scholarly journals On Solution Existence of Mhd Casson Nanofluid Transportation Across an Extending Cylinder Through Porous Media and Evaluation of Priori Bounds

2020 ◽  
Author(s):  
Sohaib Abdal ◽  
Sajjad Hussain ◽  
Imran Siddique
Keyword(s):  
Magnetic Parameter ◽  
Porous Matrix ◽  
Momentum Equation ◽  
Similarity Functions ◽  
Shooting Technique ◽  
Casson Nanofluid ◽  
Uniqueness Results ◽  
Runge Kutta Method ◽  
Large Injection ◽  
Flow Through

It is a theoretical exportation for mass transpiration and thermal transpiration of Casson nanofluid over an extending cylindrical surface. The Stagnation point flow through porous matrix is influenced by magnetic field of form strength. Appropriate similarity functions are availed to yield the transmuted system of leading differential equations. Existence for the solution of momentum equation is proved for various values of Casson parameter β, magnetic parameter M, porosity parameter Kp and Raynolds number Re in two situations of mass transpiration (suction/injuction). Moreover, uniqueness results are discussed and for skin friction factor are established to attain accuracy for large injection values. Thermal and concentration profiles are delineated numerically by applying Runge-Kutta method and shooting technique.

scholarly journals On solution existence of MHD Casson nanofluid transportation across an extending cylinder through porous media and evaluation of priori bounds

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Sohaib Abdal ◽  
Sajjad Hussain ◽  
Imran Siddique ◽  
Ali Ahmadian ◽  
Massimiliano Ferrara
Keyword(s):  
Porous Matrix ◽  
Momentum Equation ◽  
Flow Speed ◽  
Existence Of Solution ◽  
Similarity Functions ◽  
Shooting Technique ◽  
Casson Nanofluid ◽  
Runge Kutta Method ◽  
Large Injection ◽  
Flow Through

AbstractIt is a theoretical exportation for mass transpiration and thermal transportation of Casson nanofluid over an extending cylindrical surface. The Stagnation point flow through porous matrix is influenced by magnetic field of uniform strength. Appropriate similarity functions are availed to yield the transmuted system of leading differential equations. Existence for the solution of momentum equation is proved for various values of Casson parameter $$\beta $$ β , magnetic parameter M, porosity parameter $$K_p$$ K p and Reynolds number Re in two situations of mass transpiration (suction/injuction). The core interest for this study aroused to address some analytical aspects. Therefore, existence of solution is proved and uniqueness of this results is discussed with evaluation of bounds for existence of solution. Results for skin friction factor are established to attain accuracy for large injection values. Thermal and concentration profiles are delineated numerically by applying Runge-Kutta method and shooting technique. The flow speed retards against M, $$\beta $$ β and $$K_p$$ K p for both situations of mass injection and suction. The thermal boundary layer improves with Brownian and thermopherotic diffusions.

scholarly journals The Importance of Nanoparticles Addition in a Base Fluid Flow through a Porous Medium

2013 ◽  
Vol 8-9 ◽  
pp. 225-234
Author(s):  
Dalia Sabina Cimpean
Keyword(s):  
Porous Medium ◽  
Fluid Flow ◽  
Boundary Conditions ◽  
Mixed Convection ◽  
Mathematical Models ◽  
Base Fluid ◽  
Porous Matrix ◽  
Fluid Properties ◽  
Flow Through ◽  
Energy Equations

The present study is focused on the mixed convection fluid flow through a porous medium, when a different amount of nanoparticles is added in the base fluid. The nanofluid saturates the porous matrix and different situations of the flow between two walls are presented and discussed. Alternatively mathematical models are presented and discussed. A solution of a system which contains the momentum, Darcy and energy equations, together with the boundary conditions involved, is given. The behavior of different nanofluids, such thatAu-water, Ag-waterandFe-wateris graphically illustrated and compared with the previous results.The research target is to observe the substantial increase of the thermophysical fluid properties, when the porous medium issaturated by a nanofluid instead of a classical Newtonian fluid.

