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Article
Publication date: 18 April 2017

Gauri Shanker Seth, Rohit Sharma, Manoj Kumar Mishra and Ali J. Chamkha

The purpose of this paper is to assess steady, two-dimensional natural convection flow of a viscoelastic, incompressible, electrically conducting and optically thick…

Abstract

Purpose

The purpose of this paper is to assess steady, two-dimensional natural convection flow of a viscoelastic, incompressible, electrically conducting and optically thick heat-radiating nanofluid over a linearly stretching sheet in the presence of uniform transverse magnetic field taking Dufour and Soret effects into account.

Design/methodology/approach

The governing boundary layer equations are transformed into a set of highly non-linear ordinary differential equations using suitable similarity transforms. Finite element method is used to solve this boundary value problem. Effects of pertinent flow parameters on the velocity, temperature, solutal concentration and nanoparticle concentration are described graphically. Also, effects of pertinent flow parameters on the shear stress, rate of heat transfer, rate of solutal concentration and rate of nanoparticle concentration at the sheet are discussed with the help of numerical values presented in graphical form. All numerical results for mono-diffusive nanofluid are compared with those of double-diffusive nanofluid.

Findings

Numerical results obtained in this paper are compared with earlier published results and are found to be in excellent agreement. Viscoelasticity, magnetic field and nanoparticle buoyancy parameter tend to enhance the wall velocity gradient, whereas thermal buoyancy force has a reverse effect on it. Radiation, Brownian and thermophoretic diffusions tend to reduce wall temperature gradient, whereas viscoelasticity has a reverse effect on it. Nanofluid Lewis number tends to enhance wall nanoparticle concentration gradient.

Originality/value

Study of this problem may find applications in engineering and biomedical sciences,e.g. in cooling and process industries and in cancer therapy.

Details

Engineering Computations, vol. 34 no. 2
Type: Research Article
ISSN: 0264-4401

Keywords

Article
Publication date: 4 January 2016

T. Hayat, M. Waqas, Sabir Ali Shehzad and A. Alsaedi

The purpose of this paper is to examine the effects of variable thermal conductivity in mixed convection flow of viscoelastic nanofluid due to a stretching cylinder with…

Abstract

Purpose

The purpose of this paper is to examine the effects of variable thermal conductivity in mixed convection flow of viscoelastic nanofluid due to a stretching cylinder with heat source/sink.

Design/methodology/approach

The authors have computed the existence of the solution for Walter’s B and second grade fluids corresponding to Pr=0.5 and Pr=1.5. Skin-friction coefficient, local Nusselt and Sherwood numbers are computed numerically for different values of emerging parameters.

Findings

A comparative study with the existing solutions in a limiting sense is made and analyzed. The authors found that the dimensionless velocity filed and momentum boundary layer thickness are increased when the values of viscoelastic parameter increase. The present non-Newtonian fluid flow reduces to the viscous flow in the absence of viscoelastic parameter. The larger values of viscoelastic parameter corresponds to the higher values of local Nusselt and Sherwood numbers.

Originality/value

No such analysis exists in the literature yet.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 26 no. 1
Type: Research Article
ISSN: 0961-5539

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.

188

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: 11 September 2019

Muhammad Ayub, Muhammad Yousaf Malik, Misbah Ijaz, Marei Saeed Alqarni and Ali Saeed Alqahtani

The purpose of this paper is to explore the novel aspects of activation energy in the nonlinearly convective flow of Walter-B nanofluid in view of Cattaneo–Christov…

Abstract

Purpose

The purpose of this paper is to explore the novel aspects of activation energy in the nonlinearly convective flow of Walter-B nanofluid in view of Cattaneo–Christov double-diffusion model over a permeable stretched sheet. Features of nonlinear thermal radiation, dual stratification, non-uniform heat generation/absorption, MHD and binary chemical reaction are also evaluated for present flow problem. Walter-B nanomaterial model is employed to describe the significant slip mechanism of Brownian and thermophoresis diffusions. Generalized Fourier’s and Fick’s laws are examined through Cattaneo–Christov double-diffusion model. Modified Arrhenius formula for activation energy is also implemented.

