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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: 23 September 2021

Yu Bai, Huiling Fang and Yan Zhang

This paper aims to present the effect of entropy generation on the unsteady flow of upper-convected Maxwell nanofluid past a wedge embedded in a porous medium in view of…

Abstract

Purpose

This paper aims to present the effect of entropy generation on the unsteady flow of upper-convected Maxwell nanofluid past a wedge embedded in a porous medium in view of buoyancy force. Cattaneo-Christov double diffusion theory simulates the processes of energy phenomenon and mass transfer. Meanwhile, Brownian motion, thermophoresis and convective boundary conditions are discussed to further visualize the heat and mass transfer properties.

Design/methodology/approach

Coupled ordinary differential equations are gained by appropriate similar transformations and these equations are manipulated by the Homotopy analysis method.

Findings

The result is viewed that velocity distribution is a diminishing function with boosting the value of unsteadiness parameter. Moreover, fluid friction irreversibility is dominant as the enlargement in Brinkman number. Then controlling the temperature and concentration difference parameters can effectively regulate entropy generation.

Originality/value

This paper aims to address the effect of entropy generation on unsteady flow, heat and mass transfer of upper-convected Maxwell nanofluid over a stretched wedge with Cattaneo-Christov double diffusion, which provides a theoretical basis for manufacturing production.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 32 no. 6
Type: Research Article
ISSN: 0961-5539

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: 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: 1 June 2000

Chongbin Zhao, B.E. Hobbs, H.B. Mühlhaus, A. Ord and Ge Lin

Numerical methods are used to solve double diffusion driven reactive flow transport problems in deformable fluid‐saturated porous media. In particular, the temperature…

Abstract

Numerical methods are used to solve double diffusion driven reactive flow transport problems in deformable fluid‐saturated porous media. In particular, the temperature dependent reaction rate in the non‐equilibrium chemical reactions is considered. A general numerical solution method, which is a combination of the finite difference method in FLAC and the finite element method in FIDAP, to solve the fully coupled problem involving material deformation, pore‐fluid flow, heat transfer and species transport/chemical reactions in deformable fluid‐saturated porous media has been developed. The coupled problem is divided into two sub‐problems which are solved interactively until the convergence requirement is met. Owing to the approximate nature of the numerical method, it is essential to justify the numerical solutions through some kind of theoretical analysis. This has been highlighted in this paper. The related numerical results, which are justified by the theoretical analysis, have demonstrated that the proposed solution method is useful for and applicable to a wide range of fully coupled problems in the field of science and engineering.

Details

Engineering Computations, vol. 17 no. 4
Type: Research Article
ISSN: 0264-4401

Keywords

Article
Publication date: 18 August 2021

Manoj Kumar Nayak, Sachin Shaw, H. Waqas and Taseer Muhammad

The purpose of this study is to investigate the Cattaneo-Christov double diffusion, multiple slips and Darcy-Forchheimer’s effects on entropy optimized and thermally…

Abstract

Purpose

The purpose of this study is to investigate the Cattaneo-Christov double diffusion, multiple slips and Darcy-Forchheimer’s effects on entropy optimized and thermally radiative flow, thermal and mass transport of hybrid nanoliquids past stretched cylinder subject to viscous dissipation and Arrhenius activation energy.

Design/methodology/approach

The presented flow problem consists of the flow, heat and mass transportation of hybrid nanofluids. This model is featured with Casson fluid model and Darcy-Forchheimer model. Heat and mass transportations are represented with Cattaneo-Christov double diffusion and viscous dissipation models. Multiple slip (velocity, thermal and solutal) mechanisms are adopted. Arrhenius activation energy is considered. For graphical and numerical data, the bvp4c scheme in MATLAB computational tool along with the shooting method is used.

Findings

Amplifying curvature parameter upgrades the fluid velocity while that of porosity parameter and velocity slip parameter whittles down it. Growing mixed convection parameter, curvature parameter, Forchheimer number, thermally stratified parameter intensifies fluid temperature. The rise in curvature parameter and porosity parameter enhances the solutal field distribution. Surface viscous drag gets controlled with the rising of the Casson parameter which justifies the consideration of the Casson model. Entropy generation number and Bejan number upgrades due to growth in diffusion parameter while that enfeeble with a hike in temperature difference parameter.

Originality/value

To the best of the authors’ knowledge, this research study is yet to be available in the existing literature.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 32 no. 6
Type: Research Article
ISSN: 0961-5539

Keywords

Article
Publication date: 6 August 2019

Saritha Natesan and Senthil Kumar Arumugam

The purpose of this study is to apply Buongiorno’s two phase model to analyse double diffusion natural convection in a square enclosure filled with nanofluids.

Abstract

Purpose

The purpose of this study is to apply Buongiorno’s two phase model to analyse double diffusion natural convection in a square enclosure filled with nanofluids.

Design/methodology/approach

A computational code based on the SIMPLE algorithm and finite volume method is used to solve the non-dimensional governing equations.

Findings

The nanoparticle plays a crucial role when thermal and solutal buoyancy forces are equal and opposing.

Originality/value

This is the first paper to apply Buongiorno’s two phase model for double diffusion natural convection in enclosures filled with nanofluids.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 29 no. 10
Type: Research Article
ISSN: 0961-5539

Keywords

Article
Publication date: 13 April 2015

Spyros Papaefthymiou, Constantinos Goulas and Vasiliki Panteleakou

Identification of the critical process conditions that enhance Cu diffusion in ferrite grain boundaries and promote precipitation of Cu-rich particles in the proximity of…

155

Abstract

Purpose

Identification of the critical process conditions that enhance Cu diffusion in ferrite grain boundaries and promote precipitation of Cu-rich particles in the proximity of steel semi-finished products surface is crucial for every steel maker as it leads to the creation of hot shortness cracks in final products deteriorating surface condition. The purpose of this paper is to reveal the possible effect of Cu segregation in the metal/oxide interface, its role in surface crack initiation and, finally, to propose actions to prevent from hot shortness issues throughout the production chain of steel products.

