M. Zaytoon | The University of New Brunswick (original) (raw)
Papers by M. Zaytoon
Journal of Applied Mathematics and Physics, 2018
Flow through a channel bounded by a porous layer is considered when a transition layer exists bet... more Flow through a channel bounded by a porous layer is considered when a transition layer exists between the channel and the medium. The variable permeability in the transition layer is chosen such that Brinkman's equation governing the flow reduces to a generalized inhomogeneous Airy's differential equation. Solution to the resulting generalized Airy's equation is obtained in this work and solution to the flow through the transition layer, of the same configuration, reported in the literature, is recovered from the current solution.
WSEAS TRANSACTIONS ON FLUID MECHANICS, 2022
Flow of a fluid with pressure-dependent viscosity through a composite of two porous layers is con... more Flow of a fluid with pressure-dependent viscosity through a composite of two porous layers is considered in this work in an attempt to validate velocity and shear stress continuity conditions at the interface, and are popular in the study of flow over porous layers and through composite layers when viscosity of the fluid is constant. For the current problem, conditions at the interface between the porous layers reflect continuity assumptions of velocity and shear stress, with additional continuity assumptions on pressure and viscosity. Viscosity is assumed to vary continuously and exponentially across the layers as a function of pressure. Analytical solutions are obtained to illustrate the effects of flow and media parameters (Darcy numbers, layer thicknesses, angle of inclination, and viscosity adjustment parameter) on the dynamic behaviour of pressure-dependent viscosity fluids in porous structures. All computations, simulations and graphs in this work have been carried out and ob...
International Journal of Physical Research, 2021
The flow of fluids with pressure-dependent viscosity in free-space and in porous media is conside... more The flow of fluids with pressure-dependent viscosity in free-space and in porous media is considered in this study. The interest is to employ the physical model of flow through a porous layer down an inclined plane in order to derive velocity expressions that can be used as entry conditions in the study of two-dimensional flows through free-space and through porous channels. The generalized equations of Darcy, Forchheimer and Brinkman are used in this work. Â
International Journal of Open Problems in Computer Science and Mathematics, 2017
In this work we introduce an inverse method to analyze simple flows through variable permeability... more In this work we introduce an inverse method to analyze simple flows through variable permeability porous layers. Assuming that the velocity distribution is given, or specified as a function of the permeability, the governing equation is solved for the permeability distribution, then the velocity function is then recovered. Poiseuille-type flow involving Brinkman’s equation is considered together with other flow problems involving coupled parallel flow through composite layers. In case of flow through a Brinkman-Forchheimer layer over a Darcy layer, the governing equation was transformed into an Emden-Fowler equation whose solution provides a method for determining Beavers and Joseph slip parameter.
Equations governing the flow of a fluid with variable viscosity through an isotropic porous struc... more Equations governing the flow of a fluid with variable viscosity through an isotropic porous structure are derived using the method of intrinsic volume averaging. Viscosity of the fluid is assumed to be a variable function of pressure, and the effects of the porous microstructure are modelled in terms of Darcy resistance, Brinkman shear term, and Forchheimer effects. © 2016 Elixir All rights reserved. Elixir Appl. Math. 96 (2016) 41336-41340 Applied Mathematics Available online at www.elixirpublishers.com (Elixir International Journal) M.S. Abu Zaytoon et al./ Elixir Appl. Math. 96 (2016) 41336-41340 41337 The fraction of pore space in the REV is the same as pore space fraction in the whole porous medium, thus having the same porosity as the medium. Porous microstructure interactions with the flowing fluid are accounted for through an idealization of the pore geometry and the concept of a Representative Unit Cell (RUC), introduced in [14,15]. Typical condition on the velocity vector ...
WSEAS TRANSACTIONS ON HEAT AND MASS TRANSFER, 2021
Coupled parallel flow of fluid with pressure-dependent viscosity through an inclined channel unde... more Coupled parallel flow of fluid with pressure-dependent viscosity through an inclined channel underlain by a porous layer of variable permeability and variable thickness is initiated in this work. Conditions at the interface between the channel and the porous layer reflect continuity assumptions of velocity, shear stress, pressure and viscosity. Viscosity is assumed to vary in terms of a continuous pressure function that is valid throughout the channel and the porous layer. Model equations are cast in a form where the pressure as an independent variable and solutions are obtained to illustrate the effects of flow and media parameters on the dynamics behaviour of pressure-dependent viscosity fluid. A permeability and a viscosity adjustable control parameters are introduced to avoid unrealistic values of permeability and viscosity. This work could serve as a model for flow over a mushy zone.
