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Article

Lelanie Smith, Oliver Oxtoby, A. Malan and Josua Meyer

– The purpose of this paper is to introduce a unique technique to couple the two-integral boundary layer solutions to a generic inviscid solver in an iterative fashion.

Abstract

Purpose

The purpose of this paper is to introduce a unique technique to couple the two-integral boundary layer solutions to a generic inviscid solver in an iterative fashion.

Design/methodology/approach

The boundary layer solution is obtained using the two-integral method to solve displacement thickness point by point with a local Newton method, at a fraction of the cost of a conventional mesh-based, full viscous solution. The boundary layer solution is coupled with an existing inviscid solver. Coupling occurs by moving the wall to a streamline at the computed boundary layer thickness and treating it as a slip boundary, then solving the flow again and iterating. The Goldstein singularity present when solving boundary layer equations is overcome by solving an auxiliary velocity equation along with the displacement thickness.

Findings

The proposed method obtained favourable results when compared with the analytical solutions for flat and inclined plates. Further, it was applied to modelling the flow around a NACA0012 airfoil and yielded results similar to those of the widely used XFOIL code.

Originality/value

A unique method is proposed for coupling of the boundary layer solution to the inviscid flow. Rather than the traditional transpiration boundary condition, mesh movement is employed to simulate the boundary layer thickness in a more physically meaningful way. Further, a new auxiliary velocity equation is presented to circumvent the Goldstein singularity.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 23 no. 8
Type: Research Article
ISSN: 0961-5539

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Article

Seyed Amin Bagherzadeh, Esmaeil Jalali, Mohammad Mohsen Sarafraz, Omid Ali Akbari, Arash Karimipour, Marjan Goodarzi and Quang-Vu Bach

Water/Al2O3 nanofluid with volume fractions of 0, 0.3 and 0.06 was investigated inside a rectangular microchannel. Jet injection of nanofluid was used to enhance the heat…

Abstract

Purpose

Water/Al2O3 nanofluid with volume fractions of 0, 0.3 and 0.06 was investigated inside a rectangular microchannel. Jet injection of nanofluid was used to enhance the heat transfer under a homogeneous magnetic field with the strengths of Ha = 0, 20 and 40. Both slip velocity and no-slip boundary conditions were used.

Design/methodology/approach

The laminar flow was studied using Reynolds numbers of 1, 10 and 50. The results showed that in creep motion state, the constricted cross section caused by fluid jet is not observable and the rise of axial velocity level is only because of the presence of additional size of the microchannel. By increasing the strength of the magnetic field and because of the rise of the Lorentz force, the motion of fluid layers on each other becomes limited.

Findings

Because of the limitation of sudden changes of fluid in jet injection areas, the magnetic force compresses the fluid to the bottom wall, and this behavior limits the vertical velocity gradients. In the absence of a magnetic field and under the influence of the velocity boundary layer, the fluid motion has more variations. In creeping velocities of fluid, the presence or absence of the magnetic field does not have an essential effect on Nusselt number enhancement.

Originality/value

In lower velocities of fluid, the effect of the jet is not significant, and the thermal boundary layer affects the entire temperature field. In this case, for Hartmann numbers of 40 and 0, changing the Nusselt number on the heated wall is similar.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 30 no. 5
Type: Research Article
ISSN: 0961-5539

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Article

Prabhugouda M. Patil

The purpose of this paper is to study the effects of surface mass transfer on the steady mixed convection flow from a vertical stretching sheet in a parallel free stream…

Abstract

Purpose

The purpose of this paper is to study the effects of surface mass transfer on the steady mixed convection flow from a vertical stretching sheet in a parallel free stream with variable wall temperature and concentration.

Design/methodology/approach

An implicit finite difference scheme in combination with the quasilinearisation technique is employed to obtain non‐similar solutions of the governing boundary layer equations for momentum, temperature and concentration fields.

Findings

The numerical results are reported here to display the effects of mixed convection parameter, ratio of buoyancy forces, surface mass transfer (suction and injection), the ratio of free stream velocity to the composite reference velocity, Prandtl number and Schmidt number on velocity, temperature and concentration profiles as well as on skin friction, Nusselt number and Sherwood number.

Research limitations/implications

Thermophysical 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 density changes, and to couple in this way the temperature and concentration fields to the flow field. The concentration of diffusing species is assumed to be very small in comparison with other chemical species far away from the surface. Hence the Soret and Dufour effects are neglected. The stretching sheet is assumed to be subject to a power‐law wall temperature as well as to a power‐law wall concentration, in a parallel free stream.

Practical implications

Convective heat and mass transfer over a vertical stretching sheet in a parallel stream is very important for various design of technological process are hot rolling, wire drawing, glass‐fiber paper production, both metal and polymer sheets, for instance, in cooling of an infinite metallic plate in a cooling bath, the boundary layer along material handling conveyors, etc.

