Search results

1 – 10 of 49
Article
Publication date: 26 August 2014

Anjali Verma, Ram Jiwari and Satish Kumar

The purpose of this paper is to propose a numerical scheme based on forward finite difference, quasi-linearisation process and polynomial differential quadrature method to find…

Abstract

Purpose

The purpose of this paper is to propose a numerical scheme based on forward finite difference, quasi-linearisation process and polynomial differential quadrature method to find the numerical solutions of nonlinear Klein-Gordon equation with Dirichlet and Neumann boundary condition.

Design/methodology/approach

In first step, time derivative is discretised by forward difference method. Then, quasi-linearisation process is used to tackle the non-linearity in the equation. Finally, fully discretisation by differential quadrature method (DQM) leads to a system of linear equations which is solved by Gauss-elimination method.

Findings

The accuracy of the proposed method is demonstrated by several test examples. The numerical results are found to be in good agreement with the exact solutions and the numerical solutions exist in literature. The proposed scheme can be expended for multidimensional problems.

Originality/value

The main advantage of the present scheme is that the scheme gives very accurate and similar results to the exact solutions by choosing less number of grid points. Secondly, the scheme gives better accuracy than (Dehghan and Shokri, 2009; Pekmen and Tezer-Sezgin, 2012) by choosing less number of grid points and big time step length. Also, the scheme can be extended for multidimensional problems.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 24 no. 7
Type: Research Article
ISSN: 0961-5539

Keywords

Article
Publication date: 20 October 2023

Sapna Pandit, Pooja Verma, Manoj Kumar and Poonam

This article offered two meshfree algorithms, namely the local radial basis functions-finite difference (LRBF-FD) approximation and local radial basis functions-differential…

Abstract

Purpose

This article offered two meshfree algorithms, namely the local radial basis functions-finite difference (LRBF-FD) approximation and local radial basis functions-differential quadrature method (LRBF-DQM) to simulate the multidimensional hyperbolic wave models and work is an extension of Jiwari (2015).

Design/methodology/approach

In the evolvement of the first algorithm, the time derivative is discretized by the forward FD scheme and the Crank-Nicolson scheme is used for the rest of the terms. After that, the LRBF-FD approximation is used for spatial discretization and quasi-linearization process for linearization of the problem. Finally, the obtained linear system is solved by the LU decomposition method. In the development of the second algorithm, semi-discretization in space is done via LRBF-DQM and then an explicit RK4 is used for fully discretization in time.

Findings

For simulation purposes, some 1D and 2D wave models are pondered to instigate the chastity and competence of the developed algorithms.

Originality/value

The developed algorithms are novel for the multidimensional hyperbolic wave models. Also, the stability analysis of the second algorithm is a new work for these types of model.

Article
Publication date: 12 June 2017

Ali Saleh Alshomrani, Sapna Pandit, Abdullah K. Alzahrani, Metib Said Alghamdi and Ram Jiwari

The main purpose of this work is the development of a numerical algorithm based on modified cubic trigonometric B-spline functions for computational modelling of hyperbolic-type…

Abstract

Purpose

The main purpose of this work is the development of a numerical algorithm based on modified cubic trigonometric B-spline functions for computational modelling of hyperbolic-type wave equations. These types of equations describe a variety of physical models in the vibrations of structures, nonlinear optics, quantum field theory and solid-state physics, etc.

Design/methodology/approach

Dirichlet boundary conditions cannot be handled easily by cubic trigonometric B-spline functions. Then, a modification is made in cubic trigonometric B-spline functions to handle the Dirichlet boundary conditions and a numerical algorithm is developed. The proposed algorithm reduced the hyperbolic-type wave equations into a system of first-order ordinary differential equations (ODEs) in time variable. Then, stability-preserving SSP-RK54 scheme and the Thomas algorithm are used to solve the obtained system. The stability of the algorithm is also discussed.

Findings

A different technique based on modified cubic trigonometric B-spline functions is proposed which is quite different from the schemes developed (Abbas et al., 2014; Nazir et al., 2016) and depicts the computational modelling of hyperbolic-type wave equations.

Originality/value

To the best of the authors’ knowledge, this technique is novel for solving hyperbolic-type wave equations and the developed algorithm is free from quasi-linearization process and finite difference operators for time derivatives. This algorithm gives better results than the results discussed in literature (Dehghan and Shokri, 2008; Batiha et al., 2007; Mittal and Bhatia, 2013; Jiwari, 2015).

Article
Publication date: 4 January 2019

Abhishek Kumar Singh, A.K. Singh and S. Roy

The purpose of the present study is to analyze the mixed convection water boundary layer flows over moving vertical plate with variable viscosity and Prandtl number. The…

Abstract

Purpose

The purpose of the present study is to analyze the mixed convection water boundary layer flows over moving vertical plate with variable viscosity and Prandtl number. The non-linear partial differential equation governing the flow and thermal fields are presented in non-dimensional form by using appropriate transformation. The quasi-linearization technique in combination with implicit finite difference scheme has been adopted to solve the nonlinear-coupled partial differential equation. The numerical results are displayed graphically to illustrate the influence of various non-dimensional physical parameters on velocity and temperature. Further, the numerical results for local skin-friction coefficient and local Nusselt number are also reported. The present findings are compared with previously reported results, and these comparisons are found to be in excellent agreement.

