On the Heat Flow Through a Porous Tube Filled with Incompressible Viscous Fluid

2020 ◽  
Vol 75 (4) ◽  
pp. 333-342
Author(s):  
Igor Pažanin ◽  
Marko Radulović
Keyword(s):  
Viscous Fluid ◽  
Order Approximation ◽  
Surrounding Medium ◽  
Isothermal Flow ◽  
Incompressible Viscous Fluid ◽  
Porous Tube ◽  
Rigid Tube ◽  
Higher Order Terms ◽  
Flow Through ◽  
The One

AbstractWe studied the non-isothermal flow of an incompressible viscous fluid through a porous tube. Motivated by filtration problems, Darcy’s law was incorporated on the walls of the tube and the flow was pressure driven. The main goal was to investigate the thermodynamic part of the system, assuming that the hydrodynamic part is known. In view of the applications we wanted to model, the fluid inside the tube was supposed to be cooled (or heated) by the surrounding medium. Using asymptotic analysis with respect to the small parameter (being the ratio between the tube’s thickness and its length), we constructed the explicit second-order approximation for the temperature distribution of the fluid. Numerical examples are provided to compare the obtained solution with the one derived for a rigid tube and also to show the corrections due to higher-order terms.

scholarly journals On compressible and piezo-viscous flow in thin porous media

2018 ◽  
Vol 474 (2209) ◽  
pp. 20170601 ◽  
Author(s):  
F. Pérez-Ràfols ◽  
P. Wall ◽  
A. Almqvist
Keyword(s):  
Porous Media ◽  
Pressure Drop ◽  
Viscous Fluid ◽  
Linear Equation ◽  
Nonlinear Function ◽  
Viscous Fluids ◽  
Total Flow ◽  
Thin Porous Media ◽  
Flow Through ◽  
The One

In this paper, we study flow through thin porous media as in, e.g. seals or fractures. It is often useful to know the permeability of such systems. In the context of incompressible and iso-viscous fluids, the permeability is the constant of proportionality relating the total flow through the media to the pressure drop. In this work, we show that it is also relevant to define a constant permeability when compressible and/or piezo-viscous fluids are considered. More precisely, we show that the corresponding nonlinear equation describing the flow of any compressible and piezo-viscous fluid can be transformed into a single linear equation. Indeed, this linear equation is the same as the one describing the flow of an incompressible and iso-viscous fluid. By this transformation, the total flow can be expressed as the product of the permeability and a nonlinear function of pressure, which represents a generalized pressure drop.

Twisted-Pore Effect on Fluid Flow, Solid Deformation and Stress in a Poro-Elastic Cylinder

1979 ◽  
Vol 46 (4) ◽  
pp. 784-788
Author(s):  
M. Kurashige
Keyword(s):  
Fluid Flow ◽  
Viscous Fluid ◽  
Elastic Material ◽  
Mathematical Analysis ◽  
Elastic Cylinder ◽  
Numerical Computations ◽  
Rigid Tube ◽  
Solid Deformation ◽  
Linearized Theory ◽  
Flow Through

The linearized theory of viscous-fluid-saturated poro-elastic material proposed by Crochet and Naghdi is summarized and applied to the problem of steady fluid flow through a “twisted pore” elastic cylinder. The cylinder is encased in and bonded to an impermeable rigid tube. Deformations and stresses of the cylinder due to the flow are considered. The results of the mathematical analysis and some numerical computations cast light on the “twisted pore” effect.

scholarly journals Numerical Method in Two Dimensional Boundary Layer Theory for Incompressible Viscous Fluid

2013 ◽  
Vol 38 ◽  
pp. 61-73
Author(s):  
MA Haque
Keyword(s):  
Boundary Layer ◽  
Viscous Fluid ◽  
Initial Value Problem ◽  
Shooting Method ◽  
Boundary Layer Equation ◽  
Incompressible Viscous Fluid ◽  
Initial Value ◽  
Box Scheme ◽  
Runge Kutta Method ◽  
Dimensional Boundary

In this paper laminar flow of incompressible viscous fluid has been considered. Here two numerical methods for solving boundary layer equation have been discussed; (i) Keller Box scheme, (ii) Shooting Method. In Shooting Method, the boundary value problem has been converted into an equivalent initial value problem. Finally the Runge-Kutta method is used to solve the initial value problem. DOI: http://dx.doi.org/10.3329/rujs.v38i0.16549 Rajshahi University J. of Sci. 38, 61-73 (2010)

An approach to simulation of dual drainage

1999 ◽  
Vol 39 (9) ◽  
pp. 95-103 ◽  
Author(s):  
S. Djordjević ◽  
D. Prodanović ◽  
Č. Maksimović
Keyword(s):  
Numerical Model ◽  
Model Development ◽  
Ground Level ◽  
Surface Flow ◽  
Surface Excess ◽  
Runoff Simulation ◽  
Sewer System ◽  
Excess Water ◽  
Flow Through ◽  
The One

The paper presents the development of the field of urban drainage modelling known as dual drainage - an approach to rainfaill runoff simulation in which the numerical model takes into account not only the flow through the sewer system, but also the flow on the surface. The steps in model development are described, and necessary data, assumptions used and operations to be performed using GIS are discussed. The numerical model simultaneously handles the full dynamic equations of flow through the sewer system and simplified equations of the surface flow. The surface excess water (due to the limited capacity of inlets or to the hydraulic head in the sewer system reaching the ground level) is routed to the neighbour subcatchment (not necessarily the one attached to the downstream network node), using surface retentions, if any.

Laminar flow in symmetrical channels with slightly curved walls II. An asymptotic series for the stream function

1963 ◽  
Vol 272 (1350) ◽  
pp. 406-428 ◽  
Keyword(s):  
Laminar Flow ◽  
Asymptotic Series ◽  
Radius Of Curvature ◽  
Two Dimensional ◽  
The Third ◽  
Higher Order Terms ◽  
Curvature Parameter ◽  
Leading Term ◽  
Flow Through ◽  
Curved Walls

A class of two-dimensional channels, with walls whose radius of curvature is uniformly large relative to local channel width, is described, and the velocity field of laminar flow through these channels is obtained as a power series in the small curvature parameter. The leading term is the Jeffery-Hamel solution considered in part I, and it is shown here how the higher-order terms are found. Terms of the third approximation have been computed. The theory is applied to two examples, for one of which experimental results are available and confirm the theoretical values with fair accuracy.

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