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Article
Publication date: 2 May 2017

Syed Tauseef Mohyud-din, Muhammad Asad Iqbal, Umar Khan and Xiao-Jun Yang

This paper aims to propose a method by merging Legendre wavelets method and quasilinearization technique to tackle with the nonlinearity and to get better and more…

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Abstract

Purpose

This paper aims to propose a method by merging Legendre wavelets method and quasilinearization technique to tackle with the nonlinearity and to get better and more accurate results.

Design/methodology/approach

To test the significance of the proposed scheme, the authors applied the method on the model representing magneto-hydrodynamic squeezing flow of a viscous fluid between two parallel infinite disks, where one disk is impermeable and the other is porous with either suction or injection of the fluid. For the sake of comparison, numerical solution by using RK-4 is also computed. From the graphs and tables, it is evident that the proposed method shows an excellent accordance with the numerical solution.

Findings

The solution converges to the numerical solution when the degree of Legendre polynomials m is increased. For m = 20 in all the three cases, for different values of S, M and A, the graphs of solutions obtained by Legendre wavelet quasilinearization technique show an excellent agreement with numerical solution. Also, it is evident from figures that suction and injection affects the velocity profile in opposite way. For suction, maximum velocity is seen to be at the center of the channel. Magnetic field can be used to regularize the flow and it stabilizes the flow behavior.

Originality/value

Magnetic field can be used to regularize the flow and it stabilizes the flow behavior.

Details

Engineering Computations, vol. 34 no. 3
Type: Research Article
ISSN: 0264-4401

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Article
Publication date: 24 September 2019

Mangwiro Magodora, Hiranmoy Mondal and Precious Sibanda

The purpose of this paper is to focus on the application of Chebyshev spectral collocation methodology with Gauss Lobatto grid points to micropolar fluid over a stretching…

Abstract

Purpose

The purpose of this paper is to focus on the application of Chebyshev spectral collocation methodology with Gauss Lobatto grid points to micropolar fluid over a stretching or shrinking surface. Radiation, thermophoresis and nanoparticle Brownian motion are considered. The results have attainable scientific and technological applications in systems involving stretchable materials.

Design/methodology/approach

The model equations governing the flow are transformed into non-linear ordinary differential equations which are then reworked into linear form using the Newton-based quasilinearization method (SQLM). Spectral collocation is then used to solve the resulting linearised system of equations.

Findings

The validity of the model is established using error analysis. The velocity, temperature, micro-rotation, skin friction and couple stress parameters are conferred diagrammatically and analysed in detail.

Originality/value

The study obtains numerical explanations for rapidly convergent solutions using the spectral quasilinearization method. Convergence of the numerical solutions was monitored using the residual error analysis. The influence of radiation, heat and mass parameters on the flow are depicted graphically and analysed. The study is an extension on the work by Zheng et al. (2012) and therefore the novelty is that the authors tend to take into account nanoparticles, Brownian motion and thermophoresis in the flow of a micropolar fluid.

Details

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

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Article
Publication date: 24 August 2018

R.C. Mittal and Sapna Pandit

The main purpose of this work is to develop a novel algorithm based on Scale-3 Haar wavelets (S-3 HW) and quasilinearization for numerical simulation of dynamical system…

Abstract

Purpose

The main purpose of this work is to develop a novel algorithm based on Scale-3 Haar wavelets (S-3 HW) and quasilinearization for numerical simulation of dynamical system of ordinary differential equations.

Design/methodology/approach

The first step in the development of the algorithm is quasilinearization process to linearize the problem, and then Scale-3 Haar wavelets are used for space discretization. Finally, the obtained system is solved by Gauss elimination method.

Findings

Some numerical examples of fractional dynamical system are considered to check the accuracy of the algorithm. Numerical results show that quasilinearization with Scale-3 Haar wavelet converges fast even for small number of collocation points as compared of classical Scale-2 Haar wavelet (S-2 HW) method. The convergence analysis of the proposed algorithm has been shown that as we increase the resolution level of Scale-3 Haar wavelet error goes to zero rapidly.

Originality/value

To the best of authors’ knowledge, this is the first time that new Haar wavelets Scale-3 have been used in fractional system. A new scheme is developed for dynamical system based on new Scale-3 Haar wavelets. These wavelets take less time than Scale-2 Haar wavelets. This approach extends the idea of Jiwari (2015, 2012) via translation and dilation of Haar function at Scale-3.

