Search results

1 – 10 of 404
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: 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 conductivity is…

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: 16 April 2020

Keerthi R, B. Mahanthesh and Smita Saklesh Nagouda

The study of instability due to the effects of Maxwell–Cattaneo law and internal heat source/sink on Casson dielectric fluid horizontal layer is an open question. Therefore, in…

Abstract

Purpose

The study of instability due to the effects of Maxwell–Cattaneo law and internal heat source/sink on Casson dielectric fluid horizontal layer is an open question. Therefore, in this paper, the impact of internal heat generation/absorption on Rayleigh–Bénard convection in a non-Newtonian dielectric fluid with Maxwell–Cattaneo heat flux is investigated. The horizontal layer of the fluid is cooled from the upper boundary, while an isothermal boundary condition is utilized at the lower boundary.

Design/methodology/approach

The Casson fluid model is utilized to characterize the non-Newtonian fluid behavior. The horizontal layer of the fluid is cooled from the upper boundary, while an isothermal boundary condition is utilized at the lower boundary. The governing equations are non-dimensionalized using appropriate dimensionless variables and the subsequent equations are solved for the critical Rayleigh number using the normal mode technique (NMT).

Findings

Results are presented for two different cases namely dielectric Newtonian fluid (DNF) and dielectric non-Newtonian Casson fluid (DNCF). The effects of Cattaneo number, Casson fluid parameter, heat source/sink parameter on critical Rayleigh number and wavenumber are analyzed in detail. It is found that the value Rayleigh number for non-Newtonian fluid is higher than that of Newtonian fluid; also the heat source aspect decreases the magnitude of the Rayleigh number.

Originality/value

The effect of Maxwell–Cattaneo heat flux and internal heat source/sink on Rayleigh-Bénard convection in Casson dielectric fluid is investigated for the first time.

Details

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

Keywords

Article
Publication date: 14 November 2016

Rajneesh Kumar, Richa Vohra and M.G. Gorla

The purpose of this paper is to study the reflection of plane waves in thermoelastic medium with double porosity structure.

Abstract

Purpose

The purpose of this paper is to study the reflection of plane waves in thermoelastic medium with double porosity structure.

Design/methodology/approach

A two-dimensional model is considered of an isotropic thermoelastic half-space with double porosity. Thermoelasticity with one relaxation time given by Lord and Shulman (1967) has been used to study the problem. It is found that there exists four coupled longitudinal waves, namely, longitudinal wave (P), longitudinal thermal wave (T), longitudinal volume fractional wave corresponding to pores (PVI) and longitudinal volume fractional wave corresponding to fissures (PVII), in addition to an uncoupled transverse wave (SV).

Findings

The formulae for amplitude ratios of various reflected waves are obtained in closed form. It is found that these amplitude ratios are functions of angle of incidence. Effect of porosity and thermal relaxation time is shown graphically on the amplitude ratios with angle of incidence for a particular model.

Originality/value

Reflection of plane waves is of great practical importance. There are many organic and inorganic deposits beneath the earth surface. Wave propagation is the simplest and most economical technique to detect these. The model discussed in the present paper can provide useful information for experimental researchers working in the field of geophysics and earthquake engineering, along with seismologist working in the field of mining tremors and drilling into the crust of the earth.

Details

Multidiscipline Modeling in Materials and Structures, vol. 12 no. 4
Type: Research Article
ISSN: 1573-6105

Keywords

Article
Publication date: 14 May 2019

Ravisha M., I.S. Shivakumara and Mamatha A.L.

The onset of convection in a ferrofluid-saturated porous layer has been investigated using a local thermal nonequilibrium (LTNE) model by allowing the solid phase to transfer heat…

Abstract

Purpose

The onset of convection in a ferrofluid-saturated porous layer has been investigated using a local thermal nonequilibrium (LTNE) model by allowing the solid phase to transfer heat via a Cattaneo heat flux theory while the fluid phase to transfer heat via usual Fourier heat-transfer law. The flow in the porous medium is governed by modified Brinkman-extended Darcy model. The instability of the system is discussed exactly for stress-free boundaries, while for rigid-ferromagnetic/paramagnetic boundaries the results are obtained numerically using the Galerkin method. The presence of Cattaneo effect introduces oscillatory convection as the preferred mode of instability contrary to the occurrence of instability via stationary convection found in its absence. Besides, oscillatory ferroconvection is perceived when the solid thermal relaxation time parameter exceeds a threshold value and increase in its value is to hasten the oscillatory onset. The effect of different boundary conditions on the instability of the system is noted to be qualitatively same. The paper aims to discuss these issues.

Design/methodology/approach

The investigators would follow the procedure of Straughan (2013) to obtain the expression for Rayleigh number. The Brinkman-extended Darcy model is used to describe the flow in a porous medium. The investigators have used a Galerkin method to obtain the numerical results for rigid-ferromagnetic/paramagnetic boundaries, while the instability of the system is discussed exactly for stress-free boundaries.

