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Papers by Ahmed K. Abu-Nab

Keldysh Institute Preprints, 2022

In the work, the method of splitting by physical processes is consistently applied to the problem... more In the work, the method of splitting by physical processes is consistently applied to the problems of underground hydromechanics associated with gas hydrates and taking into account the presence of ice and the ice-water phase transition, as well as the presence of salt. The systems are reduced to the block form, with the separation of the dissipative and hyperbolic parts. It was shown by the method of characteristics that the usual approximation of the upwind coefficients should be modified here. Using the Gibbs phase rule, a choice was made of the determining variables in the flow zones that differ from each other in the number of phases and components. A general mathematical model has been built for the entire area of the process.

Mathematics

The purpose of this paper is to present a one-dimensional model that simulates the thermo-physica... more The purpose of this paper is to present a one-dimensional model that simulates the thermo-physical processes for methane hydrate decomposition in porous media. The mathematical model consists of equations for the conservation of energy, gas, and liquid as well as the thermodynamic equilibrium equation for temperature and pressure (P−T) in the hydrate stability region. The developed model is solved numerically by using the implicit finite difference technique on the grid system, which correctly describes the appearance of phase, latency, and boundary conditions. The Newton–Raphson method was employed to solve a system of nonlinear algebraic equations after defining and preparing the Jacobean matrix. Additionally, the proposed model describes the decomposition of methane hydrate by thermal catalysis of the components that make up the medium through multiple phases in porous media. In addition, the effect of thermodynamic processes during the hydrate decomposition on the pore saturatio...

Case Studies in Thermal Engineering

The European Physical Journal Special Topics

Archive of Applied Mechanics

International Journal of Biomathematics

The motivation of this research is to study the effect of suction process on a growing gas bubble... more The motivation of this research is to study the effect of suction process on a growing gas bubble and concentration distribution around this bubble in tissues of divers who surface too quickly. The effect of bubble motion is also considered. The method of combined variables is used to solve the problem by combining the radial and time variables into one variable by using a suitable similarity transformation that enables to divide the diffusion equation into two ODEs, the first concerns to concentration distribution and the other concerns to the bubble radius evolution. The resultant formulae are valid for both growth stages whenever the ambient pressure is variable at ascending of the diver, or constant as the diving stops or at sea-level. The effects of physical parameters are discussed when applying suction process and show that the dominant parameter is the initial void fraction. The research findings reveal the role of suction process to activate the systemic blood circulation a...

Journal of Physics: Condensed Matter

Monitoring bubble cavitations and bubble dynamics are essential in enhancing non-invasive ultraso... more Monitoring bubble cavitations and bubble dynamics are essential in enhancing non-invasive ultrasonic ablation methods like histotripsy that mechanically fractionates tissue into acellular debris using microcavitation. Histotripsy can totally fractionate tissue into a liquid-appearing homogenate with no cellular features with enough pulses. In this paper, we present the analysis of the dynamics of cavitation bubbles in a viscoelastic medium subjected to a histotripsy pulse using different fidelities in depicting compressibility and viscoelasticity effects. The mathematical formulation is described based on the Keller–Miksis equation in two models for cavitation bubbles in viscoelastic tissue through histotripsy process; the first model is in neo-Hookean, and the second is in quadratic law Kelvin–Voigt model. The governing model is solved analytically based on the modified Plesset–Zwick method. Analysis of the results reveals that the parameters of Young modulus, viscosity effects and...