Friction factor analysis for a nanofluid circulating in a microchannel filled with a homogeneous porous medium

2022 ◽  
Author(s):  
Francisco Fernando Hernandez ◽  
Federico Mendez ◽  
Jose Joaquin Lizardi ◽  
Ian Guillermo Monsivais
Keyword(s):  
Porous Medium ◽  
Friction Factor ◽  
Porous Matrix ◽  
Velocity Profiles ◽  
Momentum Equation ◽  
Volumetric Concentration ◽  
Forchheimer Equation ◽  
Viscosity Models ◽  
Friction Factors ◽  
Homogeneous Porous Medium

Abstract This work presents the numerical solution for different velocity profiles and friction factors on a rectangular porous microchannel fully saturated by the flow of a nanofluid introducing different viscosity models, including one nanofluid density model. The Darcy-Brinkman-Forchheimer equation was used to solve the momentum equation in the porous medium. The results show that the relative density of the fluid, the nanoparticle diameters and their volumetric concentration have a direct influence on the velocity profiles only when the inertial effects caused by the presence of the porous matrix are important. Finally, it was found that only viscosity models that depend on temperature and nanoparticle diameter reduce the friction factor by seventy percent compared to a base fluid without nanoparticles; furthermore, these models show a velocity reduction of even ten percent along the symmetry axis of the microchannel.

scholarly journals Numerical solution of hydromagnetic peristaltic flow in a porous-saturated heated channel

2019 ◽  
Vol 23 (5 Part B) ◽  
pp. 3075-3091 ◽  
Author(s):  
Raheel Ahmed ◽  
Nasir Ali
Keyword(s):  
Flow Velocity ◽  
Mass Concentration ◽  
Porous Matrix ◽  
Momentum Equation ◽  
Radius Of Curvature ◽  
Governing Equations ◽  
Long Wavelength ◽  
Implicit Finite Difference Scheme ◽  
Permeability Parameter ◽  
Implicit Finite Difference

The hydromagnetic-flow in sinusoidally heated porous channel is studied by utilizing Darcy-Forchiemmer law with Joule heating effect. The Darcy?s resistance term in the momentum equation is acquired by using modified Darcy?s law. The governing equations for flow velocity, temperature, and mass concentration are developed under lubrication approximation, commonly known as long wavelength assumption in the realm of peristaltic flows. A well-tested implicit finite difference scheme is employed to solve the set of these equations along with appropriate boundary conditions. The governing equations involve important parameters namely, Forchiemmer parameter, dimensionless radius of curvature, permeability parameter, Hartmann, Brinkmann, Schmidt, and Soret numbers. The effect of these important parameters on velocity, temperature and mass concentration is illustrated through graphs. The pressure-flow rate relationship and streamlines are also shown. The presence of porous matrix inside the channel impedes the flow velocity and reduces the peristaltic transport and mingling. Moreover, temperature of the fluid rises with decreasing permeability of porous-matrix and Hartmann number.

scholarly journals Analysis of Brinkman-Forchheimer extended Darcy's model in a fluid saturated anisotropic porous channel

2012 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Timir Karmakar ◽  
Meraj Alam ◽  
G. P. Raja Sekhar
Keyword(s):  
Porous Medium ◽  
Approximate Solution ◽  
Existence And Uniqueness ◽  
Perturbation Expansion ◽  
Positive Semidefinite ◽  
Darcy Number ◽  
Momentum Equation ◽  
Matched Asymptotic Expansion ◽  
Regular Perturbation ◽  
Uniqueness Results

<p style='text-indent:20px;'>We present asymptotic analysis of Couette flow through a channel packed with porous medium. We assume that the porous medium is anisotropic and the permeability varies along all the directions so that it appears as a positive semidefinite matrix in the momentum equation. We developed existence and uniqueness results corresponding to the anisotropic Brinkman-Forchheimer extended Darcy's equation in case of fully developed flow using the Browder-Minty theorem. Complemented with the existence and uniqueness analysis, we present an asymptotic solution by taking Darcy number as the perturbed parameter. For a high Darcy number, the corresponding problem is dealt with regular perturbation expansion. For low Darcy number, the problem of interest is a singular perturbation. We use matched asymptotic expansion to treat this case. More generally, we obtained an approximate solution for the nonlinear problem, which is uniformly valid irrespective of the porous medium parameter values. The analysis presented serves a dual purpose by providing the existence and uniqueness of the anisotropic nonlinear Brinkman-Forchheimer extended Darcy's equation and provide an approximate solution that shows good agreement with the numerical solution.</p>

scholarly journals Non-Newtonian Momentum Transfer past an Isothermal Stretching Sheet with Applied Suction

2017 ◽  
Vol 22 (3) ◽  
pp. 665-674
Author(s):  
P.H. Veena ◽  
B. Suresh ◽  
V.K. Pravin ◽  
A.M. Goud
Keyword(s):  
Stretching Sheet ◽  
Magnetic Parameter ◽  
Exact Analytical Solution ◽  
Saturated Porous Medium ◽  
Momentum Equation ◽  
Elastic Parameter ◽  
Boundary Layer Theory ◽  
Elastic Surface ◽  
Permeability Parameter ◽  
Self Similar