International Journal of Circuits, Systems and Signal Processing, 2021
Inhomogeneous Airy’s and Generalized Airy’s equations with initial and boundary date are consider... more Inhomogeneous Airy’s and Generalized Airy’s equations with initial and boundary date are considered in this work. Solutions are obtained for constant and variable forcing functions, and general solutions are expressed in terms of Standard and Generalized Nield-Kuznetsov functions of the first- and second-kinds. Series representations of these functions and their efficient computation methodologies are presented with examples.
JOURNAL OF ADVANCES IN PHYSICS, 2016
In this work, we provide a solution to a two-point boundary value problem that involves an inhomo... more In this work, we provide a solution to a two-point boundary value problem that involves an inhomogeneous Airy’s differential equation with a variable forcing function. The solution is expressed in terms of the recently introduced Nield-Koznetsov integral function, Ni(x), and another conveniently defined integral function, Ki(x). The resulting expressions involving these integral functions are then evaluated using asymptotic and ascending series.Â
IOSR Journal of Mechanical and Civil Engineering, 2017
The problem of flow through a Navier-Stokes channel overlying a finite Forchheimer porous layer o... more The problem of flow through a Navier-Stokes channel overlying a finite Forchheimer porous layer of variable permeability is considered. Choices of permeability distributions that will bring the Forchheimer velocity to zero on the bounding solid wall are discussed and their influence on the resulting velocity profile in the Navier-Stokes channel and on the slip velocity are analyzed.
Journal of Applied Mathematics and Physics, 2016
In this work, we consider the flow through composite porous layers of variable permeability, with... more In this work, we consider the flow through composite porous layers of variable permeability, with the middle layer representing a porous core bounded by two Darcy layers. Brinkman's equation is valid in the middle layer and has been reduced to an Airy's inhomogeneous differential equation. Solution is obtained in terms of Airy's functions and the Nield-Kuznetsov function.
International Journal of Open Problems in Computer Science and Mathematics, 2016
Weber's inhomogeneous differential equation is analyzed and solved in this work when initial and ... more Weber's inhomogeneous differential equation is analyzed and solved in this work when initial and boundary data are given. In the process, a new parametric function that represents an extension to the Nield-Kuznetsov function is introduced.
International Journal of Circuits, Systems and Signal Processing, 2021
In this article, we discuss a class of functions known as the Nield-Kuznetsov functions, introduc... more In this article, we discuss a class of functions known as the Nield-Kuznetsov functions, introduced over the past decade. These functions arise in the solutions to inhomogeneous Airy’s and Weber’s equations. Derivations of these functions are provided, together with their methods of computations
Journal of Applied Mathematics and Physics, 2016
In this work we consider coupled-parallel flow through a finite channel bounded below by a porous... more In this work we consider coupled-parallel flow through a finite channel bounded below by a porous layer that is either finite or infinite in depth. The porous layer is one in which Darcy's equation is valid under the assumption of variable permeability. A suitable permeability stratification function is derived in this work and the resulting variable velocity profile is analyzed. It will be shown that when an infinite porous layer is implemented, Darcy's equation must be used with a constant permeability.
Journal of Fluids Engineering
Flow-through and over a Brinkman porous layer of variable permeability, immersed in a fluid-fille... more Flow-through and over a Brinkman porous layer of variable permeability, immersed in a fluid-filled channel, is modeled. The model governing equation through the porous layer inevitably gives rise to an inhomogeneous Weber's differential equation, solved in this work and solutions expressed in terms of parabolic cylindrical functions. Using state-of-the-art computational techniques and a body of knowledge, the parabolic cylindrical functions are evaluated for a range of flow and medium parameters in order to illustrate intrinsic characteristics of the flow quantities. The approach followed in this work is novel and sets precedent in the study of flow through general porous media configurations and flow domains with variable permeability.
WSEAS TRANSACTIONS ON APPLIED AND THEORETICAL MECHANICS
Equations governing the flow of a fluid-particle mixture with variable viscosity through a porous... more Equations governing the flow of a fluid-particle mixture with variable viscosity through a porous structure are developed. Method of intrinsic volume averaging is used to average Saffman’s dusty gas equations. A modelling flexibility is offered in this work by introducing a dust-phase partial pressure in the governing equations, interpreted as the pressure necessary to maintain a uniform particle distribution in the flow field. Viscosity of the fluid-particle mixture is assumed to be variable, with variations in viscosity being due to fluid pressure. Particles are assumed spherical and Stokes’ coefficient of resistance is expressed in terms of the pressure-dependent fluid viscosity. Both Darcy resistance and the Forchheimer micro-inertial effects are accounted for in the developed model
In thiswork, an attemptis made to relate the slip parameter in the Beavers and Joseph condtionat ... more In thiswork, an attemptis made to relate the slip parameter in the Beavers and Joseph condtionat the interface between a Darcy layer and a Navier-Stokes channel, to the slip parameter to beusedwhen the porous layer is a Forchheimer layer.