Findings

The Cattaneo–LTNE porous ferroconvection has been analyzed for different velocity and magnetic boundary conditions. The Brinkman-extended Darcy model is used to describe the flow in a porous medium. The effect of different types of velocity and magnetic boundary conditions on the instability of the system has been highlighted. The instability of the system is discussed exactly for stress-free boundaries, while for rigid-ferromagnetic/paramagnetic boundaries the results are obtained numerically using the Galerkin method.

Originality/value

The novelty of the present paper is to combine LTNE and second sound effects in solids on thermal instability of a ferrofluid-saturated porous layer by retaining the usual Fourier heat-transfer law in the ferrofluid. The Brinkman-extended Darcy model is used to describe the flow in a porous medium. The effect of different types of velocity and magnetic boundary conditions on the instability of the system is discussed.

Details

Multidiscipline Modeling in Materials and Structures, vol. 15 no. 4
Type: Research Article
ISSN: 1573-6105

Keywords

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.

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

Keywords

Article
Publication date: 19 December 2018

Vasu B. and Atul Kumar Ray

To achieve material-invariant formulation for heat transfer of Carreau nanofluid, the effect of Cattaneo–Christov heat flux is studied on a natural convective flow of Carreau…

Abstract

Purpose

To achieve material-invariant formulation for heat transfer of Carreau nanofluid, the effect of Cattaneo–Christov heat flux is studied on a natural convective flow of Carreau nanofluid past a vertical plate with the periodic variations of surface temperature and the concentration of species. Buongiorno model is considered for nanofluid transport, which includes the relative slip mechanisms, Brownian motion and thermophoresis.

Design/methodology/approach

The governing equations are non-dimensionalized using suitable transformations, further reduced to non-similar form using stream function formulation and solved by local non-similarity method with homotopy analysis method. The numerical computations are validated and verified by comparing with earlier published results and are found to be in good agreement.

Findings

The effects of varying the physical parameters such as Prandtl number, Schmidt number, Weissenberg number, thermophoresis parameter, Brownian motion parameter and buoyancy ratio parameter on velocity, temperature and species concentration are discussed and presented through graphs. The results explored that the velocity of shear thinning fluid is raised by increasing the Weissenberg number, while contrary response is seen for the shear thickening fluid. It is also found that heat transfer in Cattaneo–Christov heat conduction model is less than that in Fourier’s heat conduction model. Furthermore, the temperature and thermal boundary layer thickness expand with the increase in thermophoresis and Brownian motion parameter, whereas nanoparticle volume fraction increases with increase in thermophoresis parameter, but reverse trend is observed with increase in Brownian motion parameter.

Originality/value

The present investigation is relatively original as very little research has been reported on Carreau nanofluids under the effect of Cattaneo–Christov heat flux model.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 29 no. 2
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 buoyancy…

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: 1 January 2004

Christianne V.D.R. Anderson and Kumar K. Tamma

We first provide an overview of some predominant theoretical methods currently used for predicting thermal conductivity of thin dielectric films: the equation of radiative…

2789

Abstract

We first provide an overview of some predominant theoretical methods currently used for predicting thermal conductivity of thin dielectric films: the equation of radiative transfer, the temperature‐dependent thermal conductivity theories based on the Callaway model, and the molecular dynamics simulation. This overview also highlights temporal and spatial scale issues by looking at a unified theory that bridges physical issues presented in the Fourier and Cattaneo models. This newly developed unified theory is the so‐called C‐ and F‐processes constitutive model. This model introduces the notion of a new dimensionless heat conduction model number, which is the ratio of the thermal conductivity of the fast heat carrier F‐processes to the total thermal conductivity comprised of both the fast heat carriers F‐processes and the slow heat carriers C‐processes. Illustrative numerical examples for prediction of thermal conductivity in thin films are primarily presented.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 14 no. 1
Type: Research Article
ISSN: 0961-5539

Keywords

Article
Publication date: 23 June 2020

M. Gnaneswara Reddy, P. Vijaya Kumari, G. Upender Reddy, K. Ganesh Kumar and B. C. Prasannakumara

The main theme of this paper is the effect of viscous dissipation Darcy–Forchheimer flow and heat transfer augmentation of a viscoelastic fluid over an incessant moving needle.

Abstract

Purpose

The main theme of this paper is the effect of viscous dissipation Darcy–Forchheimer flow and heat transfer augmentation of a viscoelastic fluid over an incessant moving needle.

Design/methodology/approach

The governing partial differential equations of the current problem are diminished into a set of ordinary differential equations using requisite similarity transformations. Energy equation is extended by using Cattaneo–Christov heat flux model with variable thermal conductivity. By applying boundary layer approximation system of equations is framed.

Findings

Convective condition is also introduced in this analysis. Obtained set of similarity equations are then solved with the help of efficient numerical method four–fifth-order RKF-45.

Originality/value

The outcomes of various pertinent parameters on the velocity, temperature distributions are analysed by using portraits.

Details

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

Keywords

1 – 10 of 404