AbstractThe paper discusses the flow of an incompressible non-Newtonian fluid due to stretching of a plane elastic surface in a saturated porous medium in the approximation of boundary layer theory. An exact analytical solution of non-linear MHD momentum equation governing the self-similar flow is given. The skin friction co-efficient decreases with an increase in the visco-elastic parameterk1and increase in the values of both the magnetic parameter and permeability parameter.

scholarly journals Tracer Test in Fractured Chalk

1993 ◽  
Vol 24 (4) ◽  
pp. 263-274 ◽  
Author(s):  
R. Jakobsen ◽  
K. Høgh Jensen ◽  
K. L. Brettmann
Keyword(s):  
Short Duration ◽  
Transport Mechanism ◽  
Arrival Time ◽  
Porous Matrix ◽  
Tracer Test ◽  
Breakthrough Curves ◽  
Advective Transport ◽  
Long Tail ◽  
Flow Through ◽  
Chalk Aquifer

A two-well tracer test was conducted in eastern Denmark, in which a short duration pulse of lithium chloride was injected into a recharge well and made to flow through a fractured chalk aquifer to a discharge well. The wells were 25 m apart, and the concentration of lithium arriving at the discharge well was monitored at five vertical intervals in the well for a 21-day period. The observed breakthrough curves show a sharp breakthrough front, with an arrival time that is consistent with advective transport through the fractures in the chalk. The breakthrough curves also exhibit a long tail in the falling limb, suggesting the influence of a secondary transport mechanism of diffusion into the porous matrix.

scholarly journals Magnetohydrodynamics Mixed Convective Couple Stress Hybrid Nanofluid Darcy-Forchheimer Flow through a Rotating Porous Space

2021 ◽  
Author(s):  
F.M Alharbi ◽  
Muhammad Jawad ◽  
Muhammad Zubair ◽  
Muhammad Naeem ◽  
Ibn-i- Amin ◽  
...  
Keyword(s):  
Couple Stress ◽  
Magnetic Parameter ◽  
Local Heat Transfer ◽  
Velocity Slip ◽  
Hybrid Nanofluid ◽  
Porous Space ◽  
Radiation Parameter ◽  
Aluminum Oxides ◽  
Flow Through ◽  
Forchheimer Flow

Abstract In this study, we consider the magnetohydrodynamics mixed convective couple stress hybrid nanofluid Darcy-Forchheimer flow through a rotating porous space with velocity slip condition. The nonlinear thermal stratification and thermal radiation of Magnetohydrodynamics (MHD) are discussed in detail. For relative analysis, we have taken the nanoparticals samples of Aluminum oxides (Al2O3) and Titanium dioxide (TiO2). The rotation in the disk is produces for the generation of the flow in the system.Furthermore, the variable permeability and porosity of porous space is regarded as Darcy-Forchheimer expression. The resulting nonlinear system of ODE’s are solved by Homotopy Analysis Method (HAM). The governing of several sundry parameters i.e. “Couple Stress, coefficient of inertia, radiation parameter, magnetic parameter, Prandtl number, heat source or sink parameter” are presented both graphically as well as in numerical tables. The behavior of the flow predicted that the increase of both mixed convection and couple stress parameters cause increase in the momentum profile. Temperature of the system rises for higher values of radiation parameter and magnetic parameter. The higher local heat transfer rate of Aluminum oxides (Al2O3) and Titanium oxide (TiO2)or water is examined as compared to hybrid nanofluid.

Forced Convection Flow Through an Unsaturated Wellbore

2003 ◽  
Author(s):  
Maria Laura Martins-Costa ◽  
Roge´rio M. Saldanha da Gama
Keyword(s):  
Nonlinear Partial Differential Equations ◽  
Operator Splitting ◽  
Mixture Theory ◽  
Porous Matrix ◽  
Convection Flow ◽  
Theory Approach ◽  
Splitting Technique ◽  
Nonlinear Hyperbolic System ◽  
Implicit Finite Difference Scheme ◽  
Flow Through

This work studies the dynamics of the filling up of a rigid cylindrical shell porous matrix by a Newtonian fluid and the heat transfer associated phenomenon. A mixture theory approach is employed to obtain a preliminary local model for nonisothermal flows through a wellbore. The mixture consists of three overlapping continuous constituents: a solid (porous medium), a liquid and an inert gas included to account for the compressibility of the mixture as a whole. Assuming the convection flow on radial direction only, a set of four nonlinear partial differential equations describes the problem. Its hydrodynamic part — a nonlinear hyperbolic system — is approximated by means of a Glimm’s scheme, combined with an operator splitting technique, while an implicit finite difference scheme is used to simulate the thermal part.

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