Details

Engineering Computations, vol. 35 no. 5
Type: Research Article
ISSN: 0264-4401

Keywords

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Article
Publication date: 1 July 2020

Ankita Bisht and Rajesh Sharma

The main purpose of this study is to present a non-similar analysis of two-dimensional boundary layer flow of non-Newtonian nanofluid over a vertical stretching sheet with…

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Abstract

Purpose

The main purpose of this study is to present a non-similar analysis of two-dimensional boundary layer flow of non-Newtonian nanofluid over a vertical stretching sheet with variable thermal conductivity. The Sisko fluid model is used for non-Newtonian fluid with an exponent (n* > 1), that is, shear thickening fluid. Buongiorno model for nanofluid accounting Brownian diffusion and thermophoresis effects is used to model the governing differential equations.

Design/methodology/approach

The governing boundary layer equations are converted into nondimensional coupled nonlinear partial differential equations using appropriate transformations. The resultant differential equations are solved numerically using implicit finite difference scheme in association with the quasilinearization technique.

Findings

This analysis shows that the temperature raises for thermal conductivity parameter and velocity ratio parameter while decreases for the thermal buoyancy parameter. The thermophoresis and Brownian diffusion parameter that characterizes the nanofluid flow enhances the temperature and reduces the heat transfer rate. Skin friction drag can be effectively reduced by proper control of the values of thermal buoyancy and velocity ratio parameter.

Practical implications

The wall heating and cooling investigation result in the analysis of the control parameters that are related to the designing and manufacturing of thermal systems for cooling applications and energy harvesting. These control parameters have practical significance in the designing of heat exchangers and solar thermal collectors, in glass and polymer industries, in the extrusion of plastic sheets, the process of cooling of the metallic plate, etc.

Originality/value

To the best of authors’ knowledge, it is found from the literature survey that no similar work has been published which investigates the non-similar solution of Sisko nanofluid with variable thermal conductivity using finite difference method and quasilinearization technique.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 31 no. 1
Type: Research Article
ISSN: 0961-5539

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Article
Publication date: 30 June 2021

Umer Saeed

The purpose of the present work is to propose a wavelet method for the numerical solutions of Caputo–Hadamard fractional differential equations on any arbitrary interval.

Abstract

Purpose

The purpose of the present work is to propose a wavelet method for the numerical solutions of Caputo–Hadamard fractional differential equations on any arbitrary interval.

Design/methodology/approach

The author has modified the CAS wavelets (mCAS) and utilized it for the solution of Caputo–Hadamard fractional linear/nonlinear initial and boundary value problems. The author has derived and constructed the new operational matrices for the mCAS wavelets. Furthermore, The author has also proposed a method which is the combination of mCAS wavelets and quasilinearization technique for the solution of nonlinear Caputo–Hadamard fractional differential equations.

Findings

The author has proved the orthonormality of the mCAS wavelets. The author has constructed the mCAS wavelets matrix, mCAS wavelets operational matrix of Hadamard fractional integration of arbitrary order and mCAS wavelets operational matrix of Hadamard fractional integration for Caputo–Hadamard fractional boundary value problems. These operational matrices are used to make the calculations fast. Furthermore, the author works out on the error analysis for the method. The author presented the procedure of implementation for both Caputo–Hadamard fractional initial and boundary value problems. Numerical simulation is provided to illustrate the reliability and accuracy of the method.

Originality/value

Many scientist, physician and engineers can take the benefit of the presented method for the simulation of their linear/nonlinear Caputo–Hadamard fractional differential models. To the best of the author’s knowledge, the present work has never been proposed and implemented for linear/nonlinear Caputo–Hadamard fractional differential equations.

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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…

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

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Article
Publication date: 20 December 2019

Ankita Bisht and Rajesh Sharma

The purpose of this study is to provide a numerical investigation of Casson nanofluid along a vertical nonlinear stretching sheet with variable thermal conductivity and viscosity.

Abstract

Purpose

The purpose of this study is to provide a numerical investigation of Casson nanofluid along a vertical nonlinear stretching sheet with variable thermal conductivity and viscosity.

