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Article
Publication date: 7 May 2020

S. Das, R.R. Patra and R.N. Jana

The purpose of this study is to present the significance of Joule heating, viscous dissipation, magnetic field and slip condition on the boundary layer flow of an…

Abstract

Purpose

The purpose of this study is to present the significance of Joule heating, viscous dissipation, magnetic field and slip condition on the boundary layer flow of an electrically conducting Boussinesq couple-stress fluid induced by an exponentially stretching sheet embedded in a porous medium under the effect of the magnetic field of the variable kind. The heat transfer phenomenon is accounted for under thermal radiation, Joule and viscous dissipation effects.

Design/methodology/approach

The governing nonlinear partial differential equations are transformed to the nonlinear ordinary differential equations (ODEs) by using some appropriate dimensionless variables and then the consequential nonlinear ODEs are solved numerically by making the use of the well-known shooting iteration technique along with the standard fourth-order Runge–Kutta integration scheme. The impact of emerging flow parameters on velocity and temperature profiles, streamlines, local skin friction coefficient and Nusselt number are described comprehensively through graphs and tables.

Findings

Results reveal that the velocity profile is observed to diminish considerably within the boundary layer in the presence of a magnetic field and slip condition. The enhanced radiation parameter is to decline the temperature field. The slip effect is favorable for fluid flow.

Originality/value

Till now, slip effect on Boussinesq couple-stress fluid over an exponentially stretching sheet embedded in a porous medium has not been explored. The present results are validated with the previously published study and found to be highly satisfactory.

Details

Multidiscipline Modeling in Materials and Structures, vol. 16 no. 5
Type: Research Article
ISSN: 1573-6105

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Article
Publication date: 3 September 2018

Jayarami Reddy Konda, Madhusudhana N.P. and Ramakrishna Konijeti

The purpose of this paper is to discuss the flow of Casson nanofluid past a nonlinear permeable stretching sheet in the presence of thermal radiation, chemical reaction…

Abstract

Purpose

The purpose of this paper is to discuss the flow of Casson nanofluid past a nonlinear permeable stretching sheet in the presence of thermal radiation, chemical reaction, viscous dissipation, heat source, and magnetohydrodynamics.

Design/methodology/approach

Appropriate transformations are used to convert the boundary layer equations into nonlinear ODEs which are then solved numerically by using the Runge-Kutta-Fehlberg fourth-fifth order method along with shooting technique.

Findings

Solution of this systems is obtained for velocity, temperature, and concentration profiles. Graphical illustrations are added to discuss the effect of evolving parameters against above-mentioned distributions. Tabular values of local skin friction factor, local Nusselt number, and local Sherwood number are also added and studied accordingly.

Originality/value

A good agreement of the present results has been observed by comparing with the existing literature results. It is noted that skin friction coefficient, Nusselt number, and Sherwood number decrease with Casson parameter and increase with suction parameter.

Details

Multidiscipline Modeling in Materials and Structures, vol. 14 no. 3
Type: Research Article
ISSN: 1573-6105

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Article
Publication date: 7 December 2020

S. Das, Akram Ali and R.N. Jana

In this communication, a theoretical simulation is aimed to characterize the Darcy–Forchheimer flow of a magneto-couple stress fluid over an inclined exponentially…

Abstract

Purpose

In this communication, a theoretical simulation is aimed to characterize the Darcy–Forchheimer flow of a magneto-couple stress fluid over an inclined exponentially stretching sheet. Stokes’ couple stress model is deployed to simulate non-Newtonian microstructural characteristics. Two different kinds of thermal boundary conditions, namely, the prescribed exponential order surface temperature (PEST) and prescribed exponential order heat flux, are considered in the heat transfer analysis. Joule heating (Ohmic dissipation), viscous dissipation and heat source/sink impacts are also included in the energy equation because these phenomena arise frequently in magnetic materials processing.

Design/methodology/approach

The governing partial differential equations are transformed into nonlinear ordinary differential equations (ODEs) by adopting suitable similar transformations. The resulting system of nonlinear ODEs is tackled numerically by using the Runge–Kutta fourth (RK4)-order numerical integration scheme based on the shooting technique. The impacts of sundry parameters on stream function, velocity and temperature profiles are viewed with the help of graphical illustrations. For engineering interests, the physical implication of the said parameters on skin friction coefficient, Nussult number and surface temperature are discussed numerically through tables.

Findings

As a key outcome, it is noted that the augmented Chandrasekhar number, porosity parameter and Forchhemeir parameter diminish the stream function as well as the velocity profile. The behavior of the Darcian drag force is similar to the magnetic field on fluid flow. Temperature profiles are generally upsurged with the greater magnetic field, couple stress parameter and porosity parameter, and are consistently higher for the PEST case.

