scholarly journals Perturbation solutions for a micropolar fluid flow in a semi-infinite expanding or contracting pipe with large injection or suction through porous wall

Open Physics ◽  
2016 ◽  
Vol 14 (1) ◽  
pp. 231-238 ◽  
Author(s):  
Xinhui Si ◽  
Lili Yuan ◽  
Limei Cao ◽  
Liancun Zheng ◽  
Yanan Shen ◽  
...  
Keyword(s):  
Numerical Solutions ◽  
Pipe Wall ◽  
Porous Wall ◽  
Singular Boundary ◽  
High Order Derivative ◽  
Similarity Transformations ◽  
Micropolar Fluid Flow ◽  
Porous Pipe ◽  
Expansion Matching ◽  
Large Injection

AbstractWe investigate an unsteady incompressible laminar micropolar flow in a semi-infinite porous pipe with large injection or suction through a deforming pipe wall. Using suitable similarity transformations, the governing partial differential are transformed into a coupled nonlinear singular boundary value problem. For large injection, the asymptotic solutions are constructed using the Lighthill method, which eliminates singularity of solution in the high order derivative. For large suction, a series expansion matching method is used. Analytical solutions are validated against the numerical solutions obtained by Bvp4c.

Ohmic and viscous dissipation effects on micropolar non-Newtonian nanofluid Al2O3 flow through a non-Darcy porous media

2022 ◽  
pp. 1-13
Author(s):  
Nabil T. Eldabe ◽  
Mohamed Y. Abou zeid ◽  
Sami M. El Shabouri ◽  
Tarek N. Salama ◽  
Aya M. Ismael
Keyword(s):  
Magnetic Field ◽  
Heat Source ◽  
Numerical Solutions ◽  
Tangential Velocity ◽  
Darcy Number ◽  
Physical Parameters ◽  
Fluid Temperature ◽  
High Concentration ◽  
Ohmic Dissipation ◽  
Similarity Transformations

Inclined uniform magnetic field and mixed convention effects on micropolar non-Newtonian nanofluid Al2O3 flow with heat transfer are studied. The heat source, both viscous and ohmic dissipation and temperature micropolarity properties are considered. We transformed our system of non-linear partial differential equations into ordinary equations by using suitable similarity transformations. These equations are solved by making use of Rung–Kutta–Merson method in a shooting and matching technique. The numerical solutions of the tangential velocity, microtation velocity, temperature and nanoparticle concentration are obtained as functions of the physical parameters of the problem. Moreover, we discussed the effects of these parameters on the numerical solutions and depicted graphically. It is obvious that these parameters control the fluid flow. It is noticed that the tangential velocity magnifies with an increase in the value of Darcy number. Meanwhile, the value of the tangential velocity reduces with the elevation in the value of the magnetic field parameter. On the other hand, the elevation in the value of Brownian motion parameter leads to a reduction in the value of fluid temperature. Furthermore, increasing in the value of heat source parameter makes an enhancement in the value of nanoparticles concentration. The current study has many accomplishments in several scientific areas like medical industry, medicine, and others. Therefore, it represents the depiction of gas or liquid motion over a surface. When particles are moving from areas of high concentration to areas of low concentration.

scholarly journals Nature Inspired Computational Technique for the Numerical Solution of Nonlinear Singular Boundary Value Problems Arising in Physiology

2014 ◽  
Vol 2014 ◽  
pp. 1-10
Author(s):  
Suheel Abdullah Malik ◽  
Ijaz Mansoor Qureshi ◽  
Muhammad Amir ◽  
Ihsanul Haq
Keyword(s):  
Numerical Solution ◽  
Boundary Value Problems ◽  
Numerical Solutions ◽  
Fitness Function ◽  
Boundary Value ◽  
Computational Technique ◽  
Singular Boundary ◽  
Interior Point Algorithm ◽  
Singular Boundary Value Problems ◽  
Hybrid Heuristic

We present a hybrid heuristic computing method for the numerical solution of nonlinear singular boundary value problems arising in physiology. The approximate solution is deduced as a linear combination of some log sigmoid basis functions. A fitness function representing the sum of the mean square error of the given nonlinear ordinary differential equation (ODE) and its boundary conditions is formulated. The optimization of the unknown adjustable parameters contained in the fitness function is performed by the hybrid heuristic computation algorithm based on genetic algorithm (GA), interior point algorithm (IPA), and active set algorithm (ASA). The efficiency and the viability of the proposed method are confirmed by solving three examples from physiology. The obtained approximate solutions are found in excellent agreement with the exact solutions as well as some conventional numerical solutions.