Case Studies in Thermal Engineering

Journal of Nanofluids, 2022

The present manuscript is devoted to study the theoretical analysis of pressure relaxation time (... more The present manuscript is devoted to study the theoretical analysis of pressure relaxation time (PRT) of N-dimensional spherical bubble dynamics immersed in Fe3O4/H2O nanofluid. The mathematical model consists of mass equation in N-dimensions nanofluids, thermal and physical properties of Fe3O4/H2O-nanoparticles (NPs), and PRT in N-dimensions nanofluids. The proposed model of PRT is studied theoretically and solved analytically by using the modified Plesset and Zwick (MPZ) technique taking into account, through the relaxed model with unequal pressure of the thermally-limited bubble dynamics and non-steady pressure field concerning the collapsing and growing of bubble dynamics. Additionally, the PRT is estimated in an N-dimensional vapour bubble under influence of the thermophysical properties of particles nanofluids. Furthermore, The current research also looks at the elements that influence the dynamics of vapour bubble growth in N-dimensions nanofluids. Our results show that the a...

Mathematical Methods in the Applied Sciences

Physica Scripta

The aim of this study is to focus mainly on the behavior of gas bubble growth under the effect of... more The aim of this study is to focus mainly on the behavior of gas bubble growth under the effect of a magnetic field in N -dimensions of non-Newtonian hybrid nanomaterials. Many types of nanoparticles with base nanofluids have been used to study the problems that arise in the nanotechnology industrial processes. Considering these problems in nanomaterials, the effects of thermophysical parameters, such as nanoparticle size and type, nanoparticle volume fraction, N -dimensions, thermal diffusivity, and thermal conductivity are discussed. This investigation has demonstrated that the magnetic field B and electrical conductivity σ E have a significant impact on the dynamics of gas bubbles, showing that they play an important role in decreasing the growth processes. Furthermore, we examine the behavior of the gas bubble radius in the cases of pure water, mono nanoparticles, and hybrid nanofluid of nanomaterials (such as Cu − A l 2 O 3 / H 2 O , and Ti O 2 − A l 2 O 3 / H 2 O ) in N-dimensi...

Case Studies in Thermal Engineering

The European Physical Journal Plus

Mathematical Modelling of Engineering Problems, 2021

This paper is devoted to study the effect of heat transfer on the temperature distribution in a s... more This paper is devoted to study the effect of heat transfer on the temperature distribution in a superheated liquid during the growth of vapour bubbles immersed in different types of nanoparticles/water nanofluids between two-phase turbulent flow. The mathematical model is formulated and solved analytically depending on Scriven's theory and using the modification of the method of the similarity parameters between two finite boundaries. The characteristics of vapour bubble growth and temperature distribution are obtained by using the thermo-physical properties of nanoparticles nanofluids. The results indicate that the nanoparticle volume concentration reduces the bubble growth process under the effect of heat transfer. The better agreements are achieved, for bubble dynamics in turbulent nanofluid using the appropriate numerical and theoretical data for the values of concentration rate of nanoparticles χ=0,0.2,0.4. The temperature distribution surrounding the regime of bubble growt...

The study of hadron properties at hot and dense medium in the framework of quantum chromodynamics... more The study of hadron properties at hot and dense medium in the framework of quantum chromodynamics (QCD) theory plays an important role in particles physics and high energy physics. Scientists have managed to put models which share the QCD theory in its properties. In this book, the authors have modified the chiral quark sigma model at zero, finite temperature and chemical potential. The book has shown interest in using the modified linear sigma model to study the hadron properties in hot and dense medium, and the chiral phase transition.

A modi…ed logarithmic mesonic potential is investigated in the framework of quantum chromodynamic... more A modi…ed logarithmic mesonic potential is investigated in the framework of quantum chromodynamics (QCD) theory. The …eld equations have been solved in the mean-…eld approximation using the iteration method. The obtained results of nucleon properties are strongly improved in comparison with the original quark-sigma model. A comparison with the recent quark models such as the extended Skyrme model and the perturbative quark model is discussed. We conclude that the modi…ed logarithmic quark model successfully predicts the nucleon properties that are in good agreement with experimental data. In addition, we avoid the physical di¢ culty found in previous works. 1. INTRODUCTION To understand the nucleon properties from a microscopic theory of the hadronic interaction discussed earlier QCD is not yet calculative tractable, so theorist have turned their attention to various models of the hadronic interaction which incorporate the important symmetries (e. g. chiral symmetry) of QCD [1]. One...

