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Article
Publication date: 26 September 2019

Muhammad Sohail, Rahila Naz and Rabeeah Raza

The purpose of this paper is to address the entropy analysis of the 3D flow of Maxwell nanofluid containing gyrotactic microorganism in the presence of homogeneous–heterogeneous…

79

Abstract

Purpose

The purpose of this paper is to address the entropy analysis of the 3D flow of Maxwell nanofluid containing gyrotactic microorganism in the presence of homogeneous–heterogeneous reactions with improved heat conduction and mass diffusion models over a stretched surface. Improved models are supported out by utilizing Cattaneo–Christov heat flux and generalized Fick’s law, respectively.

Design/methodology/approach

Governing equations which present the given flow phenomenon are modeled in the form of PDEs by applying boundary layer analysis and then suitable makeovers are engaged to transfigure prevailing partial differential equations into a set of ordinary differential equations. Transformed equations are handled via optimal homotopy analysis process in computational tool Mathematica and also a special case of already published work is substantiated and found to be in excellent settlement.

Findings

The bearing of innumerable convoluted physical parameters on velocity, temperature, concentration, reaction rate, the concentration of motile microorganism and entropy generation are presented and deliberated through graphs. Moreover, the convergence of the homotopic solution is presented in tabular form which confirms the reliability of the proposed scheme. It is perceived that mounting values of the magnetic parameter and Brinkman number boosts the irreversibility analysis and Bejan number diminishes for these parameters. Moreover, the growing values of Prandtl and Schmidt numbers reduce the temperature and concentration fields, respectively.

Practical implications

The work contained in this paper has applications in a different industry.

Originality/value

The work contained in this paper is original work and it is good for the researcher in the field of applied mathematics.

Details

Multidiscipline Modeling in Materials and Structures, vol. 16 no. 2
Type: Research Article
ISSN: 1573-6105

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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…

110

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 )andu 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 , whereu m ( x ) = 1 m ! mu 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 = 0andχ m = | 0m 11m > 1 .

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

(8) u m ( x ) = χ m u m 1 ( x ) + hL 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

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Article
Publication date: 17 June 2019

Arif Hussain, Muhammad Yousaf Malik, Mair Khan and Taimoor Salahuddin

The purpose of current flow configuration is to spotlights the thermophysical aspects of magnetohydrodynamics (MHD) viscoinelastic fluid flow over a stretching surface.

123

Abstract

Purpose

The purpose of current flow configuration is to spotlights the thermophysical aspects of magnetohydrodynamics (MHD) viscoinelastic fluid flow over a stretching surface.

Design/methodology/approach

The fluid momentum problem is mathematically formulated by using the Prandtl–Eyring constitutive law. Also, the non-Fourier heat flux model is considered to disclose the heat transfer characteristics. The governing problem contains the nonlinear partial differential equations with appropriate boundary conditions. To facilitate the computation process, the governing problem is transmuted into dimensionless form via appropriate group of scaling transforms. The numerical technique shooting method is used to solve dimensionless boundary value problem.

Findings

The expressions for dimensionless velocity and temperature are found and investigated under different parametric conditions. The important features of fluid flow near the wall, i.e. wall friction factor and wall heat flux, are deliberated by altering the pertinent parameters. The impacts of governing parameters are highlighted in graphical as well as tabular manner against focused physical quantities (velocity, temperature, wall friction factor and wall heat flux). A comparison is presented to justify the computed results, it can be noticed that present results have quite resemblance with previous literature which led to confidence on the present computations.

Originality/value

The computed results are quite useful for researchers working in theoretical physics. Additionally, computed results are very useful in industry and daily-use processes.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 30 no. 6
Type: Research Article
ISSN: 0961-5539

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Article
Publication date: 23 June 2020

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

The purpose of this article is to analyze the heat and mass transfer with entropy generation during magnetohydrodynamics (MHD) flow of non-Newtonian Sisko nanofluid over a…

87

Abstract

Purpose

The purpose of this article is to analyze the heat and mass transfer with entropy generation during magnetohydrodynamics (MHD) flow of non-Newtonian Sisko nanofluid over a linearly stretching cylinder under the influence of velocity slip, chemical reaction and thermal radiation. The Brownian motion, thermophoresis and activation energy are assimilated in this nanofluid model. Convective boundary conditions on heat and mass transfer are considered. The physical model may have diverse applications in several areas of technology underlying thermohydrodynamics including supercritical fluid extraction, refrigeration, ink-jet printing and so on.

Design/methodology/approach

The dimensional governing equations are nondimensionalized by using appropriate similarity variables. The resulting boundary value problem is converted into initial value problem using the method of superposition and numerically computed by employing well-known fourth-order Runge–Kutta–Fehlberg approach along with shooting technique (RKF4SM). The quantitative impacts of emerging physical parameters on the velocity, temperature, concentration, skin friction coefficient, Nusselt number, Sherwood number, entropy generation rate and Bejan number are presented graphically and in tabular form, and the salient features are comprehensively discussed.

