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Article
Publication date: 12 December 2018

Sahin Yigit and Nilanjan Chakraborty

This paper aims to conduct numerical simulations to investigate steady-state laminar Rayleigh–Bénard convection of yield stress fluids obeying Bingham model in rectangular…

88

Abstract

Purpose

This paper aims to conduct numerical simulations to investigate steady-state laminar Rayleigh–Bénard convection of yield stress fluids obeying Bingham model in rectangular cross-sectional cylindrical annular enclosures. In this investigation, axisymmetric simulations have been carried out for nominal Rayleigh number range Ra = 103 to 105, aspect ratio range AR = 0.25 to 4 (i.e. AR = H/L where H is the enclosure height and L is the difference between outer and inner radii) and normalised inner radius range ri/L = 0 to 16 (where ri is internal cylinder radius) for a nominal representative Prandtl number Pr = 500. Both constant wall temperature (CWT) and constant wall heat flux (CWHF) boundary conditions have been considered for differentially heated horizontal walls to analyse the effects of wall boundary condition.

Design/methodology/approach

The bi-viscosity Bingham model is used to mimic Bingham fluids for Rayleigh–Bénard convection of Bingham fluids in vertical cylindrical annuli. The conservation equations of mass, momentum and energy have been solved in a coupled manner using the finite volume method where a second-order central differencing scheme is used for the diffusive terms and a second-order up-wind scheme is used for the convective terms. The well-known semi-implicit method for pressure-linked equations algorithm is used for the coupling of the pressure and velocity.

Findings

It is found that the convective transport strengthens (weakens) with an increase in Ra (AR) for both Newtonian (i.e. Bn = 0) and Bingham fluids, regardless of the boundary conditions. Moreover, the strength of convection is stronger in the CWT configuration than that is for CWHF boundary condition due to higher temperature difference between horizontal walls for both Newtonian (i.e. Bn = 0) and Bingham fluids. The mean Nusselt number Nūcy does not show a monotonic increase with increasing Ra for AR = 1 and ri/L = 4 because of the change in flow pattern (i.e. number of convection rolls/cells) in the CWT boundary condition, whereas a monotonic increase of Nūcy with increasing Ra is obtained for the CWHF configuration. In addition, Nūcy increases with increasing ri/L and asymptotically approaches the corresponding value obtained for rectangular enclosures (ri/L → ∞) for both CWT and CWHF boundary conditions for large values of ri/L. It is also found that both the flow pattern and the mean Nusselt number Nūcy are dependent on the initial conditions for Bingham fluid cases, as hysteresis is evident for AR = 1 for both CWT and CWHF boundary conditions.

Originality value

Finally, the numerical findings have been used to propose a correlation for Nūcy in the range of 0.25 ≤ ri/L ≤ 16, 0.25 ≤ AR ≤ 2 and 5 × 104Ra ≤ 105 for the CWHF configuration.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 29 no. 1
Type: Research Article
ISSN: 0961-5539

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Article
Publication date: 1 August 1954

H.L. Bingham

THIS paper dealt with a very important branch of lubricant testing. Methods of field testing cutting oils have presented difficult problems since they were first used and…

37

Abstract

THIS paper dealt with a very important branch of lubricant testing. Methods of field testing cutting oils have presented difficult problems since they were first used and laboratory tests are also difficult because of the many varying operating conditions during test. The author described tests for drilling and turning which are designed to evaluate cutting oils. This work emphasises the difficulties involved. The efficiency of a cutting tool is dependent mainly upon cooling and lubrication, the physical requirements of the former being known. Reduction in friction will lower the cutting forces at the tool and result in more economical cutting, but the complex nature of the cutting process does not lend itself readily to a fundamental study of these properties, for the many variables present influence the chip form on which depends the ability of the lubricant to penetrate into the cutting region.

Details

Industrial Lubrication and Tribology, vol. 6 no. 8
Type: Research Article
ISSN: 0036-8792

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Article
Publication date: 1 October 1959

THE MODERN INTERNAL COMBUSTION ENGINE has been developed to a high level of efficiency and when used in cither public transport vehicle or privately owned motor, will run for…

15

Abstract

THE MODERN INTERNAL COMBUSTION ENGINE has been developed to a high level of efficiency and when used in cither public transport vehicle or privately owned motor, will run for thousands of miles before repair or replacements of worn parts is necessary. The problems which have up to now occupied the attention of lubricant manufacturers have, so far as the engine itself is concerned, been in the main connected with improving the quality of the engine oil in respect of oxidation resistance and carbon dispersing properties. Hydrodynamically a simple overall drop in viscosity level has gone a long way to ease starting torque and battery life. As might be expected, more attention has been paid to the transmission where the major mechanical development of the last few decades was the hypoid gear which could never have been economically applied unless special lubricants had become available.

