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Article
Publication date: 1 August 1998

Ò. À. Bèg, H.S. Takhar and V.M. Soundalgekar

Numerical results generated by a highly efficient finite‐difference method (originated by Keller for aerodynamical flows at the California Institute of Technology in 1970), and a…

Abstract

Numerical results generated by a highly efficient finite‐difference method (originated by Keller for aerodynamical flows at the California Institute of Technology in 1970), and a robust double shooting Runge‐Kutta‐Merson scheme are presented for the boundary layer equations representing the convection flow of a viscous incompressible fluid past a hot vertical flat plate embedded in a non‐Darcy porous medium. Viscous dissipation due to mechanical work is included in the temperature field equation. The computations for both solution techniques are compared at the leading edge (ξ = 0.0) and found to be in excellent agreement. The effects of the viscous heating parameter (Ec), thermal conductivity ratio (λ) and a Darcy porous parameter (Re/GrDa) on the fluid velocities, temperatures, local shear stress and wall heat transfer rate are discussed with applications to geothermal and industrial flows.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 8 no. 5
Type: Research Article
ISSN: 0961-5539

Keywords

Article
Publication date: 25 February 2014

S. Abbasbandy, T. Hayat, A. Alsaedi and M.M. Rashidi

– In this paper, analysis is presented to investigate the Falkner-Skan flow of magnetohydrodynamic (MHD) Oldroyd-B fluid. The paper aims to discuss these issues.

Abstract

Purpose

In this paper, analysis is presented to investigate the Falkner-Skan flow of magnetohydrodynamic (MHD) Oldroyd-B fluid. The paper aims to discuss these issues.

Design/methodology/approach

In this paper, the authors used two methods: homotopy analysis method and numerical Keller-box method.

Findings

It is observed that skin friction coefficient in Oldroyd-B fluid is larger when compared with viscous fluid. Further, the relaxation and retardation times have opposite effects on the velocity components.

Practical implications

A comparative study between the series and numerical solutions for the skin friction is shown in the paper. The results indicated that both solutions are in well agreement.

Originality/value

This model is investigated for the first time, as the authors know.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 24 no. 2
Type: Research Article
ISSN: 0961-5539

Keywords

Article
Publication date: 20 September 2011

T. Javed, M. Sajid, Z. Abbas and N. Ali

This paper looks into the rotating flow of an incompressible viscous fluid over an exponentially stretching continuous surface. The flow is governed by non‐linear partial…

Abstract

Purpose

This paper looks into the rotating flow of an incompressible viscous fluid over an exponentially stretching continuous surface. The flow is governed by non‐linear partial differential equations. A non‐similar solution is developed after transforming the governing equations using two different numerical techniques namely Keller‐box and shooting methods. The influence of the non‐dimensional local rotating parameter Ω on the velocity fields and skin friction coefficients is analyzed and discussed.

Design/methodology/approach

In this paper, the authors have used the well‐known numerical methods, Keller‐box and shooting.

Findings

It is observed that for the increase in the rotation velocity of the frame there is a reduction in the boundary layer thickness and an increase in the drag force at the surface.

Originality/value

The present study is concerned with the boundary layer flow of a rotating viscous fluid over an exponentially stretching sheet. Numerical solutions are found. To the best of the authors' knowledge, this is the first investigation of the topic.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 21 no. 7
Type: Research Article
ISSN: 0961-5539

Keywords

Article
Publication date: 10 July 2017

Khalid Mahmood, Muhammad Sajid, Nasir Ali and Tariq Javed

An attempt is made to study magnetohydrodynamic viscous fluid impinging orthogonally toward a stagnation point on a vertical surface lubricated with power law fluid. It has been…

Abstract

Purpose

An attempt is made to study magnetohydrodynamic viscous fluid impinging orthogonally toward a stagnation point on a vertical surface lubricated with power law fluid. It has been assumed that the surface temperature varies linearly with the distance from the stagnation point. The problem is governed by system of partial differential equations for both the base fluid and the lubricant. The continuity of velocity and shear stress is assumed at the interface layer between the base fluid and the lubricant. Dimensionless variables are introduced to transform original problem into ordinary differential equations. An implicit finite-difference scheme known as the Keller-Box method is implemented to obtain the numerical solutions. The influence of various important parameters is presented in the form of graphs and tables. The limiting cases for full and no-slip conditions are deduced from the present solutions. A comparison of the present results with the existing results in the special case validates the obtained numerical solutions. The purpose of this study is to see the behaviour of flow characteristics in the presence of lubrication.