Design/methodology/approach

The here presented study was based on S355 steel plate production starting from re-melting of scrap in an EAF, followed by metallurgical treatment in a Ladle Furnace, continuous casting, re-heating (RH) and thermo-mechanical rolling in a reversing mill. For the purposes of this study, more than ten heats, 100 t of steel each, were analyzed. Here presented are depicted steels in the high and low end of the permitted Cu-wt-% spectrum, 0.4 wt-% Cu (0.15 wt-% C, 1.1 wt-% Mn, VTi micro-alloyed steel) and 0.25 wt-% Cu (0.09 wt-% C, 1.2 wt-% Mn, NbTi micro alloyed steel), respectively.

Findings

Although Cu levels of 0.25-0.40 wt-% are well below the Cu solubility in austenite and ferrite (8 percent wt-% and 3 wt-% Cu, respectively) and within specifications, precipitation of Cu-rich particles is observed in industrial semi-finished and/or final products. Cu-rich precipitates and Cu segregation along grain boundaries near the steel surface lead to hot shortness cracks in industrial products.

Research limitations/implications

Hot shortness surface defects related to Cu presence in steel having significantly lower Cu amounts than its maximum solubility in austenite and ferrite does not make sense in first place. Correctly, Cu is expected to remain in solid solution. Identification of Cu-rich particles is explained on the basis of the development of double diffusion actions: interstitial diffusion of carbon (decarburization) and substitution diffusion of copper. Root cause analysis and reliable countermeasures will save financial and material resources during steel production.

Originality/value

Automobile scrap re-melting results in noticeable Cu amounts in EAF produced steel. Presence of Cu-rich particles in grain boundaries near the surface of intermediate or final products deteriorates surface quality through relevant surface defects. Identification of Cu-rich particles is explained on the basis of the development of double diffusion actions: interstitial diffusion of carbon and substitution diffusion of copper. Pre condition for metallic Cu precipitation in ferrite is the Cu amount to be above 3 wt-%, which is ten times higher than the usual permitted Cu amount in such steel grades. This pre-condition is met through austenite oxidation during RH.

Details

International Journal of Structural Integrity, vol. 6 no. 2
Type: Research Article
ISSN: 1757-9864

Keywords

Article
Publication date: 4 January 2013

Fausto Arpino, Nicola Massarotti, Alessandro Mauro and Perumal Nithiarasu

The purpose of the paper is to numerically simulate steady‐state thermo‐solutal convection in rectangular cavities with different aspect ratios, subject to horizontal…

Abstract

Purpose

The purpose of the paper is to numerically simulate steady‐state thermo‐solutal convection in rectangular cavities with different aspect ratios, subject to horizontal temperature and concentration gradients, and validate the results against numerical and experimental data available from literature.

Design/methodology/approach

The fully explicit Artificial Compressibility (AC) version of the Characteristic Based Split (CBS) scheme is adopted to solve double diffusion (DD) problems. A stabilization analysis is carried out to efficiently solve the problems considered in the present work. The thermal and solutal buoyancy forces acting on the fluid have been taken into account in case of aiding and opposing flow conditions.

Findings

The stability limits derived by the authors for the thermo‐solutal convection assume a fundamental role to efficiently solve the DD problems considered. In the cases characterized by higher Rayleigh number the convergent solution is obtained only by employing the new stability conditions. The efficient matrix free procedure employed is a powerful tool to study complex DD problems.

Originality/value

In this paper, the authors extend the stabilization analysis for the AC‐CBS scheme to the solution of DD, fundamental to efficiently solve the present problems, and apply the present fully explicit matrix free scheme, based on finite elements, to the solution of DD natural convection in cavities.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 23 no. 1
Type: Research Article
ISSN: 0961-5539

Keywords

Article
Publication date: 27 November 2020

Abdelraheem M. Aly and Ehab Mahmoud Mohamed

The purpose of this study is to use an incompressible smoothed particle hydrodynamics (ISPH) method for simulating buoyancy ratio and magnetic field effects on double…

Abstract

Purpose

The purpose of this study is to use an incompressible smoothed particle hydrodynamics (ISPH) method for simulating buoyancy ratio and magnetic field effects on double diffusive natural convection of a cooper-water nanofluid in a cavity. An open pipe is embedded inside the center of a cavity, and it is occupied by solid particles.

Design/methodology/approach

The dimensionless governing equations in Lagrangian form were solved by ISPH method. Two different thermal conditions were considered for the solid particles. The actions of the solid particles were tracked inside a cavity. The effects of Hartman parameter, Rayleigh number, nanoparticles volume fraction and Lewis number on features of heat and mass transfer and flow field were tested.

Findings

The results showed that the buoyancy ratio changes the directions of the solid particles diffusion in a cavity. The hot solid particles were raised upwards at aiding mode (N > 0) and downwards at an opposing mode (N < 0). A comparison is made with experimental and numerical simulation results, and it showed a well agreement.

Originality/value

Novel studies for the impacts of buoyancy ratio on the diffusion of solid particles embedded in an open pipe during double-diffusive flow were conducted.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 31 no. 6
Type: Research Article
ISSN: 0961-5539

Keywords

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