Findings

From graphical outcomes, it is concluded that the slip parameters greatly influence the flow characteristics. Fluid temperature is elevated with rising radiation parameter and thermal Biot number. Nanoparticle concentration is reported in decreasing form with activation energy parameter. Entropy is found to be an increasing function of magnetic field, Brownian motion and material parameters. The entropy is less generated for shear-thinning fluid compared to shear-thickening as well as Newtonian fluids in the system.

Originality/value

Till now no study has been documented to explore the impact of binary chemical reaction with Arrhenius activation energy on entropy generation in an MHD boundary layer flow of non-Newtonian Sisko nanofluid over a linear stretching cylinder with velocity slip and convective boundary conditions.

Details

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

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Article
Publication date: 23 November 2018

Gangadhar Kotha, Keziya Kukkamalla and S.M. Ibrahim

The purpose of this paper is to examine the magneto hydrodynamic flow and heat transfer of nanofluids over a permeable wedge based on engine oil which is under the effects of…

79

Abstract

Purpose

The purpose of this paper is to examine the magneto hydrodynamic flow and heat transfer of nanofluids over a permeable wedge based on engine oil which is under the effects of thermal radiation and convective heating.

Design/methodology/approach

The equations governing the flow are transformed into differential equations by applying similarity transformations. Keller box method is used to bring out the numerical solution.

Findings

The discovery interprets that temperature as well as the velocity of Ag-engine oil nanofluids are more noticeable than Cu-engine oil nanofluids. Thermal boundary layer increases for radiation parameter as well as Biot number. Fluctuations of co-efficient of drag skin friction as well heat transfer rate at the wall are also tested.

Originality/value

Till now, no numerical studies are reported on the heat transfer enhancement of the permeable wedge under thermal radiation on engine oil nanofluid flow by considering convective heating.

Details

Multidiscipline Modeling in Materials and Structures, vol. 15 no. 1
Type: Research Article
ISSN: 1573-6105

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Article
Publication date: 29 November 2018

Gireesha B.J., M. Archana, B. Mahanthesh and Prasannakumara B.C.

The purpose of this paper is to explore the effects of binary chemical reaction and activation energy on nano Casson liquid flow past a stretched plate with non-linear radiative…

81

Abstract

Purpose

The purpose of this paper is to explore the effects of binary chemical reaction and activation energy on nano Casson liquid flow past a stretched plate with non-linear radiative heat, and also, the effect of a novel exponential space-dependent heat source (ESHS) aspect along with thermal-dependent heat source (THS) effect in the analysis of heat transfer in nanofluid. Comparative analysis is carried out between the flows with linear radiative heat process and non-linear radiative heat process.

Design/methodology/approach

A similarity transformation technique is utilised to access the ODEs from the governed PDEs. The manipulation of subsequent non-linear equations is carried out by a well-known numerical approach called Runge–Kutta–Fehlberg scheme. Obtained solutions are briefly discussed with the help of graphical and tabular illustrations.

Findings

The effects of various physical parameters on temperature, nanoparticles volume fraction and velocity fields within the boundary layer are discussed for two different flow situations, namely, flow with linear radiative heat and flow with non-linear radiative heat. It is found that an irregular heat source/sink (ESHS and THS) and non-linear solar radiation play a vital role in the enhancement of the temperature distributions.

Originality/value

The problem is relatively original to study the effects of activation energy and binary chemical reaction along with a novel exponential space-based heat source on laminar boundary flow past a stretched plate in the presence of non-linear Rosseland radiative heat.

Details

Multidiscipline Modeling in Materials and Structures, vol. 15 no. 1
Type: Research Article
ISSN: 1573-6105

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Article
Publication date: 8 August 2019

Jawad Raza, Fateh Mebarek-Oudina and B. Mahanthesh

The purpose of this paper is to present an exploration of multiple slips and temperature dependent thermal conductivity effects on the flow of nano Williamson fluid over a…

82

Abstract

Purpose

The purpose of this paper is to present an exploration of multiple slips and temperature dependent thermal conductivity effects on the flow of nano Williamson fluid over a slendering stretching plate in the presence of Joule and viscous heating aspects. The effectiveness of nanoparticles is deliberated by considering Brownian moment and thermophoresis slip mechanisms. The effects of magnetism and radiative heat are also deployed.

Design/methodology/approach

The governing partial differential equations are non-dimensionalized and reduced to multi-degree ordinary differential equations via suitable similarity variables. The subsequent non-linear problem treated for numerical results. To measure the amount of increase/decrease in skin friction coefficient, Nusselt number and Sherwood number, the slope of linear regression line through the data points are calculated. Statistical approach is implemented to analyze the heat transfer rate.

Findings

The results show that temperature distribution across the flow decreases with thermal conductivity parameter. The maximum friction factor is ascertained at stronger magnetic field.

Originality/value

In the current paper, the magneto-nano Williamson fluid flow inspired by a stretching sheet of variable thickness is examined numerically. The rationale of the present study is to generalize the studies of Mebarek-Oudina and Makinde (2018) and Williamson (1929).

