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.

Satyajit Roy

Department of Mathematics

Finite difference method

Heat transfer

Viscosity

NON-LINEAR SLOT INJECTION

Boundary layer flow

Boundary layer

injection

SLOT

sphere

Suction

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IIT Madras

Non-uniform slot injection (suction) into steady laminar water boundary layer flow over a rotating sphere

International Journal of Heat and Mass Transfer

Boundary layer flow phenomenons on a stretching sheet find numerous applications in industrial processes such as manufacture and extraction of rubber and polymer sheets. The current study focuses on two-dimensional water boundary layer flow on exponential stretching surface with a vertical plate for variable physical properties of fluid such as viscosity and Prandtl number. The Quasilinearization technique has been used on governing equations to transform nonlinear to linear equations and these equations are discretized by finite difference techniques to get numerical solutions. The effect of buoyancy parameters (λ), velocity ratio parameter (ε) and streamwise coordinator (ξ) on velocity profiles (F), temperature profiles (θ), local skin-friction coefficient (Cfx(ReLξexp(ξ))1/2) and the local Nusselt number (Nux(ReLξexp(ξ))−1/2) has been analyzed graphically based on numerical outcome. The magnitude of velocity profiles (F) increases and temperature profile decreases approximately by 4% and 16% with increases the buoyancy parameter from λ = 1 to λ = 3 at = 0.5 and ξ = 1.0. The skinfriction and heat transfer coefficient increases approximately by 22% and 27% with an increase in ξ from 0.5 to 1.0 at fixed ε = 0.5 and λ = 1.0. The variations of velocity profiles and temperature profiles have more impact with ε as compared to ξ and λ. The benchmark studies were carried out to validate the current results with previously published work and found to be in excellent agreement. © 2019 Wiley Periodicals, Inc.

Heat Transfer - Asian Research

Analysis of a boundary layer flow over moving an exponentially stretching surface with variable viscosity and Prandtl number

Purpose The purpose of the present study is to analyze the mixed convection water boundary layer flows over moving vertical plate with variable viscosity and Prandtl number. The non-linear partial differential equation governing the flow and thermal fields are presented in non-dimensional form by using appropriate transformation. The quasi-linearization technique in combination with implicit finite difference scheme has been adopted to solve the nonlinear-coupled partial differential equation. The numerical results are displayed graphically to illustrate the influence of various non-dimensional physical parameters on velocity and temperature. Further, the numerical results for local skin-friction coefficient and local Nusselt number are also reported. The present findings are compared with previously reported results, and these comparisons are found to be in excellent agreement.Design/methodology/approach The nonlinear partial differential equations governing the flow and thermal fields have been solved numerically using the implicit finite difference scheme in combination with the quasi-linearization technique. The numerical results are presented in terms of skin friction and heat transfer rate which are useful in determining the surface heat requirements for stabilizing the laminar boundary layer flow over a moving plate in water.Findings The effect of the ratio of free-stream velocity to the composite reference velocity is significant on the velocity profile. Near the wall region, as ratio of free stream velocity to composite reference velocity increases form 0.1 to 0.5, the velocity overshoot gets enhanced from 3 per cent to 41 per cent. The influence of buoyancy parameter and ration of free stream velocity to composite reference velocity on temperature profile is comparatively less than on velocity profiles. The increase in the skin friction coefficient is dependent on the increase in the value of ratio of free stream velocity to composite reference velocity if the buoyancy parameter λ is fixed and vice versa and increases in ΔT results in a decrease in N and Pr.Originality/value The present investigation is to deal with the solution of steady laminar water boundary layer flows over a moving plate with temperature-dependent viscosity and Prandtl number applicable for water using practical data. The fluid considered here is water, as it is one of the most common working fluids found in engineering applications.

