The objective of the present article is to investigate the Dufour (diffusion-thermo) and Soret (thermal diffusion) effects on the steady double diffusive mixed convection boundary layer flows over an impermeable exponentially stretching sheet in an exponentially moving free stream under the influence of chemically reactive species. The nonlinear partial differential equations governing the flow, temperature and species concentration fields are expressed in non-dimensional form with the help of suitable non-similar transformations. The resulting final non-dimensional set of coupled nonlinear partial differential equations is solved by using an implicit finite difference scheme in conjunction with the Newton's linearization technique. The effects of various governing parameters involved in the velocity, temperature and species concentration fields are discussed in this article. The results display that the streamwise co-ordinate ξ (non-similarity variable) profoundly influences the flow, thermal and concentration fields which reveal the accountability of non-similar solutions. Results also indicate that the Dufour number Df decreases the heat transfer coefficient while the Soret number Sr decreases the mass transfer coefficient. © 2016 Elsevier Ltd.

Satyajit Roy

Department of Mathematics

Boundary layer flow

Boundary layers

Diffusion

Finite difference method

Heat transfer

MASS TRANSFER

Mathematical transformations

Mixed convection

Partial differential equations

Thermal diffusion

DIFFUSION-THERMO EFFECTS

EXPONENTIALLY STRETCHING SURFACES

FINITE DIFFERENCE SCHEME

Implicit finite-difference schemes

MIXED CONVECTION BOUNDARY LAYER FLOW

NONLINEAR PARTIAL DIFFERENTIAL EQUATIONS

SORET EFFECTS

Nonlinear equations

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IIT Madras

International Journal of Heat and Mass Transfer

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

Triple diffusive mixed convection from an exponentially decreasing mainstream velocity

This paper presents a numerical investigation on steady triple diffusive mixed convection boundary layer flow past a vertical plate moving parallel to the free stream in the upward direction. The temperature of the plate is assumed to be hotter compared to the surrounded fluid temperature. Sodium chloride and Sucrose are chosen as solutal components which are added in the flow stream from below with various concentration levels. The concentrations of NaCl-Water and Sucrose-Water are considered to be higher near the wall compared to the concentrations of NaCl-Water and Sucrose-Water within the free stream. The coupled nonlinear partial differential equations are transformed using the non-similarity variables and solved numerically by an implicit finite difference scheme with quasi-linearization technique. The effects of Richardson numbers, velocity ratio parameters, ratio of buoyancy parameters and Schmidt numbers of both the solutal components on the fluid flow, thermal and species concentration fields are investigated. Results indicate that 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 4.36% and 64.56% for NaCl and Sucrose, respectively. © 2017 Elsevier Ltd

Triple diffusive mixed convection along a vertically moving surface

This paper is devoted to obtain non-similar solutions for the effect of viscous dissipation on the steady double diffusive mixed convection flow over a vertical exponentially permeable stretching surface. The non-linear partial differential equations governing the flow, thermal and species concentration fields are written in the non-dimensional form by using suitable group of transformations. The final non-dimensional set of coupled partial differential equations is solved using the implicit finite difference method in combination with the Newton's linearization technique. The effects of various non-dimensional physical parameters on velocity, temperature and species concentration fields are discussed. The presence of the suction/injection at the surface expedites the mass transfer phenomena. The numerical results in terms of the skin friction coefficient, the rate of heat transfer in terms of local Nusselt number and mass transfer rate in terms of Sherwood number shown graphically for various physical parameter involved in the problem. The present results are compared with previously published work, and these comparisons are found to be in excellent agreement. © 2017 Elsevier Ltd

Double diffusive mixed convection flow from a vertical exponentially stretching surface in presence of the viscous dissipation