Journal of Applied Mathematics and Physics, 2018
Flow through a channel bounded by a porous layer is considered when a transition layer exists bet... more Flow through a channel bounded by a porous layer is considered when a transition layer exists between the channel and the medium. The variable permeability in the transition layer is chosen such that Brinkman's equation governing the flow reduces to a generalized inhomogeneous Airy's differential equation. Solution to the resulting generalized Airy's equation is obtained in this work and solution to the flow through the transition layer, of the same configuration, reported in the literature, is recovered from the current solution.
WSEAS TRANSACTIONS ON FLUID MECHANICS, 2022
Flow of a fluid with pressure-dependent viscosity through a composite of two porous layers is con... more Flow of a fluid with pressure-dependent viscosity through a composite of two porous layers is considered in this work in an attempt to validate velocity and shear stress continuity conditions at the interface, and are popular in the study of flow over porous layers and through composite layers when viscosity of the fluid is constant. For the current problem, conditions at the interface between the porous layers reflect continuity assumptions of velocity and shear stress, with additional continuity assumptions on pressure and viscosity. Viscosity is assumed to vary continuously and exponentially across the layers as a function of pressure. Analytical solutions are obtained to illustrate the effects of flow and media parameters (Darcy numbers, layer thicknesses, angle of inclination, and viscosity adjustment parameter) on the dynamic behaviour of pressure-dependent viscosity fluids in porous structures. All computations, simulations and graphs in this work have been carried out and ob...
International Journal of Physical Research, 2021
The flow of fluids with pressure-dependent viscosity in free-space and in porous media is conside... more The flow of fluids with pressure-dependent viscosity in free-space and in porous media is considered in this study. The interest is to employ the physical model of flow through a porous layer down an inclined plane in order to derive velocity expressions that can be used as entry conditions in the study of two-dimensional flows through free-space and through porous channels. The generalized equations of Darcy, Forchheimer and Brinkman are used in this work. Â
International Journal of Open Problems in Computer Science and Mathematics, 2017
In this work we introduce an inverse method to analyze simple flows through variable permeability... more In this work we introduce an inverse method to analyze simple flows through variable permeability porous layers. Assuming that the velocity distribution is given, or specified as a function of the permeability, the governing equation is solved for the permeability distribution, then the velocity function is then recovered. Poiseuille-type flow involving Brinkman’s equation is considered together with other flow problems involving coupled parallel flow through composite layers. In case of flow through a Brinkman-Forchheimer layer over a Darcy layer, the governing equation was transformed into an Emden-Fowler equation whose solution provides a method for determining Beavers and Joseph slip parameter.
Equations governing the flow of a fluid with variable viscosity through an isotropic porous struc... more Equations governing the flow of a fluid with variable viscosity through an isotropic porous structure are derived using the method of intrinsic volume averaging. Viscosity of the fluid is assumed to be a variable function of pressure, and the effects of the porous microstructure are modelled in terms of Darcy resistance, Brinkman shear term, and Forchheimer effects. © 2016 Elixir All rights reserved. Elixir Appl. Math. 96 (2016) 41336-41340 Applied Mathematics Available online at www.elixirpublishers.com (Elixir International Journal) M.S. Abu Zaytoon et al./ Elixir Appl. Math. 96 (2016) 41336-41340 41337 The fraction of pore space in the REV is the same as pore space fraction in the whole porous medium, thus having the same porosity as the medium. Porous microstructure interactions with the flowing fluid are accounted for through an idealization of the pore geometry and the concept of a Representative Unit Cell (RUC), introduced in [14,15]. Typical condition on the velocity vector ...
WSEAS TRANSACTIONS ON HEAT AND MASS TRANSFER, 2021
Coupled parallel flow of fluid with pressure-dependent viscosity through an inclined channel unde... more Coupled parallel flow of fluid with pressure-dependent viscosity through an inclined channel underlain by a porous layer of variable permeability and variable thickness is initiated in this work. Conditions at the interface between the channel and the porous layer reflect continuity assumptions of velocity, shear stress, pressure and viscosity. Viscosity is assumed to vary in terms of a continuous pressure function that is valid throughout the channel and the porous layer. Model equations are cast in a form where the pressure as an independent variable and solutions are obtained to illustrate the effects of flow and media parameters on the dynamics behaviour of pressure-dependent viscosity fluid. A permeability and a viscosity adjustable control parameters are introduced to avoid unrealistic values of permeability and viscosity. This work could serve as a model for flow over a mushy zone.