International Journal of Numerical Methods for Heat and Fluid Flow

Analysis of mixed convection in water boundary layer flows over a moving vertical plate with variable viscosity and Prandtl number

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

Purpose: The purpose of this paper is to consider steady two-dimensional mixed convection flow along a vertical semi-infinite power-law stretching sheet. The velocity and temperature of the sheet are assumed to vary in a power-law form. Design/methodology/approach: The problem is formulated in terms of non-similar equations. These equations are solved numerically by an efficient implicit, iterative, finite-difference method in combination with a quasi-linearization technique. Findings: It was found that the skin-friction coefficient increased with the ratio of free-stream velocity to the composite reference velocity and the buoyancy parameter while it decreased with exponent parameter. The heat transfer rate increased with the Prandtl number, buoyancy parameter and the exponent parameter. Practical implications: A very useful source of information for researchers on the subject of convective flow over stretching sheets. Originality/value: This paper illustrates mixed convective flow over a power-law stretched surface with variable wall temperature. © Emerald Group Publishing Limited.

Fulltext

Mixed convection flow over a vertical power-law stretching sheet

The objective of this work is to study the effect of non-uniform double slot suction (injection) into steady laminar water boundary layers over a sphere with variable viscosity and Prandtl number. The implicit finite difference scheme with quasi-linearization technique has been applied to find the non-similar solutions and also to overcome the difficulties arising at the starting point of the stream-wise coordinate, at the edges of the slot and at the point of separation. Results indicate that the separation can be delayed by non-uniform double slot suction and also by moving the slots downstream direction but the effect of non-uniform double slot injection is just the opposite. © 2009 Elsevier Ltd. All rights reserved.

International Communications in Heat and Mass Transfer

Influence of double slot suction (injection) into water boundary layer flows over sphere

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

An analysis is performed to study the influence of temperature-dependent viscosity and Prandtl number on the steady nonsimilar laminar forced convection flow over a rotating sphere up to the point of separation. The difficulties arising at the starting point of the streamwise coordinate and at the point of separation are overcome by applying the method of quasilinear implicit finite difference scheme with an appropriate selection of finer step size along the streamwise direction. The results indicate that the effect of variable viscosity and Prandtl number is to move the point of separation downstream, but the rotation parameter has the reverse effect. For higher wall temperature than the free stream temperature, beyond a certain critical value of the dissipation parameter, the cooler free stream is unable to cool the hot wall due to the "heat cushion" provided by the frictional heating. The heat transfer rate is found to depend strongly on viscous dissipation but the skin frictions are little affected by it. In general, the results pertaining to variable fluid properties differ significantly from those of constant fluid properties.

Acta Mechanica

Steady nonsimilar axisymmetric water boundary layers with variable viscosity and Prandtl number

An analysis is performed to obtain the non-similar solution of a steady compressible laminar boundary layer flow over a yawed infinite circular cylinder with non-uniform slot injection (or suction) and non-uniform wall enthalpy. The difficulties arising at the starting point of the streamwise coordinate, at the edges of the slot and at the point of separation are overcome by applying the method of quasilinear implicit finite-difference scheme. 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 the reverse. An increase in March number and total enthalpy at wall causes the separation to occur earlier while cooling delays it. The non-uniform total enthalpy at the wall (i.e., the cooling or heating of the wall in a slot) has very little effect on the skin friction and hence on the point of separation. © 2001 Elsevier Science Ltd. All rights reserved.

Non-uniform mass transfer or wall enthalpy into a compressible flow over yawed cylinder

Journal of the American Chemical Society

CRC Handbook of Chemistry and Physics, 2009−2010, 90th ed. CRC Handbook of Chemistry and Physics, 2009−2010, 90th ed . Edited by David R. Lide , Editor-in-Chief, and W. M. “Mickey” Haynes , Associate Editor (National Institute of Standards and Technology, Gaithersburg, MD, USA). CRC Press (an imprint of Taylor & Francis Group): Boca Raton, FL.  2009 . $149.95. ISBN 978-1-4200-9084-0 .

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