Design/methodology/approach

The boundary-layer equations are presented in the dimensionless form using proper non-similar transformations. The subsequent non-dimensional nonlinear partial differential equations are solved using the implicit finite difference technique. To linearize the nonlinear terms present in these equations, the quasilinearization technique is used.

Findings

The investigation showed graphically the temperature, velocity and nanoparticle volume fraction for particular included physical parameters. It is observed that the velocity profile decreases with an increase in the values of Casson fluid parameter while increases with an increase in the viscosity variation parameter. The temperature profile enhances for large values of velocity variation parameter and thermal conductivity parameter while it reduces for large values of thermal buoyancy parameter. Further, the Nusselt number and skin-friction coefficient are introduced which are helpful in determining the physical aspects of Casson nanofluid flow.

Practical implications

The immediate control of heat transfer in the industrial system is crucial because of increasing energy prices. Recently, nanotechnology is proposed to control the heat transfer phenomenon. Ongoing research in complex nanofluid has been fruitful in various applications such as solar thermal collectors, nuclear reactors, electronic equipment and diesel–electric conductor. A reasonable amount of nanoparticle when added to the base fluid in solar thermal collectors serves to deeper absorption of incident radiation, and hence it upgrades the efficiency of the solar thermal collectors.

Originality/value

The non-similar solution of Casson nanofluid due to a vertical nonlinear stretching sheet with variable viscosity and thermal conductivity is discussed in this work.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 22 no. 8
Type: Research Article
ISSN: 0961-5539

Keywords

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Article
Publication date: 5 June 2017

Ram Jiwari, Vikas Kumar, Ram Karan and Ali Saleh Alshomrani

This paper aims to deal with two-dimensional magneto-hydrodynamic (MHD) Falkner–Skan boundary layer flow of an incompressible viscous electrically conducting fluid over a…

Abstract

Purpose

This paper aims to deal with two-dimensional magneto-hydrodynamic (MHD) Falkner–Skan boundary layer flow of an incompressible viscous electrically conducting fluid over a permeable wall in the presence of a magnetic field.

Design/methodology/approach

Using the Lie group approach, the Lie algebra of infinitesimal generators of equivalence transformations is constructed for the equation under consideration. Using these suitable similarity transformations, the governing partial differential equations are reduced to linear and nonlinear ordinary differential equations (ODEs). Further, Haar wavelet approach is applied to the reduced ODE under the subalgebra 4.1 for constructing numerical solutions of the flow problem.

Findings

A new type of solutions was obtained of the MHD Falkner–Skan boundary layer flow problem using the Haar wavelet quasilinearization approach via Lie symmetric analysis.

Originality/value

To find a solution for the MHD Falkner–Skan boundary layer flow problem using the Haar wavelet quasilinearization approach via Lie symmetric analysis is a new approach for fluid problems.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 27 no. 6
Type: Research Article
ISSN: 0961-5539

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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…

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

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Article
Publication date: 5 October 2018

Prabhugouda Mallanagouda Patil and Shashikant A.

The purpose of this paper is to consider the influence of slip flow and thermal jump and to investigate its effects on unsteady mixed convection along an exponentially…

Abstract

Purpose

The purpose of this paper is to consider the influence of slip flow and thermal jump and to investigate its effects on unsteady mixed convection along an exponentially stretching surface. It is also intended to explore the influence of suction/injection and volumetric heat source/sink on the fluid flow.

Design/methodology/approach

The assumed problem is modelled into governing equations which are dimensional non-linear partial differential equations in nature. To obtain solutions, initially the governing equations were made non-dimensional by the suitable non-similar transformations. Then, the dimensionless non-linear partial differential equations are linearized with the aid of Quasilinearization technique. The so obtained equations are discretized by the implicit finite difference method.

Findings

The detailed analysis of the considered problem displays that the non-similarity variable reduces the velocity and temperature profiles. For higher values of mixed convection parameter, the magnitude of velocity profile as well as the Nusselt number increase. The unsteady variable diminishes the fluid flow. The higher values of velocity ratio parameter reduce the skin-friction coefficient. Further, the magnitude of skin-friction coefficient and heat transfer rate are to minimize for increasing values of partial slip and thermal jump parameters, respectively. Volumetric heat source and injection parameters are to rise the flow behavior within the momentum and thermal boundary layers significantly.

Originality/value

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

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 28 no. 9
Type: Research Article
ISSN: 0961-5539

Keywords

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