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Article
Publication date: 5 October 2018

Prabhugouda Mallanagouda Patil and Shashikant A.

The purpose of this paper is to consider the influence of slip flow and thermal jump and to investigate its effects on unsteady mixed convection along an exponentially stretching

Abstract

Purpose

The purpose of this paper is to consider the influence of slip flow and thermal jump and to investigate its effects on unsteady mixed convection along an exponentially stretching surface. It is also intended to explore the influence of suction/injection and volumetric heat source/sink on the fluid flow.

Design/methodology/approach

The assumed problem is modelled into governing equations which are dimensional non-linear partial differential equations in nature. To obtain solutions, initially the governing equations were made non-dimensional by the suitable non-similar transformations. Then, the dimensionless non-linear partial differential equations are linearized with the aid of Quasilinearization technique. The so obtained equations are discretized by the implicit finite difference method.

Findings

The detailed analysis of the considered problem displays that the non-similarity variable reduces the velocity and temperature profiles. For higher values of mixed convection parameter, the magnitude of velocity profile as well as the Nusselt number increase. The unsteady variable diminishes the fluid flow. The higher values of velocity ratio parameter reduce the skin-friction coefficient. Further, the magnitude of skin-friction coefficient and heat transfer rate are to minimize for increasing values of partial slip and thermal jump parameters, respectively. Volumetric heat source and injection parameters are to rise the flow behavior within the momentum and thermal boundary layers significantly.

Originality/value

To the best of authors’ knowledge, no such investigation has been found in the literature.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 28 no. 9
Type: Research Article
ISSN: 0961-5539

Keywords

Article
Publication date: 7 April 2015

Tasawar Hayat, Bilal Ashraf, Sabir Ali Shehzad and Elbaz Abouelmagd

The purpose of this paper is to analyze the Eyring Powell fluid over an exponentially stretching surface. Heat and mass transfer effects are taken into account with nanoparticles…

Abstract

Purpose

The purpose of this paper is to analyze the Eyring Powell fluid over an exponentially stretching surface. Heat and mass transfer effects are taken into account with nanoparticles.

Design/methodology/approach

Appropriate transformations are employed to reduce the boundary layer partial differential equations into ordinary differential equations. Series solutions of the problem are obtained and impacts of physical parameters on the velocities, temperature and concentration profiles are discussed.

Findings

Numerical values of local Nusselt and Sherwood numbers for all the involved physical parameters are computed and analyzed. A comparative study between the present and previous results is made in a limiting sense. Local Nusselt number −′(0) increases by increasing ε, Pr, λ and N while it decreases for δ, N_{t{, N_{b} and Sc.

Originality/value

This analysis has not been discussed in the literature yet.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 25 no. 3
Type: Research Article
ISSN: 0961-5539

Keywords

Article
Publication date: 11 October 2018

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, impacts of…

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

Keywords

Article
Publication date: 6 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 electrically…

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

Keywords

Article
Publication date: 2 March 2015

Tasawar Hayat, Bilal Ashraf, Sabir Ali Shehzad, A. Alsaedi and N. Bayomi

– The purpose of this paper is to investigate the three-dimensional mixed convection flow of viscoelastic nanofluid induced by an exponentially stretching surface.

200

Abstract

Purpose

The purpose of this paper is to investigate the three-dimensional mixed convection flow of viscoelastic nanofluid induced by an exponentially stretching surface.

Design/methodology/approach

Similarity transformations are utilized to reduce the partial differential equations into the ordinary differential equations. The corresponding non-linear problems are solved by homotopy analysis method.

Findings

The authors found that an increase in thermophoresis and Brownian motion parameter enhance the temperature. Here thermal conductivity of fluid is enhanced due to which higher temperature and thicker thermal boundary layer thickness is obtained.

Practical implications

Heat and mass transfer effects in mixed convection flow over a stretching surface have numerous applications in the polymer technology and metallurgy. Such flows are encountered in metallurgical processes which involve the cooling of continuous strips or filaments by drawing them through a quiescent fluid and that in the process of drawing, these strips are sometimes stretched.

Originality/value

Three-dimensional flows over an exponentially stretching surface are very rare in the literature. Three-dimensional flow of viscoelastic nanofluid due to an exponentially stretching surface is first time investigated.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 25 no. 2
Type: Research Article
ISSN: 0961-5539

Keywords

Article
Publication date: 6 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 stretching

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. 18 no. 2
Type: Research Article
ISSN: 1708-5284

Keywords

Article
Publication date: 15 June 2018

Prabhugouda Mallanagouda Patil, Nafisabanu Kumbarwadi and Shashikant A.

The purpose of this paper is to investigate the magnetohydrodynamics mixed convection flow over an exponentially stretching surface in the presence of non-uniform heat source/sink…

Abstract

Purpose

The purpose of this paper is to investigate the magnetohydrodynamics mixed convection flow over an exponentially stretching surface in the presence of non-uniform heat source/sink and cross-diffusion. Adequate non-similar transformations are used to transform governing mixed convection boundary layer equations to dimensionless form.

Design/methodology/approach

These dimensionless partial differential equations are solved by using implicit finite difference scheme in conjunction with Quasi-linearization technique.