Food Microbiology, 2016

The paper introduces the incompressible Newtonian fluid with heat transfer in a vertical cylindri... more The paper introduces the incompressible Newtonian fluid with heat transfer in a vertical cylindrical tube under the assumptions of long wavelength and low Reynolds number. The system of mass, momentum, and energy equations are solved analytically. The velocity and temperature field are obtained for two-phase densities. The growth of vapour bubble and its velocity between two-phase densities are obtained for first time under the effect of Grashof number and constant heating source. The obtained results are compared with experiment and Mohammadein at all model with good agreement.

Journal of Thermophysics and Heat Transfer, 2021

The European Physical Journal Plus, 2021

This paper investigates the fluidized granular materials (FGM) with the van der Waals normal form... more This paper investigates the fluidized granular materials (FGM) with the van der Waals normal form (VDWF) under the effects of friction and viscosity. The system of macroscopic balance is presented, including the mass, momentum, and energy equations of local densities. For two different types of collisions, elastic and inelastic collisions, analytical solutions of the nonlinear PDEs governing the granular model are investigated using the hydrodynamic equations for granular matter motion. The integrability of the proposed model is analyzed by applying the Painleve analysis. Moreover, the Backlund transformation (BT) is established using the Painleve truncation expansion. New traveling wave solutions of the VDWF within FGM are obtained by using the BT, tanh function, Jacobi elliptic function methods to study the phase separation phenomenon. As two pairs of rarefaction and shock waves emerge and travel away giving the appearance of bubbles, the resulting solutions of the proposed model show a behavior similar to those found in the molecular dynamic simulations. The dispersion relation and their properties to the model equation are investigated. Besides, stability analysis of the VDWF in its ODE form is demonstrated using the phase portrait classifications. Finally, using two- and three-dimensional graphics for seeking model solutions under the influence of friction and viscosity, qualitative agreements with previous related works are shown.

International Journal of Ambient Energy, 2021

Keldysh Institute Preprints, 2022

In the work, the method of splitting by physical processes is consistently applied to the problem... more In the work, the method of splitting by physical processes is consistently applied to the problems of underground hydromechanics associated with gas hydrates and taking into account the presence of ice and the ice-water phase transition, as well as the presence of salt. The systems are reduced to the block form, with the separation of the dissipative and hyperbolic parts. It was shown by the method of characteristics that the usual approximation of the upwind coefficients should be modified here. Using the Gibbs phase rule, a choice was made of the determining variables in the flow zones that differ from each other in the number of phases and components. A general mathematical model has been built for the entire area of the process.

Mathematics

The purpose of this paper is to present a one-dimensional model that simulates the thermo-physica... more The purpose of this paper is to present a one-dimensional model that simulates the thermo-physical processes for methane hydrate decomposition in porous media. The mathematical model consists of equations for the conservation of energy, gas, and liquid as well as the thermodynamic equilibrium equation for temperature and pressure (P−T) in the hydrate stability region. The developed model is solved numerically by using the implicit finite difference technique on the grid system, which correctly describes the appearance of phase, latency, and boundary conditions. The Newton–Raphson method was employed to solve a system of nonlinear algebraic equations after defining and preparing the Jacobean matrix. Additionally, the proposed model describes the decomposition of methane hydrate by thermal catalysis of the components that make up the medium through multiple phases in porous media. In addition, the effect of thermodynamic processes during the hydrate decomposition on the pore saturatio...