Design/methodology/approach

The authors’ problem is governed by system of partial differential equations for both the base fluid and the lubricant. Dimensionless variables are introduced to transform original problem into ordinary differential equations. The obtained ordinary differential equation along with boundary conditions are highly nonlinear and coupled. An implicit finite-difference scheme known as the Keller-Box method is implemented to obtain the numerical solutions.

Findings

Some findings of this study are that the lubricant increases the velocity of the base fluid inside the boundary layer. In the case of full slip, the effects of viscosity are suppressed by the lubricant. The temperature of the base fluid decreases by increase in lubrication on the surface. By increasing the slip on the surface, the skin friction decreases and local Nusselt number increases, but the rate of increase or decrease is less in magnitude for the case of opposing flow. The similarity solutions only exist for n = 1/2. A non-similar solution is obtained for the other values of the power-law index n.

Originality/value

The study of flow phenomenon over a lubricated surface has important applications in machinery components such as fluid bearings and mechanical seals. Coating is another major application of lubrication including the preparation of thin films, printing, painting, etc. The authors hope that the current study will provide the roadmap for the future studies in this direction.

Details

Industrial Lubrication and Tribology, vol. 69 no. 4
Type: Research Article
ISSN: 0036-8792

Keywords

Article
Publication date: 18 December 2020

Thameem Basha Hayath, Sivaraj Ramachandran, Ramachandra Prasad Vallampati and O. Anwar Bég

Generally, in computational thermofluid dynamics, the thermophysical properties of fluids (e.g. viscosity and thermal conductivity) are considered as constant. However, in many…

Abstract

Purpose

Generally, in computational thermofluid dynamics, the thermophysical properties of fluids (e.g. viscosity and thermal conductivity) are considered as constant. However, in many applications, the variability of these properties plays a significant role in modifying transport characteristics while the temperature difference in the boundary layer is notable. These include drag reduction in heavy oil transport systems, petroleum purification and coating manufacturing. The purpose of this study is to develop, a comprehensive mathematical model, motivated by the last of these applications, to explore the impact of variable viscosity and variable thermal conductivity characteristics in magnetohydrodynamic non-Newtonian nanofluid enrobing boundary layer flow over a horizontal circular cylinder in the presence of cross-diffusion (Soret and Dufour effects) and appreciable thermal radiative heat transfer under a static radial magnetic field.

Design/methodology/approach

The Williamson pseudoplastic model is deployed for rheology of the nanofluid. Buongiorno’s two-component model is used for nanoscale effects. The dimensionless nonlinear partial differential equations have been solved by using an implicit finite difference Keller box scheme. Extensive validation with earlier studies in the absence of nanoscale and variable property effects is included.

Findings

The influence of notable parameters such as Weissenberg number, variable viscosity, variable thermal conductivity, Soret and Dufour numbers on heat, mass and momentum characteristics are scrutinized and visualized via graphs and tables.

Research limitations/implications

Buongiorno (two-phase) nanofluid model is used to express the momentum, energy and concentration equations with the following assumptions. The laminar, steady, incompressible, free convective flow of Williamson nanofluid is considered. The body force is implemented in the momentum equation. The induced magnetic field strength is smaller than the external magnetic field and hence it is neglected. The Soret and Dufour effects are taken into consideration.

Practical implications

The variable viscosity and thermal conductivity are considered to investigate the fluid characteristic of Williamson nanofluid because of viscosity and thermal conductivity have a prime role in many industries such as petroleum refinement, food and beverages, petrochemical, coating manufacturing, power and environment.

Social implications

This fluid model displays exact rheological characteristics of bio-fluids and industrial fluids, for instance, blood, polymer melts/solutions, nail polish, paint, ketchup and whipped cream.

