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Article
Publication date: 8 June 2021

Sanatan Das, Akram Ali and Rabindra Nath Jana

Outstanding features such as thermal conductivity and superior electrical conductivity of nanofluids unfold a new window in the context of their extensive applications in…

Abstract

Purpose

Outstanding features such as thermal conductivity and superior electrical conductivity of nanofluids unfold a new window in the context of their extensive applications in engineering and industrial domains. The purpose of this study to simulate numerically the magneto-nanofluid flow and heat transfer over a curved stretching surface. Heat transport is explored in the presence of viscous dissipation. At the curved surface, the convective boundary condition is adopted. Three different nanoparticles, namely, copper, aluminium oxide and titanium dioxide are taken into consideration because of easily available in nature.

Design/methodology/approach

The basic flow equations are framed in terms of curvilinear coordinates. The modelled partial differential equations are transformed into a system of non-linear ordinary differential equations by means of appropriate similarity transformation. The subsequent non-linear system of equations is then solved numerically by using the Runge–Kutta–Felhberg method with the shooting scheme via bvp4c MATLAB built-in function. Impacts of various physical parameters on velocity, pressure and temperature distributions, local skin-friction coefficient, local Nusselt number and wall temperature are portrayed through graphs and tables followed by a comprehensive debate and physical interpretation.

Findings

Graphical results divulge that augmenting values of the magnetic parameter cause a decline in velocity profiles and stream function inside the boundary layer. The magnitude of the pressure function inside the boundary layer reduces for higher estimation of curvature parameter, and it is also zero when the curvature parameter goes to infinity. Furthermore, the temperature is observed in a rising trend with growing values of the magnetic parameter and Biot number.

Practical implications

This research study is very pertinent to the expulsion of polymer sheet and photographic films, metallurgical industry, electrically-conducting polymer dynamics, magnetic material processing, rubber and polymer sheet processing, continuous casting of metals, fibre spinning, glass blowing and fibre, wire and fibre covering and sustenance stuff preparing, etc.

Originality/value

Despite the huge amount of literature available, but still, very little attention is given to simulate the flow configuration due to the curved stretching surface with the convective boundary condition. Very few papers have been examined on this topic and found that its essence inside the boundary layer is not any more insignificant than on account of a stretching sheet. A numerical comparison with the published works is conducted to verify the accuracy of the present study.

Details

World Journal of Engineering, vol. 18 no. 6
Type: Research Article
ISSN: 1708-5284

Keywords

Article
Publication date: 7 November 2016

Ioan Pop, Siti Suzilliana Putri Mohamed Isa, Norihan M. Arifin, Roslinda Nazar, Norfifah Bachok and Fadzilah M. Ali

The purpose of this paper is to theoretically study the problem of the unsteady boundary layer flow past a permeable curved stretching/shrinking surface in the presence of a…

Abstract

Purpose

The purpose of this paper is to theoretically study the problem of the unsteady boundary layer flow past a permeable curved stretching/shrinking surface in the presence of a uniform magnetic field. The governing nonlinear partial differential equations are converted into ordinary differential equations by similarity transformation, which are then solved numerically.

Design/methodology/approach

The transformed system of ordinary differential equations was solved using a fourth-order Runge-Kutta integration scheme. Results for the reduced skin friction coefficient and velocity profiles are presented through graphs and tables for several sets of values of the governing parameters. The effects of these parameters on the flow characteristics are thoroughly examined.

Findings

Results show that for the both cases of stretching and shrinking surfaces, multiple solutions exist for a certain range of the curvature, mass suction, unsteadiness, stretching/shrinking parameters and magnetic field parameter.

Originality/value

The paper describes how multiple (dual) solutions for the flow reversals are obtained. It is shown that the solutions exist up to a critical value of the shrinking parameter, beyond which the boundary layer separates from the surface and the solution based upon the boundary layer approximations is not possible.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 26 no. 8
Type: Research Article
ISSN: 0961-5539

Keywords

Article
Publication date: 3 June 2020

Taseer Muhammad

The purpose of this article is to analyze the magnetohydrodynamic viscous liquid flow with heat absorption/generation. Flow is induced by an unsteady stretching curved surface. A…

Abstract

Purpose

The purpose of this article is to analyze the magnetohydrodynamic viscous liquid flow with heat absorption/generation. Flow is induced by an unsteady stretching curved surface. A time-dependent magnetic field is utilized.