Practical implications

The findings obtained from this analysis can be applied in magnetic material processing, metallurgy, casting, filtration of liquid metals, gas-cleaning filtration, cooling of metallic sheets, petroleum industries, geothermal operations, boundary layer resistors in aerodynamics, etc.

Originality/value

From the literature review, it has been found that the Darcy–Forchheimer flow of a magneto-couple stress fluid over an inclined exponentially stretching surface with heat flux conditions is still scarce. The numerical data of the present results are validated with the already existing studies under limited cases and inferred to have good concord.

Details

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

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Article
Publication date: 5 September 2016

Macha Madhu, Naikoti Kishan and A. Chamkha

The purpose of this paper is to study the boundary layer flow and heat transfer of a power-law non-Newtonian nanofluid over a non-linearly stretching sheet.

Abstract

Purpose

The purpose of this paper is to study the boundary layer flow and heat transfer of a power-law non-Newtonian nanofluid over a non-linearly stretching sheet.

Design/methodology/approach

The governing equations describing the problem are transformed into a nonlinear ordinary differential equations by suitable similarity transformations. The resulting equations for this investigation are solved numerically by using the variational finite element method.

Findings

It was found that the local Nusselt number increases by increasing the Prandtl number, stretching sheet parameter and decreases by increasing the power-law index, thermophoresis parameter and Lewis number. Increases in the stretching sheet parameter, Prandtl number and thermophoresis parameter decrease the local Sherwood number values. The effects of Brownian motion and Lewis number lead to increases in the local Sherwood number values.

Originality/value

The work is relatively original as very little work has been reported on non-Newtonian nanofluids.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 26 no. 7
Type: Research Article
ISSN: 0961-5539

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Article
Publication date: 1 December 1943

William Schroeder and Thomas H. Hazlett

THE modern aeroplane is constructed largely from sheet metal. As such, the most important production problems are those of sheet metal forming, and assembling. Production…

Abstract

THE modern aeroplane is constructed largely from sheet metal. As such, the most important production problems are those of sheet metal forming, and assembling. Production is here considered as not only the act of forming and assembling the required number of parts, but also the making of forming tools, and all processing of parts such as heat‐treating. Only that phase of the above concept of production which deals with the tooling for production and the forming and heat‐treating will be considered here. The design of the aircraft parts will also be discussed somewhat, for it is obvious that the design of the part (designed shape and materials used) frequently determines whether the part can or cannot be readily made.

Details

Aircraft Engineering and Aerospace Technology, vol. 15 no. 12
Type: Research Article
ISSN: 0002-2667

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Article
Publication date: 20 September 2019

Rusya Iryanti Yahaya, Norihan M. Arifin, Roslinda Nazar and Ioan Pop

The purpose of this paper is to study the flow and heat transfer of a hybrid nanofluid, Cu–Al2O3/water, past a permeable stretching/shrinking sheet. The effects of…

Abstract

Purpose

The purpose of this paper is to study the flow and heat transfer of a hybrid nanofluid, Cu–Al2O3/water, past a permeable stretching/shrinking sheet. The effects of Brownian motion and thermophoresis are considered here.

Design/methodology/approach

Similarity transformations are used to reduce the governing partial differential equations to a system of ordinary (similarity) differential equations. A MATLAB solver called the bvp4c is then used to compute the numerical solutions of equations (12) to (14) subject to the boundary conditions of equation (15). Then, the effects of various physical parameters on the flow and thermal fields of the hybrid nanofluid are analyzed.

Findings

Multiple (dual) solutions are found for the basic boundary layer equations. A stability analysis is performed to see which solutions are stable and, therefore, applicable in practice and which are not stable. Besides that, a comparison is made between the hybrid nanofluid and a traditional nanofluid, Cu/water. The skin friction coefficient and Nusselt number of the hybrid nanofluid are found to be greater than that of the other nanofluid. Thus, the hybrid nanofluid has a higher heat transfer rate than the other nanofluid. However, the increase in the shrinking parameter reduces the velocity of the hybrid nanofluid.

Originality/value

The present results are original and new for the study of the flow and heat transfer past a permeable stretching/shrinking sheet in Cu–Al2O3/water hybrid nanofluid.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 30 no. 3
Type: Research Article
ISSN: 0961-5539

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Article
Publication date: 4 June 2018

Mohd Ezad Hafidz Hafidzuddin, Roslinda Nazar, Norihan M. Arifin and Ioan Pop

This study aims to investigate the unsteady two-dimensional viscous flow and heat transfer over an unsteady permeable stretching/shrinking sheet (surface) with generalized…

Abstract

Purpose

This study aims to investigate the unsteady two-dimensional viscous flow and heat transfer over an unsteady permeable stretching/shrinking sheet (surface) with generalized slip velocity condition.