Case Studies in Thermal Engineering

The European Physical Journal Special Topics

Archive of Applied Mechanics

International Journal of Biomathematics

The motivation of this research is to study the effect of suction process on a growing gas bubble... more The motivation of this research is to study the effect of suction process on a growing gas bubble and concentration distribution around this bubble in tissues of divers who surface too quickly. The effect of bubble motion is also considered. The method of combined variables is used to solve the problem by combining the radial and time variables into one variable by using a suitable similarity transformation that enables to divide the diffusion equation into two ODEs, the first concerns to concentration distribution and the other concerns to the bubble radius evolution. The resultant formulae are valid for both growth stages whenever the ambient pressure is variable at ascending of the diver, or constant as the diving stops or at sea-level. The effects of physical parameters are discussed when applying suction process and show that the dominant parameter is the initial void fraction. The research findings reveal the role of suction process to activate the systemic blood circulation a...

Journal of Physics: Condensed Matter

Monitoring bubble cavitations and bubble dynamics are essential in enhancing non-invasive ultraso... more Monitoring bubble cavitations and bubble dynamics are essential in enhancing non-invasive ultrasonic ablation methods like histotripsy that mechanically fractionates tissue into acellular debris using microcavitation. Histotripsy can totally fractionate tissue into a liquid-appearing homogenate with no cellular features with enough pulses. In this paper, we present the analysis of the dynamics of cavitation bubbles in a viscoelastic medium subjected to a histotripsy pulse using different fidelities in depicting compressibility and viscoelasticity effects. The mathematical formulation is described based on the Keller–Miksis equation in two models for cavitation bubbles in viscoelastic tissue through histotripsy process; the first model is in neo-Hookean, and the second is in quadratic law Kelvin–Voigt model. The governing model is solved analytically based on the modified Plesset–Zwick method. Analysis of the results reveals that the parameters of Young modulus, viscosity effects and...

Case Studies in Thermal Engineering

Journal of Nanofluids, 2022

The present manuscript is devoted to study the theoretical analysis of pressure relaxation time (... more The present manuscript is devoted to study the theoretical analysis of pressure relaxation time (PRT) of N-dimensional spherical bubble dynamics immersed in Fe3O4/H2O nanofluid. The mathematical model consists of mass equation in N-dimensions nanofluids, thermal and physical properties of Fe3O4/H2O-nanoparticles (NPs), and PRT in N-dimensions nanofluids. The proposed model of PRT is studied theoretically and solved analytically by using the modified Plesset and Zwick (MPZ) technique taking into account, through the relaxed model with unequal pressure of the thermally-limited bubble dynamics and non-steady pressure field concerning the collapsing and growing of bubble dynamics. Additionally, the PRT is estimated in an N-dimensional vapour bubble under influence of the thermophysical properties of particles nanofluids. Furthermore, The current research also looks at the elements that influence the dynamics of vapour bubble growth in N-dimensions nanofluids. Our results show that the a...

Mathematical Methods in the Applied Sciences

Physica Scripta

The aim of this study is to focus mainly on the behavior of gas bubble growth under the effect of... more The aim of this study is to focus mainly on the behavior of gas bubble growth under the effect of a magnetic field in N -dimensions of non-Newtonian hybrid nanomaterials. Many types of nanoparticles with base nanofluids have been used to study the problems that arise in the nanotechnology industrial processes. Considering these problems in nanomaterials, the effects of thermophysical parameters, such as nanoparticle size and type, nanoparticle volume fraction, N -dimensions, thermal diffusivity, and thermal conductivity are discussed. This investigation has demonstrated that the magnetic field B and electrical conductivity σ E have a significant impact on the dynamics of gas bubbles, showing that they play an important role in decreasing the growth processes. Furthermore, we examine the behavior of the gas bubble radius in the cases of pure water, mono nanoparticles, and hybrid nanofluid of nanomaterials (such as Cu − A l 2 O 3 / H 2 O , and Ti O 2 − A l 2 O 3 / H 2 O ) in N-dimensi...