Design/methodology/approach

The resulting nonlinear system is solved through shooting method.

Findings

An increment in the values of curvature A and unsteadiness parameters correspond to higher velocity, temperature and concentration fields. There is a reduction in the temperature and related layer via Prandtl number. Skin friction is increasing factor of magnetic number. Local Nusselt and Sherwood numbers are lower for greater magnetic number.

Originality/value

To the best of author's knowledge, no such consideration has been given in the literature yet.

Details

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

Keywords

Article
Publication date: 25 June 2019

Sumaira Qayyum, Tasawar Hayat and Ahmed Alsaedi

Investigation for convective flow of water-based nanofluid (composed of ferric oxide asnanoparticles) by curved stretching sheet of variable thickness is made. Bejan number…

Abstract

Purpose

Investigation for convective flow of water-based nanofluid (composed of ferric oxide asnanoparticles) by curved stretching sheet of variable thickness is made. Bejan number andentropy generation analysis is presented in presence of viscous dissipation, mixed convectionand porous medium.

Design/methodology/approach

In this paper, by using NDSolve of MATHEMATICA, the nonlinear system of equations is solved. Velocity, temperature, Bejan number and entropy generation for involved dimensionless variables are discussed.

Findings

Increase in velocity is depicted for larger curvature parameter, and opposite trend is witnessed for higher nanoparticle volume concentration. Enhancement in temperature is seen for higher Eckert number while reverse behavior is noticed for larger curvature parameter. Entropy rate increases for variation of curvature parameter, Brinkman number and nanoparticle volume fraction. Bejan number decays for mixed convection and curvature parameters.

Originality/value

To the authors’ knowledge, there exists no study yet which describes flow by curved sheet of variable thickness. Such consideration with nanoparticles seems important task. Thus, the main objective here is to determine entropy generation in ferromagnetic nanofluid flow due to variable thickened curved stretching surface. Additionally, effects of Joule heating, porous medium, mixed convection and viscous dissipation are taken into account.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 29 no. 9
Type: Research Article
ISSN: 0961-5539

Keywords

Article
Publication date: 28 June 2019

Muhammad Ijaz Khan, Khursheed Muhammad, Tasawar Hayat, Shahid Farooq and Ahmed Alsaedi

This paper aims to discuss the salient aspects of the Darcy–Forchheimer flow of viscous liquid in carbon nanotubes (CNTs). CNTs are considered as nanofluid, and water is taken as…

Abstract

Purpose

This paper aims to discuss the salient aspects of the Darcy–Forchheimer flow of viscous liquid in carbon nanotubes (CNTs). CNTs are considered as nanofluid, and water is taken as the continuous phase liquid. The flow features are discussed via curved surface. Water is taken as the base liquid. Flow is generated via nonlinear stretching. Energy expression is modeled subject to heat generation/absorption. Furthermore, convective conditions are considered at the boundary. The Xue model is used in the mathematical modeling which describes the features of nanomaterials. Both types of CNTs are considered, i.e. single-walled CNTs and multi-walled CNTs.

Design/methodology/approach

Appropriate transformations are used to convert the flow expressions into dimensionless differential equations. The bvp4c method is used for solution development.

Findings

Velocity enhances via higher estimations of nanoparticles volume fraction while decays for higher Forchheimer number, curvature parameter, behavior index and porosity parameter. Furthermore, thermal field is an increasing function of nanoparticle volume fraction, behavior index, Forchheimer number and porosity parameter.