Details

Industrial Lubrication and Tribology, vol. 11 no. 10
Type: Research Article
ISSN: 0036-8792

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Article
Publication date: 1 March 1952

The Institute of Petroleum held a Symposium on Gear Lubrication at Manson House, 26 Portland Place, London, W.1. on February 13th. This was timely in view of the growing use of…

109

Abstract

The Institute of Petroleum held a Symposium on Gear Lubrication at Manson House, 26 Portland Place, London, W.1. on February 13th. This was timely in view of the growing use of hypoid gears for automobile use and the need for standardized testing procedure for hypoid lubricants. The papers dealt also with gear lubrication generally, including worm gearing. An abstract of all the papers is given here. Many of the papers presented were highly technical and were intended to be of more interest to research workers and to lubrication technologists in the trade. Several of them, and some parts of all of them, however, brought out many practical points.

Details

Industrial Lubrication and Tribology, vol. 4 no. 3
Type: Research Article
ISSN: 0036-8792

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Article
Publication date: 1 April 1954

A Symposium on Metal Cutting Oils was held by the Institute of Petroleum on March 19th, and as usual where lubrication subjects are discussed, was well attended. Most valuable…

15

Abstract

A Symposium on Metal Cutting Oils was held by the Institute of Petroleum on March 19th, and as usual where lubrication subjects are discussed, was well attended. Most valuable papers were presented by many who specialize in this field both in connection with research as well as the industrial field. The Symposium was divided into two sections. Metal Cutting and Metal Forming respectively. We give here extracts from some of the papers presented in the first section and shall cover the second section in our next issue.

Details

Industrial Lubrication and Tribology, vol. 6 no. 4
Type: Research Article
ISSN: 0036-8792

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Article
Publication date: 13 November 2018

Sahin Yigit and Nilanjan Chakraborty

This paper aims to numerically analyse natural convection of yield stress fluids in rectangular cross-sectional cylindrical annular enclosures. The laminar steady-state…

90

Abstract

Purpose

This paper aims to numerically analyse natural convection of yield stress fluids in rectangular cross-sectional cylindrical annular enclosures. The laminar steady-state simulations have been conducted for a range of different values of normalised internal radius (ri/L 1/8 to 16, where L is the difference between outer and inner radii); aspect ratio (AR = H/L from 1/8 to 8 where H is the enclosure height); and nominal Rayleigh number (Ra from 103 to 106) for a single representative value of Prandtl number (Pr is 500).

Design/methodology/approach

The Bingham model has been used to mimic the yield stress fluid motion, and numerical simulations have been conducted for both constant wall temperature (CWT) and constant wall heat flux (CWHF) boundary conditions for the vertical side walls. The conservation equations of mass, momentum and energy have been solved in a coupled manner using the finite volume method where a second-order central differencing scheme is used for the diffusive terms and a second-order up-wind scheme is used for the convective terms. The well-known semi-implicit method for pressure-linked equations algorithm is used for the coupling of the pressure and velocity.

Findings

It is found that the mean Nusselt number based on the inner periphery Nu¯i increases (decreases) with an increase in Ra (Bn) due to augmented buoyancy (viscous) forces irrespective of the boundary condition. The ratio of convective to diffusive thermal transport increases with increasing ri/L for both Newtonian (i.e. Bn = 0) and Bingham fluids regardless of the boundary condition. Moreover, the mean Nusselt number Nu¯i normalised by the corresponding Nusselt number due to pure conductive transport (i.e. Nu¯i/(Nu¯i)cond) shows a non-monotonic trend with increasing AR in the CWT configuration for a given set of values of Ra, Pr, Li for both Newtonian (i.e. Bn = 0) and Bingham fluids, whereas Nu¯i/(Nu¯i)cond increases monotonically with increasing AR in the CWHF configuration. The influences of convective thermal transport strengthen while thermal diffusive transport weakens with increasing AR, and these competing effects are responsible for the non-monotonic Nu¯i/(Nu¯i)cond variation with AR in the CWT configuration.

Originality/value

Detailed scaling analysis is utilised to explain the observed influences of Ra, BN, ri/L and AR, which along with the simulation data has been used to propose correlations for Nu¯i.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 29 no. 1
Type: Research Article
ISSN: 0961-5539

Keywords

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Article
Publication date: 6 February 2017

Sahin Yigit and Nilanjan Chakraborty

This paper aims to investigate the aspect ratio (AR; ratio of enclosure height:length) dependence of steady-state Rayleigh–Bénard convection of Bingham fluids within rectangular…

171

Abstract

Purpose

This paper aims to investigate the aspect ratio (AR; ratio of enclosure height:length) dependence of steady-state Rayleigh–Bénard convection of Bingham fluids within rectangular enclosures for both constant wall temperature and constant wall heat flux boundary conditions. A nominal Rayleigh number range 103 ≤ Ra ≤ 105 (Ra defined based on the height) for a single representative value of nominal Prandtl number (i.e. Pr = 500) has been considered for 1/4 ≤ AR ≤ 4.