International Journal of Circuits, Systems and Signal Processing, 2021
Inhomogeneous Airy’s and Generalized Airy’s equations with initial and boundary date are consider... more Inhomogeneous Airy’s and Generalized Airy’s equations with initial and boundary date are considered in this work. Solutions are obtained for constant and variable forcing functions, and general solutions are expressed in terms of Standard and Generalized Nield-Kuznetsov functions of the first- and second-kinds. Series representations of these functions and their efficient computation methodologies are presented with examples.
JOURNAL OF ADVANCES IN PHYSICS, 2016
In this work, we provide a solution to a two-point boundary value problem that involves an inhomo... more In this work, we provide a solution to a two-point boundary value problem that involves an inhomogeneous Airy’s differential equation with a variable forcing function. The solution is expressed in terms of the recently introduced Nield-Koznetsov integral function, Ni(x), and another conveniently defined integral function, Ki(x). The resulting expressions involving these integral functions are then evaluated using asymptotic and ascending series.Â
IOSR Journal of Mechanical and Civil Engineering, 2017
The problem of flow through a Navier-Stokes channel overlying a finite Forchheimer porous layer o... more The problem of flow through a Navier-Stokes channel overlying a finite Forchheimer porous layer of variable permeability is considered. Choices of permeability distributions that will bring the Forchheimer velocity to zero on the bounding solid wall are discussed and their influence on the resulting velocity profile in the Navier-Stokes channel and on the slip velocity are analyzed.
Journal of Applied Mathematics and Physics, 2016
In this work, we consider the flow through composite porous layers of variable permeability, with... more In this work, we consider the flow through composite porous layers of variable permeability, with the middle layer representing a porous core bounded by two Darcy layers. Brinkman's equation is valid in the middle layer and has been reduced to an Airy's inhomogeneous differential equation. Solution is obtained in terms of Airy's functions and the Nield-Kuznetsov function.
International Journal of Open Problems in Computer Science and Mathematics, 2016
Weber's inhomogeneous differential equation is analyzed and solved in this work when initial and ... more Weber's inhomogeneous differential equation is analyzed and solved in this work when initial and boundary data are given. In the process, a new parametric function that represents an extension to the Nield-Kuznetsov function is introduced.
International Journal of Circuits, Systems and Signal Processing, 2021
In this article, we discuss a class of functions known as the Nield-Kuznetsov functions, introduc... more In this article, we discuss a class of functions known as the Nield-Kuznetsov functions, introduced over the past decade. These functions arise in the solutions to inhomogeneous Airy’s and Weber’s equations. Derivations of these functions are provided, together with their methods of computations
Journal of Applied Mathematics and Physics, 2016
In this work we consider coupled-parallel flow through a finite channel bounded below by a porous... more In this work we consider coupled-parallel flow through a finite channel bounded below by a porous layer that is either finite or infinite in depth. The porous layer is one in which Darcy's equation is valid under the assumption of variable permeability. A suitable permeability stratification function is derived in this work and the resulting variable velocity profile is analyzed. It will be shown that when an infinite porous layer is implemented, Darcy's equation must be used with a constant permeability.
Journal of Fluids Engineering
Flow-through and over a Brinkman porous layer of variable permeability, immersed in a fluid-fille... more Flow-through and over a Brinkman porous layer of variable permeability, immersed in a fluid-filled channel, is modeled. The model governing equation through the porous layer inevitably gives rise to an inhomogeneous Weber's differential equation, solved in this work and solutions expressed in terms of parabolic cylindrical functions. Using state-of-the-art computational techniques and a body of knowledge, the parabolic cylindrical functions are evaluated for a range of flow and medium parameters in order to illustrate intrinsic characteristics of the flow quantities. The approach followed in this work is novel and sets precedent in the study of flow through general porous media configurations and flow domains with variable permeability.
WSEAS TRANSACTIONS ON APPLIED AND THEORETICAL MECHANICS
Equations governing the flow of a fluid-particle mixture with variable viscosity through a porous... more Equations governing the flow of a fluid-particle mixture with variable viscosity through a porous structure are developed. Method of intrinsic volume averaging is used to average Saffman’s dusty gas equations. A modelling flexibility is offered in this work by introducing a dust-phase partial pressure in the governing equations, interpreted as the pressure necessary to maintain a uniform particle distribution in the flow field. Viscosity of the fluid-particle mixture is assumed to be variable, with variations in viscosity being due to fluid pressure. Particles are assumed spherical and Stokes’ coefficient of resistance is expressed in terms of the pressure-dependent fluid viscosity. Both Darcy resistance and the Forchheimer micro-inertial effects are accounted for in the developed model
In thiswork, an attemptis made to relate the slip parameter in the Beavers and Joseph condtionat ... more In thiswork, an attemptis made to relate the slip parameter in the Beavers and Joseph condtionat the interface between a Darcy layer and a Navier-Stokes channel, to the slip parameter to beusedwhen the porous layer is a Forchheimer layer.