Design/methodology/approach

Similarity transformation is used to reduce the system of partial differential equations into a system of nonlinear ordinary differential equations. The resulting equations are then solved numerically using “bvp4c” function in MATLAB software.

Findings

Dual solutions are found for a certain range of the unsteady, suction and stretching/shrinking parameters. Stability analysis is performed, and it is revealed that the first (upper branch) solution is stable and physically realizable, whereas the second (lower branch) solution is unstable.

Practical implications

The results obtained can be used to explain the characteristics and applications of the generalized slip in boundary layer flow. Such condition is applied for particulate fluids such as foams, emulsions, polymer solutions and suspensions. Furthermore, the phenomenon of stretching/shrinking sheet can be found on the manufacturing of polymer sheets, rising and shrinking balloon or moving and shrinking polymer film.

Originality/value

The present numerical results are original and new for the study of unsteady flow and heat transfer over a permeable stretching/shrinking sheet with generalized slip velocity.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 28 no. 6
Type: Research Article
ISSN: 0961-5539

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Article
Publication date: 18 May 2010

P.M. Patil, S. Roy and Ali J. Chamkha

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…

Abstract

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.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 20 no. 4
Type: Research Article
ISSN: 0961-5539

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Article
Publication date: 1 December 2000

K.V. Prasad, M. Subhas Abel and Sujit Kumar Khan

Visco‐elastic fluid flow and heat transfer in a porous medium over a non‐isothermal stretching sheet have been investigated. The flow is influenced by linearly stretching

Abstract

Visco‐elastic fluid flow and heat transfer in a porous medium over a non‐isothermal stretching sheet have been investigated. The flow is influenced by linearly stretching the sheet in the presence of suction, blowing and impermeability of the wall. Thermal conductivity is considered to vary linearly with temperature. The intricate non‐linear problem has been solved numerically by shooting technique with fourth order Runge‐Kutta algorithm after using perturbation method. The zeroth order solutions are obtained analytically in the form of Kummer’s function. An analysis has been carried out for two different cases, namely prescribed surface temperature (PST) and prescribed heat flux (PHF) to get the effect of porosity and visco‐elasticity at various physical situations. The important finding is that the effect of visco‐elasticity and porosity is to increase the wall temperature in case of blowing and to decrease in both the cases of suction and when the stretching sheet is impermeable.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 10 no. 8
Type: Research Article
ISSN: 0961-5539

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Article
Publication date: 26 June 2020

Asgar Ali, R.N. Jana and S. Das

This paper aims to assess the effectiveness of Hall currents and power-law slip condition on the hydromagnetic convective flow of an electrically conducting power-law…

Abstract

Purpose

This paper aims to assess the effectiveness of Hall currents and power-law slip condition on the hydromagnetic convective flow of an electrically conducting power-law fluid over an exponentially stretching sheet under the effect of a strong variable magnetic field and thermal radiation. Flow formation is developed using the rheological expression of a power-law fluid.

Design/methodology/approach

The nonlinear partial differential equations describing the flow are transformed into the nonlinear ordinary differential equations by employing the local similarity transformations and then solved numerically by an effective numerical approach, namely, fourth-order Runge–Kutta integration scheme, along with the shooting iteration technique. The numerical solution is computed for different parameters by using the computational software MATLAB bvp4c. The bvp4c function uses the finite difference code as the default. This method is a fourth-order collocation method. The impacts of thermophysical parameters on velocity and temperature distributions, skin friction coefficients and Nusselt number in the boundary layer regime are exhibited through graphs and tables and deliberated with proper physical justification.

Findings

Our investigation conveys that Hall current has an enhancing behavior on velocity profiles and reduces skin friction coefficients. An increase in the power-law index is observed to deplete velocity and temperature evolution. The temperature for the pseudo-plastic (shear-thinning) fluid is relatively higher than the corresponding temperature of the dilatant (shear-thickening) fluid. The streamlines are more distorted and have low intensity near the surface of the sheet for the dilatant fluid than the pseudo-plastic fluid.

Social implications

The study is pertinent to the expulsion of polymer sheet and photographic films, hydrometallurgical industry, electrically conducting polymer dynamics, magnetic material processing, solutions and melts of polymer processing, purification of molten metals from nonmetallic. The results obtained in this work can be relevant in fluid mechanics and heat transfer applications.

Originality/value

The present problem has, to the authors' knowledge, not communicated thus far in the scientific literature. A comparative study with the published works is conducted to verify the accuracy of the present study. The results obtained in this analysis are significant in providing the standards for validating the accuracies of some numerical or empirical methods.

Details

Multidiscipline Modeling in Materials and Structures, vol. 17 no. 1
Type: Research Article
ISSN: 1573-6105

Keywords

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