Originality/value

The outcomes disclose that the Williamson nanofluid velocity declines by enhancing the Lorentz hydromagnetic force in the radial direction. Thermal and nanoparticle concentration boundary layer thickness is enhanced with greater streamwise coordinate values. An increase in Dufour number or a decrease in Soret number slightly enhances the nanofluid temperature and thickens the thermal boundary layer. Flow deceleration is induced with greater viscosity parameter. Nanofluid temperature is elevated with greater Weissenberg number and thermophoresis nanoscale parameter.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 31 no. 5
Type: Research Article
ISSN: 0961-5539

Keywords

Article
Publication date: 7 August 2009

Anwar Hossain and Rama Subba Reddy Gorla

The paper's aim is to investigate the natural convection flow of an Ostwald‐de Waele type power law non‐Newtonian fluid past an isothermal vertical slotted surface.

Abstract

Purpose

The paper's aim is to investigate the natural convection flow of an Ostwald‐de Waele type power law non‐Newtonian fluid past an isothermal vertical slotted surface.

Design/methodology/approach

The Keller‐Box method is used to solve the governing boundary layer equations for the natural convection flow of an Ostwald‐de Waele type power law non‐Newtonian fluid past an isothermal vertical slotted surface.

Findings

As the slip parameter increases, the friction factor increases whereas the heat transfer rate decreases. Owing to increase in the value of the Prandtl number, Pr, there is decrease in the value of the skin‐friction coefficient, and augmentation of heat transfer rate. As the viscosity index n increases, both the friction factor and the heat transfer rate increase.

Research limitations/implications

The analysis is valid for steady, two‐dimensional laminar flow of an Ostwald‐de Waele type power law non‐Newtonian fluid past an isothermal vertical slotted surface. An extension to three‐dimensional flow case is left for future work.

Practical implications

The method is useful to analyze perforated plates and wire netting such as perforated wings in order to reduce the drag by suction of the boundary layer, filtration or air‐conditioning.

Originality/value

The results of this study may be of interest to engineers interested in heat transfer augmentation and drag reduction in heat exchangers.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 19 no. 7
Type: Research Article
ISSN: 0961-5539

Keywords

Article
Publication date: 9 November 2012

Mamun Molla, Suvash C. Saha and M.A.I. Khan

The purpose of this paper is to discuss, with numerical simulations, magnetohydrodynamic (MHD) natural convection laminar flow from an isothermal horizontal circular cylinder…

Abstract

Purpose

The purpose of this paper is to discuss, with numerical simulations, magnetohydrodynamic (MHD) natural convection laminar flow from an isothermal horizontal circular cylinder immersed in a fluid with viscosity proportional to a linear function of temperature.

Design/methodology/approach

The governing boundary layer equations are transformed into a non‐dimensional form and the resulting nonlinear system of partial differential equations are reduced to convenient form, which are solved numerically by two very efficient methods: implicit finite difference method together with Keller box scheme; and direct numerical scheme.

Findings

Numerical results are presented by velocity and temperature distributions of the fluid as well as heat transfer characteristics, namely the shearing stress and the local heat transfer rate in terms of the local skin‐friction coefficient and the local Nusselt number for a wide range of MHD parameter, viscosity‐variation parameter and viscous dissipation parameter.

Originality/value

MHD flow in this geometry with temperature dependent viscosity is absent in the literature. IN this paper, the results obtained from the numerical simulations have been verified by two methodologies.

Article
Publication date: 1 October 2006

Mamun Molla and Anwar Hossain

To investigate the effects of chemical reaction on natural convection heat and mass transfer from a sphere with temperature dependent viscosity.

Abstract

Purpose

To investigate the effects of chemical reaction on natural convection heat and mass transfer from a sphere with temperature dependent viscosity.

Design/methodology/approach

The governing boundary layer equations are transformed into a non‐dimensional form and the resulting nonlinear system of partial differential equations are reduced to local non‐similarity boundary layer equations, which are solved numerically by very efficient implicit finite difference method together with Keller box scheme.

Findings

The effects of chemical reaction, the skin‐friction coefficients, surface heat transfer rates, velocity and concentration distribution decrease as well as the mass transfer rates and temperature distribution increase within the boundary layer.

Research limitations/implications

The investigation is valid for steady two‐dimensional laminar flow. The concentration of the reactant is maintained at a constant value and the sphere is isothermal. An extension to unsteady flow with temperature dependent thermal conductivity is left for future work.

Originality/value

This result provides guidance to engineers about heat and mass transfer with the effects of chemical reaction from isothermal spherical surface.

