A steady two-dimensional magnetohydrodynamic boundary-layer control with uniform suction or injection is investigated. The transverse magnetic field is fixed to the semi-infinite flat plate and the electric field is assumed to be zero. A nonsimilar boundary-layer equation is solved numerically by a difference-differential method originated by Hartree and Womersley and improved by Katagiri. The velocity profiles and the coefficient of the skin friction are computed for various values of magnetic parameter and suction/injection parameter. The graphical plots indicate increasing boundary-layer thickness and decreasing skin-friction coefficient with increasing magnetic parameter, and also decreasing boundary-layer thickness and increasing skin-friction coefficient with increasing sunction/injection parameter. The magnetic field is found to be rather efficient in modifying the boundary layer, especially with the help of a proper seeding material.
The Maxwell‐Euler equations are reformulated through linear operator and generalized transform techniques into an equivalent matrix integral equation. The dispersion relation is obtained from the kernel of this integral equation for a homogeneous, anistropic, and compressible electron‐fluid plasma. Some illuminating graphs showing the propagation constants as functions of the normalized plasma frequency are developed analytically to study the dispersion relation. These kinds of graphs are usually plotted from the limited amount of numerical data available in the literature (e.g., Ginzburg, 1961). Clemmow‐Mullaly‐Allis type of diagram for the compressible plasma is sketched from these graphs. Actually, dispersion curves are obtained which are inversely related to the wave normal surfaces calculated by Allis, Buchsbaum and Bers (1963). A proper terminology for the three types of waves involved in an electron plasma is also introduced.
ENGINEERING NOTES are short manuscripts describing new developments or important results of a preliminary nature. These Notes cannot exceed 6 manuscript pages and 8 figures; a page of text may be substituted for a figure and vice versa. After informal review by the editors, they may be published within a few months of the date of receipt. Style requirements are the same as for regular contributions (see inside back cover). Nomenclaturec p = specific heat / = Darcy-Weissbach friction coefficient k = thermal conductivity N Nu = Nusselt number, Eq. (18) Np r = Prandtl number, v/k N Re = Reynolds number, 2Rub/v Nst -S tan ton number, Eq. (19) q = average heat flux R = pipe radius R + = RV*/v T = temperature T w = temperature at the wall T + = (T w -T}c pP V*/q Tb + = d'mensionless bulk temperature, Eq. 16 u = local mean axial velocity u+ = u/V* Ub = average velocity F* = shear velocity y = distance from the wall y+ = yV*/v l/i = edge of laminar sublayer y\ + = y\V*/v 2/2 = edge of buffer zone 2/2 + = y*V*/v 81 = edge of diffusion sublayer « t + = 8 t F*A 8 2 = edge of viscous sublayer 52+ = 82V*/v AB = shift in the logarithmic velocity profile v = kinematic viscosityT HE possibility of correlation between drag reduction and changes in heat transfer is examined, possible semiempirical models for the description of these phenomena are suggested.Drag reducing polymeric additives increase the thickness of the viscous sublayer in turbulent flow and thus reduce the friction loss in the flow. In smooth pipe flow this increase can be calculated from the equation 5 2 + -5.75 Iogio5 2 + = 5.5 + AB(1)where AB expresses the polymeric eftects. Several semiempirical models, by which relationships between the function AB and the properties of the polymeric additives as well as the characteristics of the flowfield, were suggested. 1 " 4 However, almost none of these models can be applied for all Institute of Technology, Haifa, Israel.kinds of polymers and usually their applications are limited to certain ranges of flow shear stresses.Fabula 5 reviewed the experimental investigations concerning drag reduction and concluded that the maximum value of AB is smaller than 30. Virk 6 found some empirical formulation for cases of maximum drag reduction in small diameter pipes; such cases are defined through the following relationships between Reynolds number and Darcy-Weissbach friction coefficient -25(2) 1/C/) 1 / 2 = 11.5 logioltfT his equation can be approximated by 7 7 = 1.682W-0 - 55 (3)Assuming logarithmic velocity profile in the turbulent region = 5.75 log 10 (7/ + A + ) (4) and integrating the velocity profile through the whole pipe cross section, one obtains -5.75-3.75 (5) By comparison of Eqs. (1) and (5) with Eq.(2), we get an expression for AB in cases of maximum drag reduction AB = 26.81og 10 [IV fle (/) 1/2 ] -68.5Assuming that AB should be smaller than 30, it seems that Eq. (6) can be assumed reliable while Reynolds number is smaller than 9 X 10 4 . The experimental results of Virk 6 in the above range of Reynolds number we...
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.
customersupport@researchsolutions.com
10624 S. Eastern Ave., Ste. A-614
Henderson, NV 89052, USA
Copyright © 2024 scite LLC. All rights reserved.
Made with 💙 for researchers
Part of the Research Solutions Family.