Originality/value

The paper studies the combined effects of thermal and mass diffusion over a vertical stretching sheet with surface mass transfer.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 22 no. 3
Type: Research Article
ISSN: 0961-5539

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Article

Prabhugouda Mallanagouda Patil, Geeta Hadimani, Shashikant A., P.S. Kulkarni and Mukesh Kumar

This paper aims to provide a detailed study on the influence of slip flow and thermal jump over mixed convection flow along an exponentially stretching surface. Also…

Abstract

Purpose

This paper aims to provide a detailed study on the influence of slip flow and thermal jump over mixed convection flow along an exponentially stretching surface. Also, impacts of suction/blowing, volumetric heat source/sink and velocity ratio parameter will be studied in this analysis.

Design/methodology/approach

The modeled governing equations for the assumed problem are dimensional nonlinear partial differential equations in nature. To reduce these equations, non-similar transformations are used to get the dimensionless nonlinear partial differential equations. Then, quasi-linearization technique is used to linearize these non-dimensional nonlinear partial differential equations. Finally, an implicit finite difference scheme is used to discretize the resulting equations.

Findings

The physical explanations are provided for the variations of various non-dimensional governing parameters over the velocity and temperature profiles. Also, the effects of these dimensionless parameters on skin friction coefficient and heat transfer rate are scrutinized in a manner which highlights their physical interpretation. The detailed discussion exhibits the fact that the streamwise co-ordinate velocity ratio parameter, partial slip parameter and the thermal jump parameter have significant influence over the flow and thermal fields.

Originality/value

This work has not been reported in the literature to the authors’ best of knowledge.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 28 no. 10
Type: Research Article
ISSN: 0961-5539

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Article

D.R. Pye

The Nature of the Boundary Layer The changes of velocity in an air stream at points close to a surface past which it is flowing have been calculated by Blasius and von…

Abstract

The Nature of the Boundary Layer The changes of velocity in an air stream at points close to a surface past which it is flowing have been calculated by Blasius and von Karman for the surfaces of a thin plate placed edgewise to the stream; and they have also been directly measured by Fage and Falkner close to the surfaces of an aerofoil, by means of an arrangement of minute pitot tubes, down to distances of a few thousands of an inch from the surface.

Details

Aircraft Engineering and Aerospace Technology, vol. 5 no. 3
Type: Research Article
ISSN: 0002-2667

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Article

MICHAEL J. NUSCA

An aerothermodynamic design code for axisymmetric projectiles has been developed using a viscous‐inviscid interaction scheme. Separate solution procedures for the inviscid…

Abstract

An aerothermodynamic design code for axisymmetric projectiles has been developed using a viscous‐inviscid interaction scheme. Separate solution procedures for the inviscid and the viscous (boundary layer) fluid dynamic equations are coupled by an iterative solution procedure. Non‐equilibrium, equilibrium and perfect gas boundary layer equations are included. The non‐equilibrium gas boundary layer equations assume a binary mixture (two species; atoms and molecules) of chemically reacting perfect gases. Conservation equations for each species include finite reaction rates applicable to high temperature air. The equilibrium gas boundary layer equations assume infinite rate reactions, while the perfect gas equations assume no chemical reactions. Projectile near‐wall and surface flow profiles (velocity, pressure, density, temperature and heat transfer) representing converged solutions to both the inviscid and viscous equations can be obtained in less than two minutes on minicomputers. A technique for computing local reverse flow regions is included. Computations for yawed projectiles are accomplished using a coordinate system transformation technique that is valid for small angle‐of‐attack. Computed surface pressure, heat transfer rates and aerodynamic forces and moments for 1.25 &le Mach No. &le 10.5 are compared to wind tunnel and free flight measurements on flat plate, blunt‐cone, and projectile geometries such as a cone‐cylinder‐flare.

Details

Engineering Computations, vol. 10 no. 5
Type: Research Article
ISSN: 0264-4401

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Article

G.V. Lachmann

Since the end of the Second World War, many spectacular advances have been made in aeronautics, thanks chiefly to the development of more powerful and economical jet…

Abstract

Since the end of the Second World War, many spectacular advances have been made in aeronautics, thanks chiefly to the development of more powerful and economical jet engines. As to the parasitic drag of manned aircraft, progress has been confined to reducing unfavourable compressibility effects (area rule, Whitcombe bodies); methods to suppress separation have been developed but no new methods to reduce the drag resulting from turbulent boundary layers developing over the exposed surfaces have as yet found practical application.

Details

Aircraft Engineering and Aerospace Technology, vol. 34 no. 3
Type: Research Article
ISSN: 0002-2667

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Article

M.A. Antar and M.A.I. El‐Shaarawi

Boundarylayer flow around a spinning liquid sphere moving steadily in a gas stream is investigated numerically. The shear stress exerted on the sphere's surface results…

Abstract

Boundarylayer flow around a spinning liquid sphere moving steadily in a gas stream is investigated numerically. The shear stress exerted on the sphere's surface results in surface rotation in the meridional direction in addition to the azimuthal velocity resulting from the spinning of the liquid sphere. The parameters controlling the flow around the sphere are the external flow Reynolds number (Re), the liquid‐to‐gas viscosity ratio (μ*) and the spinning parameter (Rer/Re)2. The effect of these parameters on the velocity components (namely the meridional, radial and azimuthal velocity components) and on the shear stress is shown. Moreover, their effect on the location of external flow point of separation is also demonstrated.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 12 no. 7
Type: Research Article
ISSN: 0961-5539

