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Nehad Ali Shah - One of the best experts on this subject based on the ideXlab platform.
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free convection flow of nanoFluids between two vertical plates with damped thermal flux
Journal of Molecular Liquids, 2019Co-Authors: Ahmad Hajizadeh, Nehad Ali Shah, Syed Inayat Ali Shah, I L Animasaun, Mohammad Rahimigorji, Ibrahim M AlarifiAbstract:Abstract In this article, we consider the transient free convection flow of nanoFluids between two vertical parallel plates in the presence of radiation and damped thermal flux. The generalized Fourier's law is considered in thermal flux constitutive equation with a weakly memory. The integral transform technique is used for finding the exact solutions of the fractional governing differential equations for Fluid temperature and velocity field. The solutions are presented in the term of the time-fractional derivative of the Wright function and Robotnov and Hartley function. Solutions to the Ordinary Fluid, corresponding to the fractional parameter equal to unit, are obtained as a particular case of the fractional problem. Numerical calculations are carried out and results are presented in graphical illustrations. The influence of the memory parameter (the fractional order of the time-derivative) on the temperature and velocity fields is analyzed and a comparison between the Fluid with thermal memory and the Ordinary Fluid is made.
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magnetohydrodynamic free convection flows with thermal memory over a moving vertical plate in porous medium
Applied and Computational Mechanics, 2019Co-Authors: Nehad Ali Shah, Najma Ahmed, Thanaa Elnaqeeb, M M RashidiAbstract:The unsteady hydro-magnetic free convection flow with heat transfer of a linearly viscous, incompressible, electrically conducting Fluid near a moving vertical plate with the constant heat is investigated. The flow domain is the porous half-space and a magnetic field of a variable direction is applied. The Caputo time-fractional derivative is employed in order to introduce a thermal flux constitutive equation with a weakly memory. The exact solutions for the fractional governing differential equations for Fluid temperature, Nusselt number, velocity field, and skin friction are obtained by using the Laplace transform method. The numerical calculations are carried out and the results are presented in graphical illustrations. The influence of the memory parameter (the fractional order of the time-derivative) on the temperature and velocity fields is analyzed and a comparison between the Fluid with the thermal memory and the Ordinary Fluid is made. It was observed that due to evolution in the time of the Caputo power-law kernel, the memory effects are stronger for the small values of the time t. Moreover, it is found that the Fluid flow is accelerated / retarded by varying the inclination angle of the magnetic field direction.
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natural convection flows and heat transfer with exponential memory of a maxwell Fluid with damped shear stress
Computers & Mathematics With Applications, 2018Co-Authors: Yasir Mahsud, Nehad Ali Shah, Dumitru VieruAbstract:Abstract Unsteady nonlinear boundary layer convection flows and heat transfer of a fractional Maxwell Fluid near a vertical plate with constant thermal flux are studied. The fractional constitutive equations for the shear stress and thermal flux are formulated for the first time with the integral time-fractional operator of type Caputo–Fabrizio. These types of fractional relationships provide a weighted average exponential to the velocity gradient and temperature gradient. The studied model is constituted from a system of nonlinear partial differential equations coupled with fractional differential equations with initial and boundary conditions. The solutions for the shear stress, velocity, thermal flux and temperature are obtained by using the Laplace transform along with a suitable transformation of variables. In order to finding solutions of the studied model, two inverse Laplace transforms of exponential type are obtained. The particular cases when only the stress or thermal flux are damped, as well as the convection flows of the Ordinary Fluid are obtained as particular cases when the stress/thermal fractional parameter tends to 1.
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unsteady free convection flow of viscous Fluids with analytical results by employing time fractional caputo fabrizio derivative without singular kernel
European Physical Journal Plus, 2017Co-Authors: Nehad Ali Shah, Yasir Mahsud, Azhar Ali ZafarAbstract:This article introduces a theoretical study for unsteady free convection flow of an incompressible viscous Fluid. The Fluid flows near an isothermal vertical plate. The plate has a translational motion with time-dependent velocity. The equations governing the Fluid flow are expressed in fractional differential equations by using a newly defined time-fractional Caputo-Fabrizio derivative without singular kernel. Explicit solutions for velocity, temperature and solute concentration are obtained by applying the Laplace transform technique. As the fractional parameter approaches to one, solutions for the Ordinary Fluid model are extracted from the general solutions of the fractional model. The results showed that, for the fractional model, the obtained solutions for velocity, temperature and concentration exhibit stationary jumps discontinuity across the plane at \( t=0\) , while the solutions are continuous functions in the case of the Ordinary model. Finally, numerical results for flow features at small-time are illustrated through graphs for various pertinent parameters.
