Search results

1 – 10 of 55
Per page
102050
Citations:
Loading...
Access Restricted. View access options
Article
Publication date: 18 May 2010

K.B. Dada and E. Momoniat

The purpose of this paper is to derive a dynamic equation for modelling the behaviour of smectic‐C liquid crystals under the effect of an electric field.

311

Abstract

Purpose

The purpose of this paper is to derive a dynamic equation for modelling the behaviour of smectic‐C liquid crystals under the effect of an electric field.

Design/methodology/approach

The model equation is solved using a finite difference approximation, method of lines and pseudo‐spectral methods. The solutions are compared for accuracy and efficiency. Comparison is made of the efficiency of finite differences, method of lines and pseudo‐spectral methods.

Findings

The Fourier pseudo‐spectral method is shown to be the most efficient approach.

Originality/value

This work is original; a computational comparison of numerical schemes applied to liquid crystals has not been found in the literature.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 20 no. 4
Type: Research Article
ISSN: 0961-5539

Keywords

Access Restricted. View access options
Article
Publication date: 23 March 2012

E. Momoniat and C. Harley

The purpose of this paper is to obtain numerical solutions of a two‐dimensional mixed space‐time PDE modelling the flow of a second‐grade.

337

Abstract

Purpose

The purpose of this paper is to obtain numerical solutions of a two‐dimensional mixed space‐time PDE modelling the flow of a second‐grade.

Design/methodology/approach

The paper derives conditionally stable Crank‐Nicolson schemes to solve both the one and two dimensional mixed‐space time PDE. For the two‐dimensional case we implement the Crank‐Nicolson scheme using a Peaceman‐Rachford ADI scheme.

Findings

For zero‐shear boundaries the Cattanneo representation of the model equation blows up whilst the representation derived by Rajagopal is stable and produces solutions which decay over time.

Originality/value

The use of a Peaceman‐Rachford ADI scheme to solve a mixed space‐time PDE is both novel and new.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 22 no. 2
Type: Research Article
ISSN: 0961-5539

Keywords

Access Restricted. View access options
Article
Publication date: 11 October 2018

Prabhugouda Mallanagouda Patil, Shashikant A. and Ebrahim Momoniat

This paper aims to investigate the unsteady mixed convection along an exponentially stretching surface in presence of transverse magnetic field applied at the wall and the…

117

Abstract

Purpose

This paper aims to investigate the unsteady mixed convection along an exponentially stretching surface in presence of transverse magnetic field applied at the wall and the opposing buoyancy flow.

Design/methodology/approach

The dimensional partial differential equations governing the flow field are transformed to non-dimensional coupled partial differential equations with the aid of suitable non-similar transformations. The resulting equations are then solved by the coalition of quasilinearization technique and the finite difference method.

Findings

Effects of volumetric heat source/sink, suction/blowing and other dimensionless parameters on velocity and temperature profiles are examined numerically. This investigation reveals that in presence of opposing buoyancy flow, the suction and volumetric heat source enhances the skin-friction coefficient, while the rise in the MHD increases the momentum boundary layer.

Originality/value

To the best of the authors’ knowledge, no such investigation has been carried out in the literature.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 28 no. 12
Type: Research Article
ISSN: 0961-5539

Keywords

Available. Open Access. Open Access
Article
Publication date: 23 September 2024

Prabhugouda Mallanagouda Patil, Bharath Goudar and Ebrahim Momoniat

Many industries use non-Newtonian ternary hybrid nanofluids (THNF) because of how well they control rheological and heat transport. This being the case, this paper aims to…

374

Abstract

Purpose

Many industries use non-Newtonian ternary hybrid nanofluids (THNF) because of how well they control rheological and heat transport. This being the case, this paper aims to numerically study the Casson-Williamson THNF flow over a yawed cylinder, considering the effects of several slips and an inclined magnetic field. The THNF comprises Al2O3-TiO2-SiO2 nanoparticles because they improve heat transmission due to large thermal conductivity.

