# Effects of injection (suction) on a steady mixed convection boundary layer flow over a vertical cone

15 May 2009-International Journal of Numerical Methods for Heat & Fluid Flow (Emerald Group Publishing Limited)-Vol. 19, pp 432-444

TL;DR: In this article, the authors study the steady mixed convection flow over a vertical cone in the presence of surface mass transfer when the axis of the cone is inline with the flow.

Abstract: Purpose – The purpose of this paper is to study the steady mixed convection flow over a vertical cone in the presence of surface mass transfer when the axis of the cone is inline with the flow.Design/methodology/approach – In this case, the numerical difficulties to obtain the non‐similar solution are overcome by applying an implicit finite difference scheme in combination with the quasilinearization technique.Findings – Numerical results are reported here to display the effects of Prandtl number, buoyancy and mass transfer (injection and suction) parameters at different stream‐wise locations on velocity and temperature profiles, and on skin friction and heat transfer coefficients.Research limitations/implications – Thermo‐physical properties of the fluid in the flow model are assumed to be constant except the density variations causing a body force term in the momentum equation. The Boussinesq approximation is invoked for the fluid properties to relate the density changes to temperature changes and to co...

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TL;DR: Roughly one in six of Walsh's 281 publications are included, photographically reproduced, and reproduction is excellent except for one paper from 1918, which is an obituary.

Abstract: a 'sleeper', receiving only modest attention for 50 years before emerging as a cornerstone of communications engineering in more recent times. Roughly one in six of Walsh's 281 publications are included, photographically reproduced. Reproduction is excellent except for one paper from 1918. The book also reproduces three brief papers about Walsh and his work, by W. E. Sewell, D. V. Widder and Morris Marden. The first two were written for a special issue of the SIAM Journal celebrating Walsh's 70th birthday; the third is an obituary.

676 citations

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VIT University

^{1}TL;DR: In this article, the authors analyzed the flow, heat and mass transfer characteristics of gyrotactic microorganisms contained magneto hydrodynamic Casson fluid flow towards a vertical rotating cone/plate in porous medium.

Abstract: Numerical investigation is carried out to analyze the flow, heat and mass transfer characteristics of gyrotactic microorganisms contained magneto hydrodynamic Casson fluid flow towards a vertical rotating cone/plate in porous medium. In the presence of thermo diffusion and diffusion thermo effects we have presented dual solutions for the flow over a rotating cone and a rotating flat plate. Further, the numerical solutions are elucidated by using Runge–Kutta–Felhberg integration Scheme. Obtained results are validated with open literature and found an excellent agreement. The influence of non-dimensional governing parameters on velocity, temperature, concentration and density of the motile microorganisms along with the friction factor, local Nusselt, Sherwood numbers and the local density of the motile microorganisms was determined and discussed with the help of graphs and tables. Results proved that there is a significant variation of heat and mass transfer in the flow over a rotating cone and a plate. It is also found that the heat and mass transfer performance of the flow over a rotating cone is significantly high while compared with the flow over a rotating plate.

149 citations

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VIT University

^{1}TL;DR: In this paper, the authors studied the flow, heat and mass transfer characteristics in the unsteady free convective flow of an incompressible viscoelastic fluid over a moving vertical cone and a flat plate in the presence of magnetic field and higher order chemical reaction.

Abstract: The present paper is concerned with the study of flow, heat and mass transfer characteristics in the unsteady free convective flow of an incompressible viscoelastic fluid over a moving vertical cone and a flat plate in the presence of magnetic field and higher order chemical reaction. The fluid viscosity and thermal conductivity are assumed to vary as a linear function of temperature. The governing partial differential equations are solved numerically using the implicit finite difference method of Crank–Nicolson type. The features of the fluid flow, heat and mass transfer characteristics are analyzed by plotting graphs and the physical aspects are discussed in detail. The results obtained show that the impact of magnetic field, buoyancy ratio parameter, viscosity variation parameter, Ecart number and chemical reaction parameter plays an important role in the viscoelastic fluid flow through porous medium. The mass transfer of the reactive species strongly depends on the chemical reaction parameter as well as the order of chemical reaction.

65 citations

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TL;DR: In this paper, the Soret and Dufour effects on the double-diffusive convective boundary layer flow of a nanofluid past a moving wedge in the presence of suction were investigated.

