the barrel surface, the upper plate, is moving across the top of the channel with a velocity at an angle to the direction of the channel.The phenomena is same as, the barrel held stationary and the screw rotates. Solutions for velocity profiles, volume flow rates, average velocity, shear and normal stresses, shear stresses at barrel surface and shear forces exerted on the fluid are obtained using analytical techniques.Adomian decomposition method is used to obtain the solutions for third-grade fluid, Eyring-Powell fluid and Oldroyd 8-constant fluid and perturbation method for co-rotational Maxwell fluid, where exact solution is obtained for Eyring fluid model.The effects of the rheological parameters, pressure gradients and flight angle on the velocity distributions are investigated and discussed.The behavior of the shear stresses is also discussed with the help of graphs for different values of non-Newtonian parameters. ² For better analysis cylindrical co-ordinates system is taken in second geometry, assuming that the outer barrel of radius r2 is stationary and the screw of radius r1 rotates with angular velocity W.Here we have used third-grade fluid model with and without flight angle and co-rotational Maxwell fluid model with nonzero flight angle in HSR.The analytical expressions for the velocities, shear and normal stresses and the shear stresses exerted by the fluid on the screw, volume flow rates and average velocity are derived using analytical techniques and the outcomes have been presented with the help of graphs.The effects of the rheological parameters and pressure gradients on the velocity distribution are investigated

Shell Balance Approach for One-Dimensional Biofluid Transport

Abstract: Analysis methods in Chap. 9 were based on a macroscopic approach to bioheat transport, in which the system of interest was assumed to have a relatively uniform temperature. The temperature might change with time, but spatial variations within the system were assumed to be negligible or unimportant. In this chapter we will turn our interest to problems where there is an important spatial gradient in temperature. The spatial temperature gradient will cause a conduction heat flux in accordance with Fourier’s law (2.9). Here we will restrict the scope of problems to those that are dimensional or nearly one-dimensional. Our analysis in each of these problems will begin by applying conservation of energy on an infinitesimally small portion of the system, known as a shell. A feature which distinguishes this approach from the more general approach to be applied in Chap. 11 is that the shells used in this chapter will shrink only in one dimension, so they might include a portion of the system boundary, while the shells used in the general approach shrink around an interior point in the system and do not include any portion of the system boundary. Consequently, energy that enters the system through the portion of the shell that includes the system boundary will be treated in this chapter as a term in the conservation equation rather than as a boundary condition. In reality, heat that enters through the system boundary often enters in a direction that is perpendicular to the assumed direction of energy flow. Although energy flow is not truly one-dimensional in such cases, the shell balance approach allows us to obtain realistic approximate solutions in which a more rigorous multidimensional approach would greatly increase the complexity but add little to the understanding or accuracy of the solution.