Design/methodology/approach

Several techniques are employed for solving nonlinear differential equations. The authors have used a homotopy technique (HAM) for our nonlinear problem to get convergent solutions. The homotopy analysis method (HAM) is a semi-analytical technique to solve nonlinear coupled ordinary/partial differential equations. The capability of the HAM to naturally display convergence of the series solution is unusual in analytical and semi-analytic approaches to nonlinear partial differential equations. This analytical method has the following great advantages over other techniques:

  • It provides a series solution without depending upon small/large physical parameters and applicable for not only weakly but also strongly nonlinear problems.

  • It guarantees the convergence of series solutions for nonlinear problems.

  • It provides us a great choice to select the base function of the required solution and the corresponding auxiliary linear operator of the homotopy.

It provides a series solution without depending upon small/large physical parameters and applicable for not only weakly but also strongly nonlinear problems.

It guarantees the convergence of series solutions for nonlinear problems.

It provides us a great choice to select the base function of the required solution and the corresponding auxiliary linear operator of the homotopy.

Brief mathematical description of HAM technique (Liao, 2012; Mabood et al., 2016) is as follows. For a general nonlinear equation:

(1) N [ u ( x ) ] = 0 ,

where N denotes a nonlinear operator, x the independent variables and u(x) is an unknown function, respectively. By means of generalizing the traditional homotopy method, Liao (1992) creates the so-called zero-order deformation equation:

(2) ( 1 q ) L [ u ˆ ( x ; q ) u o ( x ) ] = q h H ( x ) N [ u ˆ ( x ; q ) ] ,

here q∈[0, 1] is the embedding parameter, H(x) ≠ 0 is an auxiliary function, h(≠ 0) is a nonzero parameter, L is an auxiliary linear operator, uo(x) is an initial guess of u(x) and u ˆ ( x ; q ) is an unknown function, respectively. It is significant that one has great freedom to choose auxiliary things in HAM. Noticeably, when q=0 and q=1, following holds:

(3) u ˆ ( x ; 0 ) = u o ( x ) and u ˆ ( x ; 1 ) = u ( x ) ,

Expanding u ˆ ( x ; q ) in Taylor series with respect to (q), we have:

(4) u ˆ ( x ; q ) = u o ( x ) + m = 1 u m ( x ) q m , where u m ( x ) = 1 m ! m u ˆ ( x ; q ) q m | q = 0 .

If the initial guess, the auxiliary linear operator, the auxiliary h and the auxiliary function are selected properly, then the series (4) converges at q=1, then we have:

(5) u ( x ) = u o ( x ) + m = 1 + u m ( x ) .

By defining a vector u = ( u o ( x ) , u 1 ( x ) , u 2 ( x ) , , u n ( x ) ) , and differentiating Equation (2) m-times with respect to (q) and then setting q=0, we obtain the mth-order deformation equation:

(6) L [ u ˆ m ( x ) χ m u m 1 ( x ) ] = h H ( x ) R m [ u m 1 ] ,

where:

(7) R m [ u m 1 ] = 1 ( m 1 ) ! m 1 N [ u ( x ; q ) ] q m 1 | q = 0 and χ m = | 0 m 1 1 m > 1 .

Applying L−1 on both sides of Equation (6), we get:

(8) u m ( x ) = χ m u m 1 ( x ) + h L 1 [ H ( x ) R m [ u m 1 ] ] .

In this way, we obtain um for m ⩾ 1, at mth-order, we have:

(9) u ( x ) = m = 1 M u m ( x ) .

Findings

It is evident from obtained results that the nanoparticle concentration field is directly proportional to the chemical reaction with activation energy. Additionally, both temperature and concentration distributions are declining functions of thermal and solutal stratification parameters (P1) and (P2), respectively. Moreover, temperature Θ(Ω1) enhances for greater values of Brownian motion parameter (Nb), non-uniform heat source/sink parameter (B1) and thermophoresis factor (Nt). Reverse behavior of concentration ϒ(Ω1) field is remarked in view of (Nb) and (Nt). Graphs and tables are also constructed to analyze the effect of different flow parameters on skin friction coefficient, local Nusselt number, Sherwood numbers, velocity, temperature and concentration fields.

Originality/value

The novelty of the present problem is to inspect the Arrhenius activation energy phenomena for viscoelastic Walter-B nanofluid model with additional features of nonlinear thermal radiation, non-uniform heat generation/absorption, nonlinear mixed convection, thermal and solutal stratification. The novel aspect of binary chemical reaction is analyzed to characterize the impact of activation energy in the presence of Cattaneo–Christov double-diffusion model. The mathematical model of Buongiorno is employed to incorporate Brownian motion and thermophoresis effects due to nanoparticles.