Design/methodology/approach

Applying suitable nonsimilarity variables transforms the coupled highly dimensional nonlinear partial differential equations (PDEs) into a system of nondimensional PDEs. To accomplish the goal of achieving the solution, an implicit finite difference approach is used in conjunction with Quasilinearization. With the assistance of a script written in MATLAB, the numerical results and the graphical representation of those solutions were ascertained.

Findings

As the Casson parameter β increases, there is an improvement in the velocity profiles in both chord and span orientations, while the gradients Re1/2Cf,Re1/2C¯f reduce for the same variations of β. The velocities of Casson THNF are greater than those of Casson-Williamson THNF. Approximately, a 202% and a 32% ascension are remarked in the magnitudes of Re1/2Cf and Re1/2C¯f for Casson-Williamson THNF than the Casson THNF only. When velocity slip attribute S1 jumps to 1 from 0.5, magnitude of both F(ξ,η) and Re1/2Cf fell down and it is reflected to be 396% at ξ=1, Wi=1 and β=1. An augmentation in thermal jump results in advanced fluid temperature and lower Re1/2Nu. In particular, about 159% of down drift is detected when S2 taking 1.

Originality/value

There is no existing research on the effects of Casson-Williamson THNF flow over a yawed cylinder with multiple slips and an angled magnetic field, according to the literature.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 34 no. 12
Type: Research Article
ISSN: 0961-5539

Keywords

Access Restricted. View access options
Article
Publication date: 3 September 2019

Prabhugouda Mallanagouda Patil, Shashikant A. and Ebrahim Momoniat

This study aims to investigate the unsteady magnetohydrodynamic mixed convective nanofluid flow by using Buongiorno two-phase model to achieve an appropriate mechanism to improve…

111

Abstract

Purpose

This study aims to investigate the unsteady magnetohydrodynamic mixed convective nanofluid flow by using Buongiorno two-phase model to achieve an appropriate mechanism to improve the efficiency of solar energy systems by mitigating the energy losses.

Design/methodology/approach

The transport phenomena occurring in this physical problem are modelled using nonlinear partial differential equations and are non-dimensionalised by using non-similar transformations. The quasilinearisation technique is used to solve the resulting system with the help of a finite difference scheme.

Findings

The study reveals that the effect of the applied transverse magnetic parameter is to increase the temperature profile and to reduce the wall heat transfer rate. The Brownian diffusion and thermophoresis parameters that characterise the nanofluids contribute to the reduction in wall heat transfer rate. The presence of nanoparticles in the fluid gives rise to critical values for the thermophoresis parameter describing the behaviour of the wall heat and mass transfer rates. Wall heating and cooling are analysed by considering the percentage increase or percentage decrease in the heat and mass transfer rates in the presence of nanoparticles in the fluid.

Research limitations/implications

The investigation on wall cooling/heating leads to the analysis of control parameters applicable to the industrial design of thermal systems for energy storage, energy harvesting and cooling applications.

Practical implications

The analysis of the control parameters is of practical value to the solar industry.

Social implications

In countries, such as South Africa, daily power cuts are a reality. Any research into improving the quality of energy obtained from alternate sources is a national necessity.

Originality/value

From the literature survey in the present study, it is found that no similar work has been reported in the open literature that analyses the time-dependent mixed convection flow along the exponentially stretching surface in the presence of the effects of a magnetic field, nanoparticles and non-similar solutions.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 30 no. 2
Type: Research Article
ISSN: 0961-5539

Keywords

Access Restricted. View access options
Article
Publication date: 15 May 2009

R. Ravindran, Satyajit Roy and E. Momoniat

The purpose of this paper is to study the steady mixed convection flow over a vertical cone in the presence of surface mass transfer when the axis of the cone is inline with the…

459

Abstract

Purpose

The purpose of this paper is to study the steady mixed convection flow over a vertical cone in the presence of surface mass transfer when the axis of the cone is inline with the flow.

Design/methodology/approach

In this case, the numerical difficulties to obtain the non‐similar solution are overcome by applying an implicit finite difference scheme in combination with the quasilinearization technique.

Findings

Numerical results are reported here to display the effects of Prandtl number, buoyancy and mass transfer (injection and suction) parameters at different stream‐wise locations on velocity and temperature profiles, and on skin friction and heat transfer coefficients.