Keywords

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Article

Mahantesh M. Nandeppanavar, T. Srinivasulu and Shanker Bandari

The purpose of this paper is to study the flow, heat and mass transfer of MHD Casson nanofluid due to an inclined stretching sheet using similarity transformation, the…

Abstract

Purpose

The purpose of this paper is to study the flow, heat and mass transfer of MHD Casson nanofluid due to an inclined stretching sheet using similarity transformation, the governing PDE’S equations of flow, heat and mass transfer are converted into ODE’S. The resulting non-linear ODE’S are solved numerically using an implicit finite difference method, which is known as Kellor-box method. The effects of various governing parameters on velocity, temperature and concentration are plotted for both Newtonian and non-Newtonian cases. The numerical values of skin friction, Nusselt number and Sherwood number are calculated and tabulated in various tables for different values of physical parameters. It is noticed that the effect of angle of inclination enhances the temperature and concentration profile whereas velocity decreases. The temperature decreases due to the increase in the parametric values of Pr and Gr due to thickening in the boundary layer.

Design/methodology/approach

Numerical method is applied to find the results.

Findings

Flow and heat transfer analysis w.r.t various flow and temperature are analyzed for different values of the physical parameters.

Research limitations/implications

The numerical values of skin friction, Nusselt number and Sherwood number are calculated and tabulated in various tables for different values of physical parameters.

Practical implications

The study of the boundary layer flow, heat and mass transfer is important due to its applications in industries and many manufacturing processes such as aerodynamic extrusion of plastic sheets and cooling of metallic sheets in a cooling bath.

Originality/value

Here in this paper the authors have investigated the MHD boundary layer flow of a Casson nanofluid over an inclined stretching sheet along with the Newtonian nanofluid as a limited.

Details

Multidiscipline Modeling in Materials and Structures, vol. 16 no. 1
Type: Research Article
ISSN: 1573-6105

Keywords

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Article

S. Das, A.S. Banu and R.N. Jana

In various kinds of materials processes, heat and mass transfer control in nuclear phenomena, constructing buildings, turbines and electronic circuits, etc., there are…

Abstract

Purpose

In various kinds of materials processes, heat and mass transfer control in nuclear phenomena, constructing buildings, turbines and electronic circuits, etc., there are numerous problems that cannot be enlightened by uniform wall temperature. To explore such physical phenomena researchers incorporate non-uniform or ramped temperature conditions at the boundary, the purpose of this paper is to achieve the closed-form solution of a time-dependent magnetohydrodynamic (MHD) boundary layer flow with heat and mass transfer of an electrically conducting non-Newtonian Casson fluid toward an infinite vertical plate subject to the ramped temperature and concentration (RTC). The consequences of chemical reaction in the mass equation and thermal radiation in the energy equation are encompassed in this analysis. The flow regime manifests with pertinent physical impacts of the magnetic field, thermal radiation, chemical reaction and heat generation/absorption. A first-order chemical reaction that is proportional to the concentration itself directly is assumed. The Rosseland approximation is adopted to describe the radiative heat flux in the energy equation.

Design/methodology/approach

The problem is formulated in terms of partial differential equations with the appropriate physical initial and boundary conditions. To make the governing equations dimensionless, some suitable non-dimensional variables are introduced. The resulting non-dimensional equations are solved analytically by applying the Laplace transform method. The mathematical expressions for skin friction, Nusselt number and Sherwood number are calculated and expressed in closed form. Impacts of various associated physical parameters on the pertinent flow quantities, namely, velocity, temperature and concentration profiles, skin friction, Nusselt number and Sherwood number, are demonstrated and analyzed via graphs and tables.

Findings

Graphical analysis reveals that the boundary layer flow and heat and mass transfer attributes are significantly varied for the embedded physical parameters in the case of constant temperature and concentration (CTC) as compared to RTC. It is worthy to note that the fluid velocity is high with CTC and lower for RTC. Also, the fluid velocity declines with the augmentation of the magnetic parameter. Moreover, growth in thermal radiation leads to a declination in the temperature profile.

Practical implications

The proposed model has relevance in numerous engineering and technical procedures including industries related to polymers, area of chemical productions, nuclear energy, electronics and aerodynamics. Encouraged by such applications, the present work is undertaken.

Originality/value

Literature review unveils that sundry studies have been carried out in the presence of uniform wall temperature. Few studies have been conducted by considering non-uniform or ramped wall temperature and concentration. The authors are focused on an analytical investigation of an unsteady MHD boundary layer flow with heat and mass transfer of non-Newtonian Casson fluid past a moving plate subject to the RTC at the plate. Based on the authors’ knowledge, the present study has, so far, not appeared in scientific communications. Obtained analytical solutions are verified by considering particular cases of the published works.

Details

World Journal of Engineering, vol. ahead-of-print no. ahead-of-print
Type: Research Article
ISSN: 1708-5284

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