Findings

The effects of admissible parameters such as Eckert number (Ec), the ratio of buoyancy forces parameter (N), non-uniform heat source/sink, Soret and Dufour numbers on flow, temperature and concentration distributions are discussed and analysed through graphs. In addition, the results for skin friction coefficient, Sherwood number and Nusselt number are presented and discussed graphically.

Originality/value

In literature, no research work has been found in similar to this research paper.

Details

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

Keywords

Article
Publication date: 20 September 2011

T. Javed, M. Sajid, Z. Abbas and N. Ali

This paper looks into the rotating flow of an incompressible viscous fluid over an exponentially stretching continuous surface. The flow is governed by non‐linear partial…

Abstract

Purpose

This paper looks into the rotating flow of an incompressible viscous fluid over an exponentially stretching continuous surface. The flow is governed by non‐linear partial differential equations. A non‐similar solution is developed after transforming the governing equations using two different numerical techniques namely Keller‐box and shooting methods. The influence of the non‐dimensional local rotating parameter Ω on the velocity fields and skin friction coefficients is analyzed and discussed.

Design/methodology/approach

In this paper, the authors have used the well‐known numerical methods, Keller‐box and shooting.

Findings

It is observed that for the increase in the rotation velocity of the frame there is a reduction in the boundary layer thickness and an increase in the drag force at the surface.

Originality/value

The present study is concerned with the boundary layer flow of a rotating viscous fluid over an exponentially stretching sheet. Numerical solutions are found. To the best of the authors' knowledge, this is the first investigation of the topic.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 21 no. 7
Type: Research Article
ISSN: 0961-5539

Keywords

Article
Publication date: 2 March 2015

M.M. Rahman, Alin V. Rosca and I. Pop

The purpose of this paper is to numerically solve the problem of steady boundary layer flow of a nanofluid past a permeable exponentially shrinking surface with convective surface…

Abstract

Purpose

The purpose of this paper is to numerically solve the problem of steady boundary layer flow of a nanofluid past a permeable exponentially shrinking surface with convective surface condition. The Buongiorno’s mathematical nanofluid model has been used.

Design/methodology/approach

Using appropriate similarity transformations, the basic partial differential equations are transformed into ordinary differential equations. These equations have been solved numerically for different values of the governing parameters, stretching/shrinking parameter λ, suction parameter s, Prandtl number Pr, Lewis number Le, Biot number, the Brownian motion parameter Nb and the thermophoresis parameter Nt, using the bvp4c function from Matlab. The effects of these parameters on the reduced skin friction coefficient, heat transfer from the surface of the sheet, Sherwood number, dimensionless velocity, and temperature and nanoparticles volume fraction distributions are presented in tables and graphs, and are in details discussed.

Findings

Numerical results are obtained for the reduced skin-friction, heat transfer and for the velocity and temperature profiles. The results indicate that dual solutions exist for the shrinking case (λ<0). A stability analysis has been performed to show that the upper branch solutions are stable and physically realizable, while the lower branch solutions are not stable and, therefore, not physically possible. In addition, it is shown that for a regular fluid (Nb=Nt=0) a very good agreement exists between the present numerical results and those reported in the open literature.

Research limitations/implications

The problem is formulated for an incompressible nanofluid with no chemical reactions, dilute mixture, negligible viscous dissipation, negligible radiative heat transfer and a new boundary condition is imposed on nanoparticles and base fluid locally in thermal equilibrium. The analysis reveals that the boundary layer separates from the plate. Beyond the turning point it is not possible to get the solution based on the boundary-layer approximations. To obtain further solutions, the full basic partial differential equations have to be solved.

Originality/value

The present results are original and new for the boundary-layer flow and heat transfer past a shrinking sheet in a nanofluid. Therefore, this study would be important for the researchers working in the relatively new area of nanofluids in order to become familiar with the flow behavior and properties of such nanofluids. The results show that in the presence of suction the dual solutions may exist for the flow of a nanofluid over an exponentially shrinking as well as stretching surface.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 25 no. 2
Type: Research Article
ISSN: 0961-5539

Keywords

Article
Publication date: 2 August 2013

M. Mustafaa, T. Hayat and S. Obaidat

This paper aims to discuss the flow and heat transfer characteristics over an exponentially stretching sheet in a nanofluid with convective boundary conditions. The effects of…

Abstract

Purpose

This paper aims to discuss the flow and heat transfer characteristics over an exponentially stretching sheet in a nanofluid with convective boundary conditions. The effects of Brownian motion and thermophoresis are also accounted.

Design/methodology/approach

The flow is therefore governed by the Brownian motion parameter (Nb), the thermophoresis parameter (Nt), the Prandtl number (Pr), the Lewis number (Le) and the Biot number (Bi). The analytic solutions of the arising differential systems have been obtained by homotopy analysis method (HAM).

Findings

The temperature rises and the thermal boundary layer thickens with an increase in the Brownian motion and thermophoresis parameters. The surface heat and mass transfer appreciably increase with an increase in the Prandtl and Lewis numbers.

Originality/value

The presented results also include the analysis for constant wall temperature.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 23 no. 6
Type: Research Article
ISSN: 0961-5539

Keywords

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