On the Prediction of Stresses in Pipes Caused by Ice Plug Formation

1996 ◽  
Vol 210 (3) ◽  
pp. 151-158 ◽  
Author(s):  
S Syngellakis ◽  
A Keary ◽  
R J Bowen
Keyword(s):  
Shell Theory ◽  
Numerical Solutions ◽  
Pipe Wall ◽  
Interaction Mechanism ◽  
Stress Generation ◽  
Simple Analytical Model ◽  
Interface Shear ◽  
Axisymmetric Shell ◽  
Wall Interaction ◽  
Plug Formation

Stress development in pipes due to local fluid freezing is investigated through a simple analytical model based on thin axisymmetric shell theory. Particular attention is given to modelling the interaction between the pipe wall and the ice formed within the freezing jacket. The developed analysis accounts for the interface shear traction and relies on rational assumptions regarding its distribution in order to interpret and reproduce observed pipe behaviour. It is validated by comparing its predictions to available exact and numerical solutions as well as experimental data. Finally, it proves a valuable tool in understanding the ice plug-pipe wall interaction mechanism which controls stress generation and distribution.

scholarly journals The NANOFLUID FLOW BETWEEN PARALLEL PLATES AND HEAT TRANSFER IN PRESENCE OF CHEMICAL REACTION AND POROUS MATRIX

2020 ◽  
Vol 50 (4) ◽  
pp. 283-289
Author(s):  
S. Jena ◽  
S. R. Mishra ◽  
P.K. Pattnaik ◽  
Ram Prakash Sharma
Keyword(s):  
Heat Transfer ◽  
Heat Source ◽  
Chemical Reaction ◽  
Numerical Solutions ◽  
Porous Matrix ◽  
Parallel Plates ◽  
Nanofluid Flow ◽  
Similarity Transformations ◽  
Fourth Order Method ◽  
Source Sink

This paper deals with nanofluid flow between parallel plates and heat transfer through porous media with heat source /sink. The governing equations are transformed into self-similar ordinary differential equations by adopting similarity transformations and then the converted equations are solved numerically by Runge-Kutta fourth order method. Special emphasis has been given to the parameters of physical interest which include Prandtl number, magnetic parameter, porous matrix, chemical reaction parameter and heat source parameter. The results obtained for velocity, temperature and concentration are shown in graphs. The comparison of the special case of this present results with the existing numerical solutions in the literature shows excellent agreement.

scholarly journals Transportation of Al2O3-SiO2-TiO2 modified nanofluid over an exponentially stretching surface with inclined magnetohydrodynamic

2021 ◽  
Vol 25 (Spec. issue 2) ◽  
pp. 279-285
Author(s):  
Prvaeen Dadheech ◽  
Priyanka Agrawal ◽  
Anil Sharma ◽  
Kottakkaran Nisar ◽  
Sunil Purohit
Keyword(s):  
Magnetic Field ◽  
Base Fluid ◽  
Numerical Solutions ◽  
Graphical Representation ◽  
Hybrid Nanofluid ◽  
Stretching Surface ◽  
Similarity Transformations ◽  
Exponentially Stretching ◽  
Inclined Angle ◽  
Fourth Order Method

In the present study Al2O3-SiO2-TiO2/C2H6O2 modified nanofluid flow over a stretching surface is considered with imposed inclined magnetic field. Three different suspended nanoparticles in a base fluid are considered in this next generation of hybrid nanofluid called as modified nanofluid. Ethanol glycol is taken as a base fluid with suspension of three nanoparticles of Al2O3, SiO2, and TiO2. The mathematical model of the flow is encountered by Runga-Kutta fourth order method using appropriate similarity transformations. As a key result it is observed that the capacity of heat transportation of modified nanofluid is higher as compared with nanofluids and hybrid nanofluids. Numerical solutions with graphical representation are presented. With increased inclined angle, parameter of magnetic field, and volume friction parameter a decrement in velocity field has been noticed for modified nanofluid.

scholarly journals Simultaneous solutions for first order and second order slips on micropolar fluid flow across a convective surface in the presence of Lorentz force and variable heat source/sink

2019 ◽  
Vol 9 (1) ◽  
Author(s):  
K. Anantha Kumar ◽  
V. Sugunamma ◽  
N. Sandeep ◽  
M. T. Mustafa
Keyword(s):  
Heat Transfer ◽  
Heat Source ◽  
Micropolar Fluid ◽  
Velocity Slip ◽  
Second Order ◽  
Nonlinear Odes ◽  
Similarity Transformations ◽  
Runge Kutta Method ◽  
Micropolar Fluid Flow ◽  
Source Sink