Details

Multidiscipline Modeling in Materials and Structures, vol. 16 no. 1
Type: Research Article
ISSN: 1573-6105

Keywords

Article
Publication date: 12 December 2018

Yu Bai, Bo Xie, Yan Zhang, Yingjian Cao and Yunpeng Shen

The purpose of this paper is to investigate the two-dimensional stagnation-point flow, heat and mass transfer of an incompressible upper-convected Oldroyd-B MHD nanofluid

Abstract

Purpose

The purpose of this paper is to investigate the two-dimensional stagnation-point flow, heat and mass transfer of an incompressible upper-convected Oldroyd-B MHD nanofluid over a stretching surface with convective heat transfer boundary condition in the presence of thermal radiation, Brownian motion, thermophoresis and chemical reaction. The process of heat and mass transfer based on Cattaneo–Christov double-diffusion model is studied, which can characterize the features of thermal and concentration relaxations factors.

Design/methodology/approach

The governing equations are developed and similarly transformed into a set of ordinary differential equations, which are solved by a newly approximate analytical method combining the double-parameter transformation expansion method with the base function method (DPTEM-BF).

Findings

An interesting phenomenon can be found that all the velocity profiles first enhance up to a maximal value and then gradually drop to the value of the stagnation parameter, which indicates the viscoelastic memory characteristic of Oldroyd-B fluid. Moreover, it is revealed that the thickness of the thermal and mass boundary layer is increasing with larger values of thermal and concentration relaxation parameters, which indicates that Cattaneo–Christov double-diffusion model restricts the heat and mass transfer comparing with classical Fourier’s law and Fick’s law.

Originality/value

This paper focuses on stagnation-point flow, heat and mass transfer combining the constitutive relation of upper-convected Oldroyd-B fluid and Cattaneo–Christov double diffusion model.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 29 no. 3
Type: Research Article
ISSN: 0961-5539

Keywords

Article
Publication date: 18 June 2020

Kazeem Babawale Kasali, Yusuf Olatunji Tijani, Matthew Oluwafemi Lawal and Yussuff Titilope Lawal

In this paper, we studied the steady flow of a radiative magnetohydrodynamics viscoelastic fluid over an exponentially stretching sheet. This present work incorporated the…

Abstract

Purpose

In this paper, we studied the steady flow of a radiative magnetohydrodynamics viscoelastic fluid over an exponentially stretching sheet. This present work incorporated the effects of Soret, Dufour, thermal radiation and chemical reaction.

Design/methodology/approach

An appropriate semi-analytical technique called homotopy analysis method (HAM) was used to solve the resulting nonlinear dimensionless boundary value problem, and the method was validated numerically using a finite difference scheme implemented on Maple software.

Findings

It was observed that apart from excellence agreement with the results in literature, the results obtained gave further insights into the behaviour of the system.

Originality/value

The purpose of this research is to investigate heat and mass transfer profiles of a MHD viscoelastic fluid flow over an exponentially stretching sheet in the influence of chemical reaction, thermal radiation and cross-diffusion which are hitherto neglected in previous studies.

Details

Multidiscipline Modeling in Materials and Structures, vol. 16 no. 6
Type: Research Article
ISSN: 1573-6105

Keywords

Article
Publication date: 21 August 2021

Yu Bai, Qing Wang and Yan Zhang

This paper aims to examine the unsteady stagnation-point flow, heat and mass transfer of upper-convected Oldroyd-B nanofluid along a stretching sheet. The thermal…

Abstract

Purpose

This paper aims to examine the unsteady stagnation-point flow, heat and mass transfer of upper-convected Oldroyd-B nanofluid along a stretching sheet. The thermal conductivity is taken in a temperature-dependent fashion. With the aid of Cattaneo–Christov double-diffusion theory, relaxation-retardation double-diffusion model is advanced, which considers not only the effect of relaxation time but also the influence of retardation time. Convective heat transfer is not ignored. Additionally, experiments verify that with sodium carboxymethylcellulose (CMC) solutions as base fluid, not only the flow curve conforms to Oldroyd-B model but also thermal conductivity decreases linearly with the increase of temperature.

Design/methodology/approach

The suitable pseudo similarity transformations are adopted to address partial differential equations to ordinary differential equations, which are computed analytically through homotopy analysis method (HAM).