Case Studies in Thermal Engineering

The European Physical Journal Plus

Mathematical Modelling of Engineering Problems, 2021

This paper is devoted to study the effect of heat transfer on the temperature distribution in a s... more This paper is devoted to study the effect of heat transfer on the temperature distribution in a superheated liquid during the growth of vapour bubbles immersed in different types of nanoparticles/water nanofluids between two-phase turbulent flow. The mathematical model is formulated and solved analytically depending on Scriven's theory and using the modification of the method of the similarity parameters between two finite boundaries. The characteristics of vapour bubble growth and temperature distribution are obtained by using the thermo-physical properties of nanoparticles nanofluids. The results indicate that the nanoparticle volume concentration reduces the bubble growth process under the effect of heat transfer. The better agreements are achieved, for bubble dynamics in turbulent nanofluid using the appropriate numerical and theoretical data for the values of concentration rate of nanoparticles χ=0,0.2,0.4. The temperature distribution surrounding the regime of bubble growt...

The study of hadron properties at hot and dense medium in the framework of quantum chromodynamics... more The study of hadron properties at hot and dense medium in the framework of quantum chromodynamics (QCD) theory plays an important role in particles physics and high energy physics. Scientists have managed to put models which share the QCD theory in its properties. In this book, the authors have modified the chiral quark sigma model at zero, finite temperature and chemical potential. The book has shown interest in using the modified linear sigma model to study the hadron properties in hot and dense medium, and the chiral phase transition.

A modi…ed logarithmic mesonic potential is investigated in the framework of quantum chromodynamic... more A modi…ed logarithmic mesonic potential is investigated in the framework of quantum chromodynamics (QCD) theory. The …eld equations have been solved in the mean-…eld approximation using the iteration method. The obtained results of nucleon properties are strongly improved in comparison with the original quark-sigma model. A comparison with the recent quark models such as the extended Skyrme model and the perturbative quark model is discussed. We conclude that the modi…ed logarithmic quark model successfully predicts the nucleon properties that are in good agreement with experimental data. In addition, we avoid the physical di¢ culty found in previous works. 1. INTRODUCTION To understand the nucleon properties from a microscopic theory of the hadronic interaction discussed earlier QCD is not yet calculative tractable, so theorist have turned their attention to various models of the hadronic interaction which incorporate the important symmetries (e. g. chiral symmetry) of QCD [1]. One...

Food Microbiology, 2016

The paper introduces the incompressible Newtonian fluid with heat transfer in a vertical cylindri... more The paper introduces the incompressible Newtonian fluid with heat transfer in a vertical cylindrical tube under the assumptions of long wavelength and low Reynolds number. The system of mass, momentum, and energy equations are solved analytically. The velocity and temperature field are obtained for two-phase densities. The growth of vapour bubble and its velocity between two-phase densities are obtained for first time under the effect of Grashof number and constant heating source. The obtained results are compared with experiment and Mohammadein at all model with good agreement.

Journal of Thermophysics and Heat Transfer, 2021

The European Physical Journal Plus, 2021

This paper investigates the fluidized granular materials (FGM) with the van der Waals normal form... more This paper investigates the fluidized granular materials (FGM) with the van der Waals normal form (VDWF) under the effects of friction and viscosity. The system of macroscopic balance is presented, including the mass, momentum, and energy equations of local densities. For two different types of collisions, elastic and inelastic collisions, analytical solutions of the nonlinear PDEs governing the granular model are investigated using the hydrodynamic equations for granular matter motion. The integrability of the proposed model is analyzed by applying the Painleve analysis. Moreover, the Backlund transformation (BT) is established using the Painleve truncation expansion. New traveling wave solutions of the VDWF within FGM are obtained by using the BT, tanh function, Jacobi elliptic function methods to study the phase separation phenomenon. As two pairs of rarefaction and shock waves emerge and travel away giving the appearance of bubbles, the resulting solutions of the proposed model show a behavior similar to those found in the molecular dynamic simulations. The dispersion relation and their properties to the model equation are investigated. Besides, stability analysis of the VDWF in its ODE form is demonstrated using the phase portrait classifications. Finally, using two- and three-dimensional graphics for seeking model solutions under the influence of friction and viscosity, qualitative agreements with previous related works are shown.

International Journal of Ambient Energy, 2021