This paper presents a numerical investigation of the steady two-dimensional mixed convection flow along a vertical semi-infinite stretching sheet of variable thickness. The effect of double diffusion on velocity, thermal and concentration fields in presence of power-law temperature and concentration distributions at wall along with surface mass transfer is considered. The nonlinear coupled partial differential equations governing the flow, thermal and concentration fields are first transformed into a nondimensional set of coupled nonlinear partial differential equations and solved numerically using an implicit finite-difference scheme in combination with the Newton's linearization technique to obtain nonsimilar solutions at each stream-wise location. Numerical results are presented to discuss the effects of various physical parameters on the velocity, temperature, and concentration fields. Furthermore, the numerical results for the local skin friction coefficient, local Nusselt number, and local Sherwood number are also reported. For a fixed buoyancy force, the skin friction coefficient and Nusselt number increase with Prandtl number. The increase in the Prandtl number causes about a 30% reduction in the thickness of the thermal boundary layer. The wall thickness parameter enhances the thickness of the momentum boundary layer and the velocity overshoot is observed up to 20% for wall thickness parameter α = 0.9. In contrast, the increase of power-law index parameter m from m = 0.5 to m = 1.5 reduces approximately 10% to 25% the momentum and thermal boundary layer thicknesses depending on the values of other parameters. © 2017 Wiley Periodicals, Inc.

Heat Transfer - Asian Research

Double Diffusive Flows over a Stretching Sheet of Variable Thickness with or without Surface Mass Transfer

A very recent study of Patil et al. (2017) on the effects of steady mixed convection flow with an exponentially decreasing free stream velocity motivates this research investigation. The present analysis reveals the mixed convection impact over an exponentially decreasing free stream velocity in an unsteady incompressible laminar boundary layer flow involving the effects of suction or blowing and heat generation or absorption. By utilizing the appropriate non-similar transformations, the complex dimensional governing boundary layer equations are simplified into dimensionless equations. In order to prevail the mathematical convolutions in attaining the non-similar solutions at the leading edge of the streamwise coordinate as well as non-similarity variable ξ, the coalition of implicit finite difference scheme and the Quasi-linearization technique is used with the suitable step sizes along the streamwise and time directions. The effects of various dimensionless physical parameters over the momentum and thermal fields are examined. The range of the parameters studied in this analysis are taken as α(-0.5⩽α⩽1.0), ξ(0⩽ξ⩽1), τ(0⩽τ⩽1), ε(0.000001⩽ε⩽0.1), Ri(-3⩽Ri⩽10), Re(10⩽Re⩽250), A(-1⩽A⩽1) and Q(-1⩽Q⩽1). Further, the present numerical investigation is focussed towards unsteady flow and heat transfer characteristics. © 2017 Elsevier Ltd

Unsteady mixed convection over an exponentially decreasing external flow velocity

The main objective of the present paper is to obtain non-similar solutions numerically for steady two dimensional double diffusive mixed convection boundary layer flows along a vertical semi-infinite permeable surface under the influence of convective boundary condition along with surface mass transfer. The nonlinear partial differential equations governing the flow, temperature, and species concentration fields are expressed in non-dimensional form using suitable non-similar transformations. The final non-dimensional set of coupled nonlinear partial differential equations is solved by using an implicit finite difference scheme in combination with quasi-linearization technique. The effects of various governing parameters involved on the velocity, temperature and species concentration profiles are discussed in the present paper. The results show that the streamwise co-ordinate ξ significantly influences the flow, thermal, and concentration fields which indicate the importance of non-similar solutions. Results indicate that buoyancy parameter (Ri) and the ratio of buoyancy forces parameter (N) enhance the skin friction coefficient and decrease the heat transfer coefficient. Also, it is observed that the increase of suction parameter (A = 1) causes the decrease in the magnitude of temperature and concentration profiles from their values for injection parameter (A = -1). In the present investigation, dual solutions are also obtained under similarity assumptions and compared with previously published work. © 2013 Published by Elsevier Ltd.

Influence of convective boundary condition on double diffusive mixed convection from a permeable vertical surface

An unsteady mixed convection flow over a moving vertical plate in a parallel free stream is considered to investigate the combined effects of buoyancy force and thermal diffusion in presence of Newtonian heating in which heat transfer rate from the surface is proportional to the local temperature and thermal radiation effects. It is assumed that the unsteadiness is caused by the time dependent free stream velocity as well as by the moving plate velocity. The governing boundary layer equations with boundary conditions are transformed into a non-dimensional form by a group of non-similar transformations. The resulting system of coupled non-linear partial differential equations is solved by an implicit finite difference scheme in combination with the quasi-linearization technique. Computations are performed and representative set is displayed graphically to illustrate the influence of the mixed convection parameter (λ), Prandtl number (Pr), the ratio of free stream velocity to the composite reference velocity (ε), stream wise co ordinate (ξ) and thermal radiation parameter (R) on the velocity and temperature profiles. The numerical results for the local skin-friction coefficient (ReL1/2Cf) and wall temperature (GW(ξ,0)) are also presented. The numerical results are presented in graphs revealing some interesting features of flow and heat transfer phenomena in this study. Present results are also compared with previously published works and are found to be in excellent agreement. © 2013 Elsevier Ltd. All rights reserved.