Originality/value

Here, the authors have discussed two-dimensional CNTs-based nanomaterial Darcy–Forchheimer flow of viscous fluid over a curved surface. The authors believe that all the outcomes and numerical techniques are original and have not been published elsewhere.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 29 no. 9
Type: Research Article
ISSN: 0961-5539

Keywords

Article
Publication date: 14 December 2018

Rai Sajjad Saif, T. Hayat, R. Ellahi, Taseer Muhammad and A. Alsaedi

The purpose of present communication is to analyze Darcy–Forchheimer flow of viscous nanofluid by curved stretchable surface. Flow in porous medium is characterized by…

Abstract

Purpose

The purpose of present communication is to analyze Darcy–Forchheimer flow of viscous nanofluid by curved stretchable surface. Flow in porous medium is characterized by Darcy–Forchheimer relation. Brownian diffusion and thermophoresis are considered. Convective heat and mass boundary conditions are also used at the curved stretchable surface.

Design/methodology/approach

The resulting nonlinear system is solved through shooting technique.

Findings

Skin friction coefficient is enhanced for larger porosity parameter and inertia coefficient while reverse trend is noticed for curvature parameter. Local Nusselt number is enhanced for higher Prandtl number and thermal Biot number, whereas the opposite trend is seen via curvature parameter, porosity parameter, inertia coefficient, thermophoresis parameter and Brownian motion parameter. Local Sherwood number is enhanced for Schmidt number, Brownian motion parameter and concentration Biot number, while reverse trend is noticed for curvature parameter, porosity parameter, inertia coefficient and thermophoresis parameter.

Originality/value

To the best of author’s knowledge, no such consideration has been given in the literature yet.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 29 no. 1
Type: Research Article
ISSN: 0961-5539

Keywords

Article
Publication date: 7 February 2022

Nasser S. Elgazery, Asmaa F. Elelamy, Elena Bobescu and R. Ellahi

The study aims to determine an efficiency of external magnetic field on the bacteria surrounded by thousands of magnetic magnetite nanoparticles. The interstitial nanoliquid in…

Abstract

Purpose

The study aims to determine an efficiency of external magnetic field on the bacteria surrounded by thousands of magnetic magnetite nanoparticles. The interstitial nanoliquid in which an artificial bacteria swims in biological cell is utilized with variable thermal conductivity. Two dimensions unsteady motion of second grade fluid are considered. The stretching wall is taken as a curved surface pattern.

Design/methodology/approach

The mathematical results have been obtained by Chebyshev pseudospectral method.

Findings

The impact of the various governing parameters is described by numerical tables and diagrams. It is proven that the pure blood velocity curves are higher when compared with the magnetite/blood. It is demonstrated from clinical disease that dangerous tumors show diminished blood flow. This study concludes that the blood velocity profile increases by increasing the values of fluid parameters. This implies that the medication conveyance therapy lessens the tumor volume and helps in annihilating malignancy cells. The blood temperature distribution raises as the magnetite nanoparticles concentration increases. Consequently, the physical properties of the blood can be enhanced by immersing the magnetite nanoparticles. Further, the present outcomes cleared the thermal conductivity as, a variable function of the temperature, has an important role to enhance the heat transfer rate.

Originality/value

To the best of authors’ knowledge, this study is reported for the first time.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 32 no. 9
Type: Research Article
ISSN: 0961-5539

Keywords

Article
Publication date: 29 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 fluid over…

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

Article
Publication date: 22 July 2019

Waqar Azeem Khan, Muhammad Waqas, Mehboob Ali, F. Sultan, M. Shahzad and M. Irfan

This paper aims to develop a mathematical model featuring Brownian motion and thermophoresis. The idea of curved stretching subjected to time-dependent non-Newtonian (Sisko) fluid…

Abstract

Purpose

This paper aims to develop a mathematical model featuring Brownian motion and thermophoresis. The idea of curved stretching subjected to time-dependent non-Newtonian (Sisko) fluid flow is introduced.

Design/methodology/approach

Shooting scheme is implemented to compute nonlinear systems.

Findings

Velocity profile of Sisko magnetonanofluid enhances for augmented values of curvature parameter.

Originality/value

To the best of the authors’ knowledge, no such analysis has yet been reported.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 29 no. 9
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

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