Research limitations/implications

Thermo‐physical properties of the fluid in the flow model are assumed to be constant except the density variations causing a body force term in the momentum equation. The Boussinesq approximation is invoked for the fluid properties to relate the density changes to temperature changes and to couple in this way the temperature field to the flow field.

Practical implications

Convective heat transfer over a stationary cone is important for the thermal design of various types of industrial equipments such as heat exchangers, conisters for nuclear waste disposal, nuclear reactor cooling systems and geothermal reservoirs, etc.

Originality/value

The combined effects of thermal diffusion and surface mass transfer on a vertical cone has been studied.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 19 no. 3/4
Type: Research Article
ISSN: 0961-5539

Keywords

Access Restricted. View access options
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

Keywords

Available. Content available
2358

Abstract

Details

Kybernetes, vol. 41 no. 7/8
Type: Research Article
ISSN: 0368-492X

Access Restricted. View access options
Article
Publication date: 18 November 2013

Paras Ram and Vikas Kumar

The aim of the present study is to examine the ferrohydrodynamic laminar boundary layer flow of electrically non-conducting magnetic fluid on a uniformly heated and radially…

208

Abstract

Purpose

The aim of the present study is to examine the ferrohydrodynamic laminar boundary layer flow of electrically non-conducting magnetic fluid on a uniformly heated and radially stretchable disk with or without rotation in the presence of an externally applied magnetic field.

Design/methodology/approach

Governing equations give rise to highly non-linear coupled partial differential equations which are reduced to a set of ordinary differential equations in dimensionless form by the means of conventional similarity transformation. These equations are further discretized using central finite difference scheme. And, the solution is obtained in MATLAB environment by finding the missing boundary conditions using shooting method.

Findings

The effects of magnetic field dependent viscosity and rotation strength parameter on velocity and temperature profiles are investigated. Besides, the other significant physical quantities such as radial and tangential skin frictions, rate of heat transfer and boundary layer displacement thickness are also computed. The obtained results are discussed quantitatively and qualitatively.

Originality/value

Heat transfer in ferrofluid flow over a radially stretchable and uniformly heated rotating disk has not been investigated yet.

Details

Multidiscipline Modeling in Materials and Structures, vol. 9 no. 4
Type: Research Article
ISSN: 1573-6105

Keywords

Access Restricted. View access options
Article
Publication date: 2 August 2013

María José Pujol, Francisco A. Pujol, Fidel Aznar, Mar Pujol and Ramón Rizo

In this paper the authors aim to show the advantages of using the decomposition method introduced by Adomian to solve Emden's equation, a classical non‐linear equation that…

100

Abstract

Purpose

In this paper the authors aim to show the advantages of using the decomposition method introduced by Adomian to solve Emden's equation, a classical non‐linear equation that appears in the study of the thermal behaviour of a spherical cloud and of the gravitational potential of a polytropic fluid at hydrostatic equilibrium.

Design/methodology/approach

In their work, the authors first review Emden's equation and its possible solutions using the Frobenius and power series methods; then, Adomian polynomials are introduced. Afterwards, Emden's equation is solved using Adomian's decomposition method and, finally, they conclude with a comparison of the solution given by Adomian's method with the solution obtained by the other methods, for certain cases where the exact solution is known.

Findings

Solving Emden's equation for n in the interval [0, 5] is very interesting for several scientific applications, such as astronomy. However, the exact solution is known only for n=0, n=1 and n=5. The experiments show that Adomian's method achieves an approximate solution which overlaps with the exact solution when n=0, and that coincides with the Taylor expansion of the exact solutions for n=1 and n=5. As a result, the authors obtained quite satisfactory results from their proposal.

Originality/value

The main classical methods for obtaining approximate solutions of Emden's equation have serious computational drawbacks. The authors make a new, efficient numerical implementation for solving this equation, constructing iteratively the Adomian polynomials, which leads to a solution of Emden's equation that extends the range of variation of parameter n compared to the solutions given by both the Frobenius and the power series methods.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 23 no. 6
Type: Research Article
ISSN: 0961-5539

Keywords

1 – 10 of 55
Per page
102050