An analysis is performed to study the influence of non-uniform slot injection (suction) on a steady incompressible laminar boundary layer flow in a diverging channel with an exponentially decreasing free-stream velocity. The difficulties in obtaining the non-similar solutions at the starting point of the streamwise coordinate, at the edges of the slot and at the point of separation are overcome by applying an implicit finite difference scheme with the quasi-linearization technique and an appropriate selection of the finer step sizes along the streamwise direction. It is observed that the separation can be delayed by non-uniform slot suction and also by moving the slot downstream but the effect of non-uniform slot injection is just reverse. © 2009 Elsevier Ltd. All rights reserved.

Satyajit Roy

Department of Mathematics

Boundary layer separation

FINITE DIFFERENCE SCHEME

Free-stream velocity

LAMINAR BOUNDARY LAYER FLOW

NON-UNIFORM SLOT SUCTION

Nonuniform

QUASI-LINEARIZATION

SLOT INJECTION

Step size

Streamwise directions

Aerodynamics

Boundary layer flow

Boundary layers

linearization

Separation

Fulltext

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IIT Madras

Mathematical and Computer Modelling

Current paper deals with the numerical study on steady triple diffusive mixed convection boundary layer flow for exponentially decreasing external flow velocity in presence of suction/injection. Such exponentially decreasing external flows have specific applications in diverging channel flows. The temperature of the vertical surface is assumed to be higher compared to the surrounded fluid temperature. In the triple diffusive flow, the solutal components are chosen as Sodium chloride and Sucrose and the components are added in the flow stream from below with various concentration levels. The concentrations of NaCl-Water and Sucrose-Water are assumed to be lower within the free stream compared to the species concentrations of NaCl-Water and Sucrose-Water near the wall. The coupled nonlinear partial differential equations governing the flow, thermal and species concentration fields are transformed using the non-similarity variables and solved numerically by an implicit finite difference scheme with quasi-linearization technique. The effects of wall suction/injection, Richardson number, decelerating parameter, ratio of buoyancy parameters and Schmidt numbers of both the solutal components on the fluid flow, thermal and species concentration fields are analyzed and discussed. Results indicate that the thickness of the momentum boundary layer is lower for suction compared to injection for the buoyancy opposing flow. The decelerating parameter has significant impact on the flow fields. Also, the species concentration boundary layer thickness decreases with the increase of Schmidt numbers and that increases with the ratio of buoyancy parameters for both the species components. Overall, the mass transfer rate is found to increase with Schmidt numbers approximately 10% and 64% for NaCl and Sucrose, respectively. © 2018 Elsevier Ltd

International Journal of Heat and Mass Transfer

Triple diffusive mixed convection from an exponentially decreasing mainstream velocity

This article explores the influence of mixed convection in a steady incompressible laminar boundary layer flow for an exponentially decreasing free stream velocity in presence of surface mass transfer and heat source or sink. The nonlinear partial differential equations governing the flow and thermal fields are expressed in dimensionless form with the help of suitable non-similar transformations. The mathematical complexities in obtaining non-similar solutions at the leading edge of the streamwise coordinate as well as non-similarity variable ξ have overcome by using the implicit finite difference scheme in conjunction with Quasi-linearization technique by choosing an appropriate finer step sizes along the streamwise direction. The effects of various dimensionless physical parameters on velocity and thermal fields are analysed. © 2016 Elsevier Ltd

Influence of mixed convection in an exponentially decreasing external flow velocity

The development of unsteady mixed convection flow of an incompressible laminar viscous fluid over a vertical cone has been investigated when the fluid in the external stream is set into motion impulsively, and at the same time the surface temperature is suddenly changed from its ambient temperature. The problem is formulated in such a way that at t = 0, it reduces to Rayleigh type of equation and as t → ∞, it tends to Falkner-Skan type of equation. The scale of time has been selected such that the traditional infinite region of integration become finite which significantly reduce the computational time. The coupled non-linear partial differential equations governing the unsteady mixed convection flow have been solved numerically by using an implicit finite-difference scheme in combination with the quasi-linearization technique. There is a smooth transition from the initial steady state to the final steady state. The velocity, temperature, and concentration profiles and their gradients at the surface for various values of the governing parameters are reported in the present study. © 2006 Elsevier Ltd. All rights reserved.

Unsteady mixed convection flow over a vertical cone due to impulsive motion

An analysis is performed to obtain the non-similar solution of a steady laminar forced convection boundary layer flow over a horizontal slender cylinder including the effect of non-uniform slot injection (suction). The effects of transverse curvature and viscous dissipation are also included in the analysis. The governing boundary layer equations along with the boundary conditions are first cast into a dimensionless form using suitable transformations and the resulting system of nonlinear coupled partial differential equations is then solved by an implicit finite difference scheme in combination with the quasilinearization technique. Numerical results for the effect of non-uniform slot injection (suction) on skin friction coefficient and heat transfer rate are presented. The effects of transverse curvature, viscous dissipation and Prandtl number on velocity and temperature profiles and skin friction and heat transfer coefficients are also reported. © 2005 Elsevier Ltd. All rights reserved.

Effect of non-uniform slot injection (suction) on a forced flow over a slender cylinder

Non-similar solutions of steady two-dimensional and axi-symmetric compressible laminar boundary layer flows with non-uniform slot injection (or suction) have been obtained, from the starting point of the stream-wise co-ordinate to the exact point of separation. The difficulties arising at the starting point of the stream-wise co-ordinate, and at the edges of the slot and at the point of separation have been overcome by applying the method of quasi-linear implicit finite difference scheme, along with an appropriate selection of finer step size along the stream-wise direction. It is observed that the separation can be delayed by a non-uniform slot suction and also by moving the slot downstream but the effect of non-uniform slot injection is just the opposite. The increase of total enthalpy at the wall causes the separation to occur earlier while cooling delays it. The increase of Mach number shifts the point of separation upstream due to the adverse pressure gradient.

Heat and Mass Transfer/Waerme- und Stoffuebertragung

Compressible boundary layer flow with non-uniform slot injection or (suction) over i) a cylinder and ii) a sphere

The influence of non-uniform slot injection (suction) into steady axi-symmetric laminar incompressible boundary layer flows with temperature dependent viscosity and Prandtl number has been examined from the origin of the streamwise coordinate to the exact point of separation. The difficulties in obtaining the non-similar solutions at the origin of the streamwise coordinate, at the edges of the slot and at the point of separation have been overcome by applying an implicit finite difference scheme with the quasilinearization technique and an appropriate selection of finer step size along the streamwise coordinate. The results indicate that the separation can be delayed by non-uniform slot suction and also by moving the slot downstream but the effect of non-uniform slot injection is just the opposite. Further, the effect of variable fluid properties is to move the point of separation downstream but rotation parameter has the reverse effect. © 2003 Elsevier Science Ltd. All rights reserved.

Journal	Mathematical and Computer Modelling
ISSN	08957177
Open Access	Yes