Abstract This report presents the flow and heat transfer characteristics of MHD micropolar fluid due to the stretching of a surface with second order velocity slip. The influence of nonlinear radiation and irregular heat source/sink are anticipated. Simultaneous solutions are presented for first and second-order velocity slips. The PDEs which govern the flow have been transformed as ODEs by the choice of suitable similarity transformations. The transformed nonlinear ODEs are converted into linear by shooting method then solved numerically by fourth-order Runge-Kutta method. Graphs are drowned to discern the effect of varied nondimensional parameters on the flow fields (velocity, microrotation, and temperature). Along with them the coefficients of Skin friction, couple stress, and local Nussel number are also anticipated and portrayed with the support of the table. The results unveil that the non-uniform heat source/sink and non-linear radiation parameters plays a key role in the heat transfer performance. Also, second-order slip velocity causes strengthen in the distribution of velocity but a reduction in the distribution of temperature is perceived.

scholarly journals The Effect of Heat Transfer on MHD Marangoni Boundary Layer Flow Past a Flat Plate in Nanofluid

2013 ◽  
Vol 2013 ◽  
pp. 1-6 ◽  
Author(s):  
D. R. V. S. R. K. Sastry ◽  
A. S. N. Murti ◽  
T. Poorna Kantha
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
Differential Equations ◽  
Boundary Layer Flow ◽  
Numerical Solutions ◽  
Volume Fraction ◽  
Solid Volume Fraction ◽  
Convection Boundary Layer ◽  
Similarity Transformations ◽  
Layer Flow

The problem of heat transfer on the Marangoni convection boundary layer flow in an electrically conducting nanofluid is studied. Similarity transformations are used to transform the set of governing partial differential equations of the flow into a set of nonlinear ordinary differential equations. Numerical solutions of the similarity equations are then solved through the MATLAB “bvp4c” function. Different nanoparticles like Cu, Al2O3, and TiO2 are taken into consideration with water as base fluid. The velocity and temperature profiles are shown in graphs. Also the effects of the Prandtl number and solid volume fraction on heat transfer are discussed.

Dynamic Crack Propagation Analysis by Moving Singular Boundary Elements

1992 ◽  
Vol 59 (2S) ◽  
pp. S158-S162 ◽  
Author(s):  
Rafael Gallego ◽  
Jose´ Dominguez
Keyword(s):  
Crack Propagation ◽  
Boundary Element ◽  
Numerical Solutions ◽  
Dynamic Crack Propagation ◽  
Dynamic Crack ◽  
Singular Boundary ◽  
Singular Element ◽  
Infinite Domain ◽  
Propagation Analysis ◽  
Finite Domains

An efficient boundary element procedure for the dynamic analysis of crack propagation in unbounded and arbitrary shape finite bodies is presented. The procedure is based on the direct time domain formulation of the boundary element method. A moving singular element and a remeshing technique have been developed to model the asymptotic solution of the stresses near the propagating crack tip. These ideas are easily implemented for a boundary discretization as opposed to similar procedures previously developed in a finite element context. The method is applied to problems of dynamic crack propagation in finite and infinite elastic domains. The obtained numerical results are compared with infinite domain analytical solutions and with available numerical solutions for finite domains.

MHD mixed convection oblique stagnation-point flow on a vertical plate

2017 ◽  
Vol 27 (12) ◽  
pp. 2744-2767
Author(s):  
Giulia Giantesio ◽  
Anna Verna ◽  
Natalia C. Roşca ◽  
Alin V. Rosca ◽  
Ioan Pop
Keyword(s):  
Mixed Convection ◽  
Stagnation Point ◽  
Newtonian Fluid ◽  
Numerical Solutions ◽  
Stokes Equations ◽  
Boussinesq Approximation ◽  
Stagnation Point Flow ◽  
Content Type ◽  
Boundary Layer Equations ◽  
Similarity Transformations

Purpose This paper aims to study the problem of the steady plane oblique stagnation-point flow of an electrically conducting Newtonian fluid impinging on a heated vertical sheet. The temperature of the plate varies linearly with the distance from the stagnation point. Design/methodology/approach The governing boundary layer equations are transformed into a system of ordinary differential equations using the similarity transformations. The system is then solved numerically using the “bvp4c” function in MATLAB. Findings An exact similarity solution of the magnetohydrodynamic (MHD) Navier–Stokes equations under the Boussinesq approximation is obtained. Numerical solutions of the relevant functions and the structure of the flow field are presented and discussed for several values of the parameters which influence the motion: the Hartmann number, the parameter describing the oblique part of the motion, the Prandtl number (Pr) and the Richardson numbers. Dual solutions exist for several values of the parameters. Originality value The present results are original and new for the problem of MHD mixed convection oblique stagnation-point flow of a Newtonian fluid over a vertical flat plate, with the effect of induced magnetic field and temperature.

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