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effects of the fractional order and magnetic field on the blood flow in cylindrical domains
Journal of Magnetism and Magnetic Materials, 2016Co-Authors: Nehad Ali Shah, Dumitru Vieru, Constantin FetecauAbstract:Abstract In this paper, based on the magnetohydrodynamics approach, the blood flow along with magnetic particles through a circular cylinder is studied. The Fluid is acted by an oscillating pressure gradient and an external magnetic field. The study is based on a mathematical model with Caputo fractional derivatives. The model of Ordinary Fluid, corresponding to time-derivatives of integer order, is obtained as a particular case. Closed forms of the Fluid velocity and magnetic particles velocity are obtained by means of the Laplace and finite Hankel transforms. Effects of the order of Caputo's time-fractional derivatives and of the external magnetic field on flow parameters of both blood and magnetic particles are studied. Numerical simulations and graphical illustrations are used in order to study the influence of the fractional parameter α , Reynolds number and Hartmann number on the Fluid and particles velocity. The results highlights that, models with fractional derivatives bring significant differences compared to the Ordinary model. This fact can be an important advantage for some practical problems. It also results that the blood velocity, as well as that of magnetic particles, is reduced under influence of the exterior magnetic field.
Constantin Fetecau - One of the best experts on this subject based on the ideXlab platform.
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effects of the fractional order and magnetic field on the blood flow in cylindrical domains
Journal of Magnetism and Magnetic Materials, 2016Co-Authors: Nehad Ali Shah, Dumitru Vieru, Constantin FetecauAbstract:Abstract In this paper, based on the magnetohydrodynamics approach, the blood flow along with magnetic particles through a circular cylinder is studied. The Fluid is acted by an oscillating pressure gradient and an external magnetic field. The study is based on a mathematical model with Caputo fractional derivatives. The model of Ordinary Fluid, corresponding to time-derivatives of integer order, is obtained as a particular case. Closed forms of the Fluid velocity and magnetic particles velocity are obtained by means of the Laplace and finite Hankel transforms. Effects of the order of Caputo's time-fractional derivatives and of the external magnetic field on flow parameters of both blood and magnetic particles are studied. Numerical simulations and graphical illustrations are used in order to study the influence of the fractional parameter α , Reynolds number and Hartmann number on the Fluid and particles velocity. The results highlights that, models with fractional derivatives bring significant differences compared to the Ordinary model. This fact can be an important advantage for some practical problems. It also results that the blood velocity, as well as that of magnetic particles, is reduced under influence of the exterior magnetic field.
Ibrahim M Alarifi - One of the best experts on this subject based on the ideXlab platform.
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free convection flow of nanoFluids between two vertical plates with damped thermal flux
Journal of Molecular Liquids, 2019Co-Authors: Ahmad Hajizadeh, Nehad Ali Shah, Syed Inayat Ali Shah, I L Animasaun, Mohammad Rahimigorji, Ibrahim M AlarifiAbstract:Abstract In this article, we consider the transient free convection flow of nanoFluids between two vertical parallel plates in the presence of radiation and damped thermal flux. The generalized Fourier's law is considered in thermal flux constitutive equation with a weakly memory. The integral transform technique is used for finding the exact solutions of the fractional governing differential equations for Fluid temperature and velocity field. The solutions are presented in the term of the time-fractional derivative of the Wright function and Robotnov and Hartley function. Solutions to the Ordinary Fluid, corresponding to the fractional parameter equal to unit, are obtained as a particular case of the fractional problem. Numerical calculations are carried out and results are presented in graphical illustrations. The influence of the memory parameter (the fractional order of the time-derivative) on the temperature and velocity fields is analyzed and a comparison between the Fluid with thermal memory and the Ordinary Fluid is made.
Dave Sutherland - One of the best experts on this subject based on the ideXlab platform.
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quantum field theory of Fluids
Physical Review Letters, 2015Co-Authors: Ben Gripaios, Dave SutherlandAbstract:The quantum theory of fields is largely based on studying perturbations around noninteracting, or free, field theories, which correspond to a collection of quantum-mechanical harmonic oscillators. The quantum theory of an Ordinary Fluid is "freer", in the sense that the noninteracting theory also contains an infinite collection of quantum-mechanical free particles, corresponding to vortex modes. By computing a variety of correlation functions at tree and loop level, we give evidence that a quantum perfect Fluid can be consistently formulated as a low-energy, effective field theory. We speculate that the quantum behavior is radically different from both classical Fluids and quantum fields.
Ahmad Hajizadeh - One of the best experts on this subject based on the ideXlab platform.
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free convection flow of nanoFluids between two vertical plates with damped thermal flux
Journal of Molecular Liquids, 2019Co-Authors: Ahmad Hajizadeh, Nehad Ali Shah, Syed Inayat Ali Shah, I L Animasaun, Mohammad Rahimigorji, Ibrahim M AlarifiAbstract:Abstract In this article, we consider the transient free convection flow of nanoFluids between two vertical parallel plates in the presence of radiation and damped thermal flux. The generalized Fourier's law is considered in thermal flux constitutive equation with a weakly memory. The integral transform technique is used for finding the exact solutions of the fractional governing differential equations for Fluid temperature and velocity field. The solutions are presented in the term of the time-fractional derivative of the Wright function and Robotnov and Hartley function. Solutions to the Ordinary Fluid, corresponding to the fractional parameter equal to unit, are obtained as a particular case of the fractional problem. Numerical calculations are carried out and results are presented in graphical illustrations. The influence of the memory parameter (the fractional order of the time-derivative) on the temperature and velocity fields is analyzed and a comparison between the Fluid with thermal memory and the Ordinary Fluid is made.