Findings

It is worth noting that the increase of stagnation-point parameter diminishes momentum loss, so that the velocity enlarges, which makes boundary layer thickness thinner. With the increase of thermal retardation time parameter, the nanofluid temperature rises that implies heat penetration depth boosts up and the additional time required for nanofluid to heat transfer to surrounding nanoparticles is less, which is similar to the effects of concentration retardation time parameter on concentration field.

Originality/value

This paper aims to explore the unsteady stagnation-point flow, heat and mass transfer of upper-convected Oldroyd-B nanofluid with variable thermal conductivity and relaxation-retardation double-diffusion model.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 31 no. 11
Type: Research Article
ISSN: 0961-5539

Keywords

Article
Publication date: 22 May 2020

S.R. Mishra and Priya Mathur

Present investigation based on the flow of electrically conducting Williamson nanofluid embedded in a porous medium past a linearly horizontal stretching sheet. In…

Abstract

Purpose

Present investigation based on the flow of electrically conducting Williamson nanofluid embedded in a porous medium past a linearly horizontal stretching sheet. In addition to that, the combined effect of thermophoresis, Brownian motion, thermal radiation and chemical reaction is considered in both energy and solutal transfer equation, respectively.

Design/methodology/approach

With suitable choice of nondimensional variables the governing equations for the velocity, temperature, species concentration fields, as well as rate shear stress at the plate, rate of heat and mass transfer are expressed in the nondimensional form. These transformed coupled nonlinear differential equations are solved semi-analytically using variation parameter method.

Findings

The behavior of characterizing parameters such as magnetic parameter, melting parameter, porous matrix, Brownian motion, thermophoretic parameter, radiation, Lewis number and chemical particular case present result validates with earlier established results and found to be in good agreement. Finally reaction parameter is demonstrated via graphs and numerical results are presented in tabular form.

Originality/value

The said work is an original work of the authors.

Details

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

Keywords

Article
Publication date: 17 December 2019

S.U. Khan, Sabir Ali Shehzad and N. Ali

An increment in energy efficiency by employing nanoparticles is a hot topic of research in present era due to its abundant implications in modern engineering and…

Abstract

Purpose

An increment in energy efficiency by employing nanoparticles is a hot topic of research in present era due to its abundant implications in modern engineering and technological processes. Therefore, the current research analysis reported the viscoelastic nanofluid flow over porous oscillatory moving sheet in the presence of microorganisms. A rate-type fluid namely Maxwell fluid is employed with the addition of nanoparticles. The paper aims to discuss this issue.

Design/methodology/approach

First, acceptable dimensionless variables are defined to convert the system of dimensional form into the system of dimensionless forms. Later on, the self-similar solution of the boundary value problem is computed by using the homotopy analysis method. The obtained results of velocity, temperature, mass concentration and motile microorganism density profiles are interpreted through physical background.

Findings

The presence of both thermophoresis and Brownian motion parameters also improve the thermophysical features of non-Newtonian nanoparticles. It is also pointed out that the presence of porous medium and magnetic force enhances the nanoparticles concentration. Moreover, a weaker distribution of gyrotactic microorganism has been depicted with Peclet number and bioconvection Lewis parameter.

Originality/value

No such article exists in the literature yet.

Details

Multidiscipline Modeling in Materials and Structures, vol. 16 no. 4
Type: Research Article
ISSN: 1573-6105

Keywords

Article
Publication date: 4 September 2019

M. Mudassar Gulzar, Shagufta Jabeen, Muhammad Waqas, Sabir Ali Shehzad, Tasawar Hayat and Ahmed Alsaedi

The purpose of this study is to scrutinize the effects of entropy generation and nonlinear mixed convection on the boundary layer flow of second grade fluid induced by…

Abstract

Purpose

The purpose of this study is to scrutinize the effects of entropy generation and nonlinear mixed convection on the boundary layer flow of second grade fluid induced by stretching sheets. Heat transfer effects are accounted in view of viscous dissipation and nonlinear thermal radiation.

Design/methodology/approach

Optimal homotopic asymptotic method procedure is adopted to obtain the analytical solution of nonlinear ordinary differential equations.

Findings

It has been noticed that Hartmann and Brinkman number has reverse characteristics against entropy generation and Bejan number.

Originality/value

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

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 29 no. 12
Type: Research Article
ISSN: 0961-5539

Keywords

1 – 10 of 250