Searcharxiv⌕ Search

arXiv subjects

Tarek M. A. El-Mistikawy

Publications and source records attributed to Tarek M. A. El-Mistikawy.

11 recordsLinked to original sources
arXiv2022

Couette-Poiseuille flow with partial slip and uniform cross flow for power-law fluids

Exact solutions are obtained for the steady flow of a power-law fluid between parallel plates with partial slip conditions and uniform cross flow. The problem is properly formulated and similarities are exploited. The exact solutions are obtained in terms of integrals which can be performed, in closed form, in special cases of the power-law index n. Solutions to cases of n=1/2, 1, and 2; representing a pseudo-plastic, a Newtonian, and a dilatant fluid, respectively, are presented. Tendencies to corresponding degenerate cases in the literature are demonstrated. Depending on the strength of the cross flow and the pressure gradient, the flow may be of Couette type with convex, linear, or concave velocity profile; or of Poiseuille type. Borderline cases are identified. Moreover, a case in which the power-law model for the dilatant fluid fails is detected.

physics.flu-dyn↗
arXiv2019

MHD flow and heat transfer due to a linearly stretching sheet with induced magnetic field: Exact solution

The solution for the MHD flow, due to a linearly stretching sheet, has a simple form for the velocity field, with a companion simple form for the induced magnetic field. The associated thermal problem, including viscous dissipation and Joule heating, involves three temperature constituents, the solutions for two of which are obtained in terms of Kummer's function. The solution for the third temperature constituent is obtained in a convergent series form.

physics.flu-dyn↗
arXiv2018

Asymptotic structure incorporating double and triple decks, original version

The stagnation point flow toward a rotating disk of finite radius is known to develop -- near the edge of the disk -- into a triple deck structure when the flow is strictly a stagnation point flow, and into a double deck structure when the flow is strictly a rotating disk flow. It is shown here that the transfer from one structure to another is singular; requiring matching of two main decks. The double deck structure is, in essence, a triple deck structure with collapsing upper deck.

physics.flu-dyn↗
arXiv2017

Heat transfer in MHD flow due to a linearly stretching sheet with induced magnetic field

The full MHD problem of the flow and heat transfer due to a linearly stretching sheet in the presence of a transverse magnetic field is put in a self-similar form. Traditionally ignored physical processes such as induced magnetic field, viscous dissipation, Joule heating, and work shear are included and their importance is established. Cases of prescribed surface temperature, prescribed heat flux, surface feed (injection or suction), velocity slip, and thermal slip are also considered. The problem is shown to admit self similarity. Sample numerical solutions are obtained for chosen combinations of the flow parameters.

physics.flu-dyn↗
arXiv2016

MHD stagnation point flow toward a linearly-stretching thermally-insulated sheet with induced magnetic field

The equations governing the magnetohydrodynamic stagnation point flow toward a non-conducting, thermally insulated, nonporous, linearly stretching sheet are cast in a self similar form. Consistent boundary conditions on the velocity, magnetic field and temperature are invoked. The flow problem involves three parameters- the magnetic Prandtl number, the magnetic interaction number, and the ratio of the stretching rate to the strength of the stagnation point flow. The energy equation includes viscous dissipation and Joule heating, and introduces the Prandtl number as a fourth parameter. Numerical solutions are obtained and sample results are presented.

physics.flu-dyn↗
arXiv2016

MHD flow and heat transfer due to the axisymmetric stretching of a sheet with induced magnetic field

The full MHD equations, governing the flow due to the axisymmetric stretching of a sheet in the presence of a transverse magnetic field, can be cast in a self similar form. This allows evaluation of the induced magnetic field and its effect on the flow and heat transfer. The problem involves three parameters- the magnetic Prandtl number, the magnetic interaction number, and the Prandtl number. Numerical solutions are obtained for the velocity field, the magnetic field, and the temperature, at different values of the magnetic Prandtl number and the magnetic interaction number. The contributions of the viscous dissipation, Joule heating, and streamwise diffusion to the heat flux toward the sheet are assessed.

physics.flu-dyn↗
arXiv2013

Modular Analysis of Almost Block Diagonal Systems of Equations

Almost block diagonal linear systems of equations can be exemplified by two modules. This makes it possible to construct all sequential forms of band and/or block elimination methods, six old and fourteen new. It allows easy assessment of the methods on the basis of their operation counts, storage needs, and admissibility of partial pivoting. It unveils a robust partial pivoting strategy- local pivoting. Extension of modular analysis to bordered systems is also included.

math.NA↗
arXiv2012

Supersonic triple deck flow past a flat plate with an elastic stretch

The steady laminar supersonic flow past a flat plate having a stretch of an elastic membrane, the pressure on the other side of which is adjustable, is studied within the framework of the triple deck theory. The resulting lower deck problem is supplemented with a membrane equation relating the pressure difference across the membrane to its curvature. By pressurizing or depressurizing the membrane, it assumes the form of a hump or a dent that alters the flow characteristics. Numerical solutions obtained, in either case, give plausible account of the interaction between the membrane and the flow.

physics.flu-dyn↗
arXiv2012

Note on "A. Gorguis, A reliable approach to the solution of Navier-Stokes equations, Appl. Math. Lett. 25 (2012) 2015-2017"

Gorguis' claim of being able to transform Navier-Stokes equations into linear ones through the Cole-Hopf transformation is disputed. It is shown that the cases treated by Gorguis are intrinsically linear; involving a velocity potential (psi) that is governed by Laplace's equation. They require the external force to be conservative and the initial and boundary conditions to admit such cases of fluid flow. The pressure cannot be known a priori, as suggested by Gorguis, but is determined so that it can be consistent with (psi). Other errors in the cited article are also indicated.

math-ph↗
arXiv2012

Motion of a spherical solid particle in Couette flow: exact solution vs. homotopy perturbation approximation with and without Pade approximants

The motion of a spherical solid particle in plane Couette flow is governed by a linear problem that has a simple exact solution. As such, there is no need for an approximate analytical representation of the solution; specially when it is tedious, complicated, and requires hairy terms to give accurate results only at small or moderate values of the time.

math-ph↗