Design/methodology/approach

The nonlinear partial differential equations governing the flow and thermal fields have been solved numerically using the implicit finite difference scheme in combination with the quasi-linearization technique. The numerical results are presented in terms of skin friction and heat transfer rate which are useful in determining the surface heat requirements for stabilizing the laminar boundary layer flow over a moving plate in water.

Findings

The effect of the ratio of free-stream velocity to the composite reference velocity is significant on the velocity profile. Near the wall region, as ratio of free stream velocity to composite reference velocity increases form 0.1 to 0.5, the velocity overshoot gets enhanced from 3 per cent to 41 per cent. The influence of buoyancy parameter and ration of free stream velocity to composite reference velocity on temperature profile is comparatively less than on velocity profiles. The increase in the skin friction coefficient is dependent on the increase in the value of ratio of free stream velocity to composite reference velocity if the buoyancy parameter λ is fixed and vice versa and increases in ΔT results in a decrease in N and Pr.

Originality/value

The present investigation is to deal with the solution of steady laminar water boundary layer flows over a moving plate with temperature-dependent viscosity and Prandtl number applicable for water using practical data. The fluid considered here is water, as it is one of the most common working fluids found in engineering applications.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 29 no. 2
Type: Research Article
ISSN: 0961-5539

Keywords

Article
Publication date: 12 January 2010

P. Saikrishnan, Satyajit Roy, H.S. Takhar and R. Ravindran

The purpose of this paper is to study the influence of thermally stratified medium on a free convection flow from a sphere, which is rotating about the vertical axis, immersed in…

Abstract

Purpose

The purpose of this paper is to study the influence of thermally stratified medium on a free convection flow from a sphere, which is rotating about the vertical axis, immersed in a stably thermally stratified medium.

Design/methodology/approach

An implicit finite‐difference scheme in combination with the quasi‐linearization technique is applied to obtain the steady state non‐similar solutions of the governing boundary layer equations for flow and temperature fields.

Findings

The numerical results indicate that the heat transfer rate at the wall decreases significantly with an increasing thermal stratification parameter, but its effect on the skin friction coefficients is rather minimum. In fact, the presence of thermal stratification of the medium influences the heat transfer at wall to be in opposite direction, that is, from fluids to the wall above a certain height. The heat transfer rate increases but the skin frictions decrease with the increase of Prandtl number. In particular, the effect of buoyancy force is much more sensitive for low Prandtl number fluids (Pr = 0.7, air) than that of high Prandtl number fluids (Pr = 7, water). Also the skin friction in rotating direction is less sensitive to the buoyancy force as the buoyancy force acts in the streamwise direction for the present study of thermally stratified medium.

Research limitations/implications

The ambient temperature T∞∞ is assumed to increase linearly with height $h$. The viscous dissipation term, which is usually small for natural convection flows, has been neglected in the energy equation. The flow is assumed to be axi‐symmetric. The Boussinesq approximation is invoked for the fluid properties to relate density changes to temperature changes, and to couple in this way the temperature field to the flow field.

Practical implications

Free convection in a thermally stratified medium occurs in many environmental processes with temperature stratification, and in industrial applications within a closed chamber with heated walls. Also, free convections associated with heat rejection systems for long‐duration deep ocean powder modules where ocean environment is stratified are examples of such type.

Originality/value

The research presented in this paper investigates the free convection flow on a sphere, which is rotating with a constant angular velocity along its vertical axis in a stably thermally stratified fluid.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 20 no. 1
Type: Research Article
ISSN: 0961-5539

Keywords

Article
Publication date: 23 November 2018

Subrata Das, Hiranmoy Mondal, Prabir Kumar Kundu and Precious Sibanda

The focus of the paper is only on the contributions toward the use of entropy generation of non-Newtonian Casson fluid over an exponential stretching sheet. The purpose of this…

Abstract

Purpose

The focus of the paper is only on the contributions toward the use of entropy generation of non-Newtonian Casson fluid over an exponential stretching sheet. The purpose of this paper is to investigate the entropy generation and homogeneous–heterogeneous reaction. Velocity and thermal slips are considered instead of no-slip conditions at the boundary.

Design/methodology/approach

Basic equations in form of partial differential equations are converted into a system of ordinary differential equations and then solved using the spectral quasi-linearization method (SQLM).

Findings

The validity of the model is established using error analysis. Variation of the velocity, temperature, concentration profiles and entropy generation against some of the governing parameters are presented graphically. It is to be noted that the increase in entropy generation due to increase in heterogeneous reaction parameter is due to the increase in heat transfer irreversibility. It is further noted that the Bejan number decreases with Brinkman number because increase in Brinkman number reduces the total entropy generation.