Unsteady thermal radiation mixed convection flow from a moving vertical plate in a parallel free stream: Effect of Newtonian heating

An unsteady mixed convection boundary layer flow over a permeable non-linearly stretching vertical slender cylinder is considered to investigate the combined effects of buoyancy force and thermal diffusion in presence of surface mass transfer, where the slender cylinder is in line with the flow. The unsteadiness in the flow and temperature fields is caused by the continuously non-linearly stretching vertical slender cylinder. The governing boundary layer equations are transformed into a non-dimensional form by a group of non-similar transformations. The resulting system of coupled non-linear partial differential equations is solved by an implicit finite difference scheme in combination with the quasi-linearization technique. Numerical computations are performed to understand the physical situations of linear and non-linearly stretching surface for different values of parameters to display the velocity and temperature profiles graphically. The obtained results show that the buoyancy parameter λ and the Prandtl number Pr enhance the skin friction coefficient and the local Nusselt number. It is also shown that the suction parameter A (>0) is to decrease the velocity and temperature profiles, but injection parameter A (<0) does the reverse. Results are compared with previously published work and are found to be in excellent agreement. © 2011 Elsevier Ltd.

Computers and Fluids

Unsteady effects on mixed convection boundary layer flow from a permeable slender cylinder due to non-linearly power law stretching

The objective of the paper is to investigate the numerical study of an unsteady two-dimensional mixed convection flow along a vertical semi-infinite power-law stretching sheet in a parallel free stream with a power-law wall temperature distribution of the form TW(x)=T∞+Ax2m-1. The unsteadiness is caused by the free stream velocity as well as by the stretching sheet velocity. The governing non-linear partial differential equations in the velocity and temperature fields are written in non-dimensional form using suitable transformations. The resulting final set of coupled non-linear partial differential equations is solved using an implicit finite difference scheme in combination with a quasi-linearization technique. The effects of various governing parameters on the velocity and temperature profiles are discussed in the present numerical study. In addition, the numerical results for the local skin friction coefficient and local Nusselt number are also presented. The numerically computed results are compared with previously reported work and are found to be in excellent agreement. © 2010 Elsevier Ltd.

Unsteady mixed convection flow over a vertical stretching sheet in a parallel free stream with variable wall temperature

An unsteady mixed convection flow over a moving vertical plate in a parallel free stream is considered to investigate the combined effects of buoyancy force and thermal diffusion in presence of heat generation or absorption. The unsteadiness is introduced by the time dependent free stream velocity as well as by the moving plate velocity. The governing boundary layer equations are transformed into a non-dimensional form by a special group of non-similar transformations. The resulting system of coupled non-linear partial differential equations is solved by an implicit finite difference scheme in combination with the quasi-linearization technique. Computations are performed and numerical results are displayed graphically to illustrate the influence of the buoyancy (mixed convection) parameter, Prandtl number, the ratio of free stream velocity to the composite reference velocity and heat generation or absorption parameter on the velocity and temperature profiles. The numerical results for the local skin-friction coefficient and local Nusselt number are also presented. Present results are compared with previously published work and are found to be in excellent agreement. It is found that in presence of buoyancy force (λ>0), the velocity profile exhibits velocity overshoot 80% more for lower Prandtl number (Pr=0.7) as compared to the magnitude of the velocity overshoot for higher Prandtl number (Pr=7.0). © 2010 Elsevier Ltd.

Journal	Data powered by TypesetInternational Journal of Heat and Mass Transfer
Publisher	Data powered by TypesetElsevier Ltd
ISSN	00179310
Open Access	No