Group invariant solution for a pre-existing fracture driven by a power-law fluid in permeable rock

2016 ◽  
Vol 30 (28n29) ◽  
pp. 1640010 ◽  
Author(s):  
A. G. Fareo ◽  
D. P. Mason
Keyword(s):  
Newtonian Fluid ◽  
Power Law ◽  
Numerical Solutions ◽  
Invariant Solution ◽  
Two Dimensional ◽  
Initial Length ◽  
Power Law Fluid ◽  
Group Invariant ◽  
Permeable Rock ◽  
Fluid Leak

Group invariant analytical and numerical solutions for the evolution of a two-dimensional fracture with nonzero initial length in permeable rock and driven by an incompressible non-Newtonian fluid of power-law rheology are obtained. The effect of fluid leak-off on the evolution of the power-law fluid fracture is investigated.

Simultaneous Wicking-Convection Heat Transfer Process with Non-Newtonian Power-Law Fluid

2010 ◽  
Vol 297-301 ◽  
pp. 117-125
Author(s):  
Oscar Bautista ◽  
Federico Méndez ◽  
Eric Bautista
Keyword(s):  
Heat Transfer ◽  
Porous Medium ◽  
Newtonian Fluid ◽  
Power Law ◽  
Transfer Process ◽  
Numerical Solutions ◽  
Heat Transfer Process ◽  
Dimensionless Temperature ◽  
Power Law Fluid ◽  
Temperature And Pressure

In this work, we have theoretically analyzed the heat convection process in a porous medium under the influence of spontaneous wicking of a non-Newtonian power-law fluid, trapped in a capillary element, considering the presence of a temperature gradient. The capillary element is represented by a porous medium which is initially found at temperature and pressure . Suddenly the lower part of the porous medium touches a reservoir with a non-Newtonian fluid with temperature and pressure . This contact between both phases, in turn causes spontaneously the wicking process. Using a one-dimensional formulation of the average conservation laws, we derive the corresponding nondimensional momentum and energy equations. The numerical solutions permit us to evaluate the position and velocity of the imbibitions front as well as the dimensionless temperature profiles and Nusselt number. The above results are shown by considering the physical influence of two nondimensional parameters: the ratio of the characteristic thermal time to the characteristic wicking time, , the ratio of the hydrostatic head of the imbibed fluid to the characteristic pressure difference between the wicking front and the dry zone of the porous medium, , and the power-law index, n, for the non-Newtonian fluid. The predictions show that the wicking and heat transfer process are strongly dependent on the above nondimensional parameters, indicating a clear deviation in comparison with and n = 1, that represents the classical Lucas-Washburn solution.

A Non-Newtonian Fluid Flow Model for the Slip Condition on Blood Flow through a Stenosed Artery using Power-law Fluid

2018 ◽  
Vol 9 (7) ◽  
pp. 871-879
Author(s):  
Rajesh Shrivastava ◽  
R. S. Chandel ◽  
Ajay Kumar ◽  
Keerty Shrivastava and Sanjeet Kumar
Keyword(s):  
Blood Flow ◽  
Fluid Flow ◽  
Newtonian Fluid ◽  
Power Law ◽  
Flow Model ◽  
Slip Condition ◽  
Power Law Fluid ◽  
Stenosed Artery ◽  
Flow Through

scholarly journals Group-Invariant Solutions for Two-Dimensional Free, Wall, and Liquid Jets Having Finite Fluid Velocity at Orifice

2011 ◽  
Vol 2011 ◽  
pp. 1-12
Author(s):  
R. Naz
Keyword(s):  
Fluid Velocity ◽  
Invariant Solution ◽  
Jet Flows ◽  
Order Partial Differential Equation ◽  
Free Wall ◽  
Two Dimensional ◽  
Invariant Solutions ◽  
Third Order ◽  
Group Invariant ◽  
Group Invariant Solutions

The group-invariant solutions for nonlinear third-order partial differential equation (PDE) governing flow in two-dimensional jets (free, wall, and liquid) having finite fluid velocity at orifice are constructed. The symmetry associated with the conserved vector that was used to derive the conserved quantity for the jets (free, wall, and liquid) generated the group invariant solution for the nonlinear third-order PDE for the stream function. The comparison between results for two-dimensional jet flows having finite and infinite fluid velocity at orifice is presented. The general form of the group invariant solution for two-dimensional jets is given explicitly.

Reduced Order Model for a Power-Law Fluid

2014 ◽  
Vol 136 (7) ◽  
Author(s):  
M. Ocana ◽  
D. Alonso ◽  
A. Velazquez
Keyword(s):  
Newtonian Fluid ◽  
Power Law ◽  
Reduced Order Model ◽  
Processing Unit ◽  
Order Model ◽  
Power Law Fluid ◽  
Reduced Order ◽  
Polymeric Fluid ◽  
Central Processing ◽  
Highly Nonlinear

This article describes the development of a reduced order model (ROM) based on residual minimization for a generic power-law fluid. The objective of the work is to generate a methodology that allows for the fast and accurate computation of polymeric flow fields in a multiparameter space. It is shown that the ROM allows for the computation of the flow field in a few seconds, as compared with the use of computational fluid dynamics (CFD) methods in which the central processing unit (CPU) time is on the order of hours. The model fluid used in the study is a polymeric fluid characterized by both its power-law consistency index m and its power-law index n. Regarding the ROM development, the main difference between this case and the case of a Newtonian fluid is the order of the nonlinear terms in the viscous stress tensor: In the case of the polymeric fluid these terms are highly nonlinear while they are linear when a Newtonian fluid is considered. After the method is validated and its robustness studied with regard to several parameters, an application case is presented that could be representative of some industrial situations.

Nonclassical Symmetry Analysis of Heated Two-Dimensional Flow Problems

2015 ◽  
Vol 70 (12) ◽  
pp. 1031-1037
Author(s):  
Imran Naeem ◽  
Rehana Naz ◽  
Muhammad Danish Khan
Keyword(s):  
Boundary Layer ◽  
Differential Equations ◽  
Invariant Solution ◽  
Heat Transfer Analysis ◽  
Two Dimensional ◽  
Group Invariant ◽  
Boundary Layer Equations ◽  
Flow Problems ◽  
Nonclassical Symmetry ◽  
Nonclassical Symmetries

AbstractThis article analyses the nonclassical symmetries and group invariant solution of boundary layer equations for two-dimensional heated flows. First, we derive the nonclassical symmetry determining equations with the aid of the computer package SADE. We solve these equations directly to obtain nonclassical symmetries. We follow standard procedure of computing nonclassical symmetries and consider two different scenarios, ξ1≠0 and ξ1=0, ξ2≠0. Several nonclassical symmetries are reported for both scenarios. Furthermore, numerous group invariant solutions for nonclassical symmetries are derived. The similarity variables associated with each nonclassical symmetry are computed. The similarity variables reduce the system of partial differential equations (PDEs) to a system of ordinary differential equations (ODEs) in terms of similarity variables. The reduced system of ODEs are solved to obtain group invariant solution for governing boundary layer equations for two-dimensional heated flow problems. We successfully formulate a physical problem of heat transfer analysis for fluid flow over a linearly stretching porous plat and, with suitable boundary conditions, we solve this problem.

Sign in / Sign up

Export Citation Format

Share Document