Originality/value

This paper acquires realistic numerical explanations for rapidly convergent temperature and concentration profiles using the SQLM. Convergence of the numerical solutions was monitored using the residual error of the PDEs. The resulting equations are then integrated using the SQLM. The influence of emergent flow, heat and mass transfer parameters effects are shown graphically.

Details

Multidiscipline Modeling in Materials and Structures, vol. 15 no. 2
Type: Research Article
ISSN: 1573-6105

Keywords

Article
Publication date: 18 May 2010

P.M. Patil, S. Roy and Ali J. Chamkha

The purpose of this paper is to consider steady two‐dimensional mixed convection flow along a vertical semi‐infinite power‐law stretching sheet. The velocity and temperature of…

Abstract

Purpose

The purpose of this paper is to consider steady two‐dimensional mixed convection flow along a vertical semi‐infinite power‐law stretching sheet. The velocity and temperature of the sheet are assumed to vary in a power‐law form.

Design/methodology/approach

The problem is formulated in terms of non‐similar equations. These equations are solved numerically by an efficient implicit, iterative, finite‐difference method in combination with a quasi‐linearization technique.

Findings

It was found that the skin‐friction coefficient increased with the ratio of free‐stream velocity to the composite reference velocity and the buoyancy parameter while it decreased with exponent parameter. The heat transfer rate increased with the Prandtl number, buoyancy parameter and the exponent parameter.

Practical implications

A very useful source of information for researchers on the subject of convective flow over stretching sheets.

Originality/value

This paper illustrates mixed convective flow over a power‐law stretched surface with variable wall temperature.

Details

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

Keywords

Article
Publication date: 22 March 2021

Iyyappan G. and Abhishek Kumar Singh

The purpose of this paper is to analyse the force convection laminar boundary layer flow on irregular boundary in diverging channel with the presence of magnetic field effects…

Abstract

Purpose

The purpose of this paper is to analyse the force convection laminar boundary layer flow on irregular boundary in diverging channel with the presence of magnetic field effects. Effects of various fluid parameters such as suction/injection, viscous dissipation, magnetic parameter and heat source/sink on velocity and temperature profiles are numerically analyzed. Moreover, numerically investigated on skin-friction and heat transfer coefficients when suction/injection occur.

Design/methodology/approach

The governing coupled partial differential equations are transformed to dimensionless form using non-similarity transformations. The non-dimensional partial differential equations are linearized by quasi-linearization technique and solved by varga's algorithm with numerical finite difference scheme on a non-uniform mesh.

Findings

The computation results are presented in terms of temperature, heat transfer and skin friction coefficients; these are useful for determining surface heat requirements. It was found that, in finite difference scheme for non-uniform mesh with quasi-linearization technique method gives smoothness of solution compared to finite difference scheme for uniform mesh, and this evidence is graphically represented in Figure 2.

Originality/value

The impacts of viscous dissipation (Ec) and magnetic parameter (Ha) on temperature profiles, skin friction and heat transfer are analyzed, which determine the heat generation/absorption to ensure the MHD flow of the laminar boundary layer on irregular boundary over a diverging channel.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 31 no. 7
Type: Research Article
ISSN: 0961-5539

Keywords

Article
Publication date: 15 June 2018

Prabhugouda Mallanagouda Patil, Nafisabanu Kumbarwadi and Shashikant A.

The purpose of this paper is to investigate the magnetohydrodynamics mixed convection flow over an exponentially stretching surface in the presence of non-uniform heat source/sink…

Abstract

Purpose

The purpose of this paper is to investigate the magnetohydrodynamics mixed convection flow over an exponentially stretching surface in the presence of non-uniform heat source/sink and cross-diffusion. Adequate non-similar transformations are used to transform governing mixed convection boundary layer equations to dimensionless form.

Design/methodology/approach

These dimensionless partial differential equations are solved by using implicit finite difference scheme in conjunction with Quasi-linearization technique.

Findings

The effects of admissible parameters such as Eckert number (Ec), the ratio of buoyancy forces parameter (N), non-uniform heat source/sink, Soret and Dufour numbers on flow, temperature and concentration distributions are discussed and analysed through graphs. In addition, the results for skin friction coefficient, Sherwood number and Nusselt number are presented and discussed graphically.

Originality/value

In literature, no research work has been found in similar to this research paper.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 28 no. 6
Type: Research Article
ISSN: 0961-5539

Keywords

Article
Publication date: 7 June 2013

P.M. Patil and Ali J. Chamkha

The purpose of this work is to study heat and mass transfer from mixed convection flow of polar fluid along a plate in porous media with chemical reaction.

Abstract

Purpose

The purpose of this work is to study heat and mass transfer from mixed convection flow of polar fluid along a plate in porous media with chemical reaction.

Design/methodology/approach

The governing equations for this problem are solved numerically.

Findings

Polar fluids behave very differently from Newtonian fluids.

Originality/value

This work is original as little work has been reported for polar fluids.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 23 no. 5
Type: Research Article
ISSN: 0961-5539

Keywords

1 – 10 of 49