Abstract: Purpose
The purpose of this study is to investigate the Soret and Dufour effects on the double-diffusive convective boundary layer flow of a nanofluid past a moving wedge in the presence of suction.
Design/methodology/approach
The similarity transformation is applied to convert the governing nonlinear partial differential equations into ordinary differential equations. Then, they are solved numerically by the fourth-order Runge–Kutta–Gill method along with the shooting technique and the Newton–Raphson method. In addition, the ordinary differential equations are also analytically solved by the homotopy analysis method.
Findings
The results for dimensionless velocity, temperature, solutal concentration and nanoparticle volume fraction profiles, as well as local skin friction coefficient and local Nusselt and local Sherwood numbers are presented through the plots for various combinations of pertinent parameters involved in the study. The heat transfer rate increases on increasing the Soret parameter and it decreases on increasing the Dufour parameter. The mass transfer behaves oppositely to heat transfer.
Practical implication
In engineering applications, a wedge is used to hold objects in place, such as engine parts in the gate valves. A gate valve is the valve that opens by lifting a wedge-shaped disc to control the timing and quantity of fluid flow into an engine.
Originality/value
No such investigation is available in literature, and therefore, the results obtained are novel.

62 citations

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TL;DR: In this paper, a mathematical model for two dimensional steady laminar natural convective anisotropic slip boundary layer flows from a rotating vertical cone embedded in ethylene glycol bionanofluid is presented.

Abstract: A mathematical model for two dimensional steady laminar natural convective anisotropic slip boundary layer flows from a rotating vertical cone embedded in ethylene glycol bionanofluid is presented. The influence of Stefan blowing is also taken into account. Four different nonparticles namely Copper (Cu), Alumina (Al2O3), Copper Oxide (Cuo), Titanium Oxide (TiO2) are explored. Suitable similarity transformations are used to convert the governing equations into non-linear ordinary differential equations. These are then solved numerically, with appropriate boundary conditions, utilizing an implicit finite difference method (the BVP5C code in MATLAB). During computation Sc, Lb, Le and Lb are presented as unity, whilst Pr is taken as 151.The effects of the governing parameters on the dimensionless velocities,
temperature, nanoparticle volume fraction, density of motile microorganisms as well as on the local skin friction, local Nusselt, Sherwood number and motile micro-organism number density
are thoroughly examined via tables and graphs. It is found that the skin friction factor increases with tangential slip, magnetic field and Schmidt number whilst it decreases with blowing parameter and spin parameters. It is further observed that both the friction and heat transfer rates are highest for copper nanoparticles and lowest for TiO2 nanoparticles. Validation of the BVP5C numerical solutions with published results for several special cases of the general model is included. The study is relevant to electro-conductive bio-nano-materials processing.

53 citations

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##### References

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01 Jan 1955

TL;DR: The flow laws of the actual flows at high Reynolds numbers differ considerably from those of the laminar flows treated in the preceding part, denoted as turbulence as discussed by the authors, and the actual flow is very different from that of the Poiseuille flow.

Abstract: The flow laws of the actual flows at high Reynolds numbers differ considerably from those of the laminar flows treated in the preceding part. These actual flows show a special characteristic, denoted as turbulence. The character of a turbulent flow is most easily understood the case of the pipe flow. Consider the flow through a straight pipe of circular cross section and with a smooth wall. For laminar flow each fluid particle moves with uniform velocity along a rectilinear path. Because of viscosity, the velocity of the particles near the wall is smaller than that of the particles at the center. i% order to maintain the motion, a pressure decrease is required which, for laminar flow, is proportional to the first power of the mean flow velocity. Actually, however, one ob~erves that, for larger Reynolds numbers, the pressure drop increases almost with the square of the velocity and is very much larger then that given by the Hagen Poiseuille law. One may conclude that the actual flow is very different from that of the Poiseuille flow.

17,321 citations

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30 Nov 1961

TL;DR: In this article, the authors propose Matrix Methods for Parabolic Partial Differential Equations (PPDE) and estimate of Acceleration Parameters, and derive the solution of Elliptic Difference Equations.

Abstract: Matrix Properties and Concepts.- Nonnegative Matrices.- Basic Iterative Methods and Comparison Theorems.- Successive Overrelaxation Iterative Methods.- Semi-Iterative Methods.- Derivation and Solution of Elliptic Difference Equations.- Alternating-Direction Implicit Iterative Methods.- Matrix Methods for Parabolic Partial Differential Equations.- Estimation of Acceleration Parameters.

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01 Jan 1984

TL;DR: In this paper, the authors describe a transition from Laminar boundary layer flow to Turbulent Boundary Layer flow with change of phase Mass Transfer Convection in Porous Media.

Abstract: Fundamental Principles Laminar Boundary Layer Flow Laminar Duct Flow External Natural Convection Internal Natural Convection Transition to Turbulence Turbulent Boundary Layer Flow Turbulent Duct Flow Free Turbulent Flows Convection with Change of Phase Mass Transfer Convection in Porous Media.

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01 Jan 1993

TL;DR: In this paper, Bibliogr. en fin de chapitres. Index Reference Record created on 2004-09-07, modified on 2016-08-08, created on

Abstract: Note: Bibliogr. en fin de chapitres. Index Reference Record created on 2004-09-07, modified on 2016-08-08

1,445 citations