Details

Multidiscipline Modeling in Materials and Structures, vol. 15 no. 5
Type: Research Article
ISSN: 1573-6105

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Article
Publication date: 11 October 2018

A. Mahdy and Ali J. Chamkha

The purpose of this paper is to address the thermo-physical impacts of unsteady magneto-hydrodynamic (MHD) boundary layer flow of non-Newtonian tangent hyperbolic nanofluid past a…

127

Abstract

Purpose

The purpose of this paper is to address the thermo-physical impacts of unsteady magneto-hydrodynamic (MHD) boundary layer flow of non-Newtonian tangent hyperbolic nanofluid past a moving stretching wedge. To delineate the nanofluid, the boundary conditions for normal fluxes of the nanoparticle volume fraction are chosen to be vanish.

Design/methodology/approach

The local similarity transformation is implemented to reformulate the governing PDEs into coupled non-linear ODEs of higher order. Then, numerical solution is obtained for the simplified governing equations with the aid of finite difference technique.

Findings

Numerical calculations point out that pressure gradient parameter leads to improve all skin friction coefficient, rate of heat transfer and absolute value of rate of nanoparticle concentration. As well as, lager values of Weissenberg number tend to upgrade the skin friction coefficient, while power law index and velocity ratio parameter reduce the skin friction coefficient. Again, the horizontal velocity component enhances with upgrading power law index, unsteadiness parameter, velocity ratio parameter and Darcy number and it reduces with rising values of Weissenberg number.

Originality/value

A numerical treatment of unsteady MHD boundary layer flow of tangent hyperbolic nanofluid past a moving stretched wedge is obtained. The problem is original.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 28 no. 11
Type: Research Article
ISSN: 0961-5539

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Article
Publication date: 1 August 2016

M.Y. Malik, Arif Hussain, T. Salahuddin and M. Awais

– The purpose of this paper is to examine the Sisko fluid model over a stretching cylinder with heat transfer and magnetohydrodynamics.

279

Abstract

Purpose

The purpose of this paper is to examine the Sisko fluid model over a stretching cylinder with heat transfer and magnetohydrodynamics.

Design/methodology/approach

The boundary layer approach is employed to simplify the governing equations. Suitable similarity transformations are used to transform the governing partial differential equations into ordinary differential equations. In order to solve this system of ordinary differential equations numerically, shooting method in conjunction with Runge-Kutta-Fehlberg method is used.

Findings

The effects of physical parameters involved in velocity and temperature profiles are shown through graphs. It is observed that Sisko fluid parameter and curvature parameter enhances fluid velocity while motion of fluid is retarded by increasing magnetic field strength. Additionally temperature of fluid raise with curvature parameter while it fall down for larger values of Prandtl number. Skin friction coefficient and Nusselt number are computed and presented in graphs and tables for further analysis. It can be seen that curvature parameter increases both skin friction and Nusselt number while magnetic field and Prandtl number decayed skin friction and Nusselt number, respectively. Also Sisko parameter enlarges skin friction coefficient. The accuracy of solution is verified by comparing it with existing literature.

Originality/value

The computed results are interested for industrial and engineering processes, especially in cooling of nuclear reactors.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 26 no. 6
Type: Research Article
ISSN: 0961-5539

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Available. Open Access. Open Access
Article
Publication date: 2 August 2019

Mair Khan, T. Salahuddin, Muhammad Malik Yousaf, Farzana Khan and Arif Hussain

The purpose of the current flow configurations is to bring to attention the thermophysical aspects of magnetohydrodynamics (MHD) Williamson nanofluid flow under the effects of…

1582

Abstract

Purpose

The purpose of the current flow configurations is to bring to attention the thermophysical aspects of magnetohydrodynamics (MHD) Williamson nanofluid flow under the effects of Joule heating, nonlinear thermal radiation, variable thermal coefficient and activation energy past a rotating stretchable surface.

Design/methodology/approach

A mathematical model is examined to study the heat and mass transport analysis of steady MHD Williamson fluid flow past a rotating stretchable surface. Impact of activation energy with newly introduced variable diffusion coefficient at the mass equation is considered. The transport phenomenon is modeled by using highly nonlinear PDEs which are then reduced into dimensionless form by using similarity transformation. The resulting equations are then solved with the aid of fifth-order Fehlberg method.

Findings

The rotating fluid, heat and mass transport effects are analyzed for different values of parameters on velocity, energy and diffusion distributions. Parameters like the rotation parameter, Hartmann number and Weissenberg number control the flow field. In addition, the solar radiation, Joule heating, Prandtl number, thermal conductivity, concentration diffusion coefficient and activation energy control the temperature and concentration profiles inside the stretching surface. It can be analyzed that for higher values of thermal conductivity, Eckret number and solar radiation parameter the temperature profile increases, whereas opposite behavior is noticed for Prandtl number. Moreover, for increasing values of temperature difference parameter and thermal diffusion coefficient, the concentration profile shows reducing behavior.

Originality/value

This paper is useful for researchers working in mathematical and theoretical physics. Moreover, numerical results are very useful in industry and daily-use processes.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 30 no. 5
Type: Research Article
ISSN: 0961-5539

Keywords

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