Details

Engineering Computations, vol. 23 no. 7
Type: Research Article
ISSN: 0264-4401

Keywords

Article
Publication date: 28 October 2013

R.S.R. Gorla and Anwar Hossain

The purpose of this work is to study the mixed convection boundary layer flow past a vertical cylinder in a porous medium saturated with a nanofluid. Numerical results for…

Abstract

Purpose

The purpose of this work is to study the mixed convection boundary layer flow past a vertical cylinder in a porous medium saturated with a nanofluid. Numerical results for friction factor, surface heat transfer rate and mass transfer rate have been presented for parametric variations of the buoyancy ratio parameter Nr, Brownian motion parameter Nb, thermophoresis parameter Nt and Lewis number Le. The dependency of the surface heat transfer rate (Nusselt number) and mass transfer rate on these parameters has been discussed.

Design/methodology/approach

Solutions of the set of non-similarity equations are obtained by employing the implicit finite difference method together with Keller box elimination method.

Findings

It was found that the heat transfer rate decreases and mass transfer rates increase as Lewis number increases. The heat and mass transfer rates increase as the buoyancy ration parameter increases. As the thermophoresis parameter Nt increases, the heat transfer rate decreases where as the mass transfer rate increases. As the Brownian parameter Nb increases, the heat transfer rate decreases. Brownian motion decelerates the flow in the nanofluid boundary layer. Brownian diffusion promotes heat conduction. The heat and mass transfer rates increase as the buoyancy ratio number Nr increases. The Brownian motion and thermophoresis of nanoparticles increases the effective thermal conductivity of the nanofluid. Both Brownian diffusion and thermophoresis give rise to cross diffusion terms that are similar to the familiar Soret and Dufour cross-diffusion terms that arise with a binary fluid.

Research limitations/implications

The analysis is valid for steady, mixed convection two-dimensional boundary layer flow in a nanofluid-saturated Darcy porous medium. An extension to non-Darcy porous medium is left as a part of future study.

Practical implications

The research is applicable for enhancing heat exchanger effectiveness by employing nanofluids.

Originality/value

The study is useful to engineers interested in designing heat exchangers, water and atmospheric pollution.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 23 no. 8
Type: Research Article
ISSN: 0961-5539

Keywords

Article
Publication date: 14 November 2023

Muhammad Faisal, Iftikhar Ahmad and Abdur Rashid

The present study aims to encompass the bidirectional magnetized flowing of a hybrid-nanofluid over an unsteady stretching device with the inclusion of thermal radiation and…

Abstract

Purpose

The present study aims to encompass the bidirectional magnetized flowing of a hybrid-nanofluid over an unsteady stretching device with the inclusion of thermal radiation and entropy generation. Brick-shaped nanoparticles (zinc-oxide and ceria) are suspended in water, serving as the base-fluid to observe the performance of the hybrid mixture. The Maxwell thermal conductivity relation is employed to link the thermophysical attributes of the hybrid mixture with the host liquid. Additionally, a heat source/sink term is incorporated in the energy balance to enhance the impact of the investigation. Both prescribed-surface-temperature (PST) and prescribed-heat-flux (PHF) conditions are applied to inspect the thermal performance of the hybrid nanofluid.

Design/methodology/approach

The transport equations in Cartesian configuration are transformed into ordinary differential equations (ODEs), and an efficient method, namely the Keller-Box method (KBM), is utilized to solve the transformed system. Postprocessing is conducted to visually represent the velocity profile, thermal distribution, skin-friction coefficients, Bejan number, Nusselt number and entropy generation function against the variations of the involved parameters.

Findings

It is observed that more entropy is generated due to the increases in temperature difference and radiation parameters. The Bejan number initially declines but then improves with higher estimations of unsteadiness and Hartmann number. Overall, the thermal performance of the system is developed for the PST scenario than the PHF scenario for different estimations of the involved constraints.

Originality/value

To the best of the authors' knowledge, no investigation has been reported yet that explains the bidirectional flow of a CeO2-ZnO/water hybrid nanofluid with the combined effects of prescribed thermal aspects (PST and PHF) and entropy generation.

Details

Multidiscipline Modeling in Materials and Structures, vol. 20 no. 1
Type: Research Article
ISSN: 1573-6105

Keywords

1 – 10 of 88