Design/methodology/approach

The bi-viscosity Bingham model is used to mimic Bingham fluids for Rayleigh–Bénard convection of Bingham fluids in rectangular enclosures. The conservation equations of mass, momentum and energy have been solved in a coupled manner using the finite volume method where a second-order central differencing scheme is used for the diffusive terms and a second-order up-wind scheme is used for the convective terms. The well-known semi-implicit method for pressure-linked equations algorithm is used for the coupling of the pressure and velocity.

Findings

It has been found that buoyancy-driven flow strengthens with increasing nominal Rayleigh number Ra, but the convective transport weakens with increasing Bingham number Bn, because of additional flow resistance arising from yield stress in Bingham fluids. The relative contribution of thermal conduction (advection) to the total thermal transport strengthens (diminishes) with increasing AR for a given set of values of Ra and Pr for both Newtonian and Bingham fluids for both boundary conditions, and the thermal transport takes place purely because of conduction for tall enclosures.

Originality/value

Correlations for the mean Nusselt number Nu ¯ have been proposed for both boundary conditions for both Newtonian and Bingham fluids using scaling arguments, and the correlations have been demonstrated to predict Nu ¯ obtained from simulation data for 1/4 ≤ AR ≤ 4, 103Ra ≤ 105 and Pr = 500.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 27 no. 2
Type: Research Article
ISSN: 0961-5539

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Article
Publication date: 3 June 2024

Ankita Bisht and Sanjalee Maheshwari

The purpose of this article is to present a mathematical model for the fully developed flow of Bi-viscous Bingham nanofluid through a uniform-width anisotropic porous channel. The…

35

Abstract

Purpose

The purpose of this article is to present a mathematical model for the fully developed flow of Bi-viscous Bingham nanofluid through a uniform-width anisotropic porous channel. The model incorporates a generalized Brinkman-Darcy formulation for the porous layers while considering the motion of nanoparticles influenced by both Brownian diffusion and thermophoresis effects.

Design/methodology/approach

The similarity transformations derived through Lie group analysis are used to reduce the system from nonlinear partial differential equations to nonlinear ordinary differential equations. The finite difference method-based numerical routine bvp4c is employed to collect and graphically present the outcomes for velocity, temperature, and nanoparticle concentration profiles. The flow pattern is analyzed through streamlined plots. Furthermore, skin friction, heat, and mass transmission rates are investigated and presented via line plots.

Findings

It is observed that in anisotropic porous media, the temperature profile is stronger than in isotropic porous media. The thermal anisotropic parameter enhances the concentration profile while reducing the temperature.

Practical implications

Anisotropy arises in various industrial and natural systems due to factors such as preferred orientation or asymmetric geometry of fibers or grains. Hence, this study has applications in oil extraction processes, certain fibrous and biological materials, geological formations, and dendritic zones formed during the solidification of binary alloys.

Originality/value

1. The permeability and thermal conductivity are not constant; instead, they have different values in the x and y directions. 2. This study considers the dependency of thermophoresis on nanoparticle volume fraction and Brownian diffusion on the temperature in both the fluid flow equations and boundary conditions. 3. A novel similarity transformation is derived using Lie group analysis instead of using an existing transformation already available in the literature.

Details

Multidiscipline Modeling in Materials and Structures, vol. 20 no. 4
Type: Research Article
ISSN: 1573-6105

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Article
Publication date: 1 May 2001

D. Peric and S. Slijepcevic

This work is concerned with computational modelling of viscoplastic fluids. The flows considered are assumed to be incompressible, while the viscoplastic laws are obtained by…

794

Abstract

This work is concerned with computational modelling of viscoplastic fluids. The flows considered are assumed to be incompressible, while the viscoplastic laws are obtained by incorporating a yield stress below which the fluid is assumed to remain non‐deformable. The Bingham fluid is chosen as a model problem and is considered in detail in the text. The finite element formulation adopted in this work is based on a version of the stabilised finite element method, known as the Galerkin/least‐squares method, originally developed by Hughes and co‐workers. This methodology allows use of low and equal order interpolation of the pressure and velocity fields, thus providing an efficient finite element framework. The Newton‐Raphson method has been chosen for solution of the incremental non‐linear problem arising through the temporal discretisation of the evolution problem. Numerical examples are provided to illustrate the main features of the described methodology.

Details

Engineering Computations, vol. 18 no. 3/4
Type: Research Article
ISSN: 0264-4401

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Article
Publication date: 28 March 2022

Subhasree Dutta, Somnath Bhattacharyya and Ioan Pop

The purpose of this study is to analyze the nonhomogeneous model on the mixed convection of Al2O3–Fe3O4 Bingham plastic hybrid nanofluid in a ventilated enclosure subject to an…

374

Abstract

Purpose

The purpose of this study is to analyze the nonhomogeneous model on the mixed convection of Al2O3–Fe3O4 Bingham plastic hybrid nanofluid in a ventilated enclosure subject to an externally imposed uniform magnetic field. Entropy generation and the pressure drop are determined to analyze the performance of the heat transfer. The significance of Joule heating arising due to the applied magnetic field on the heat transfer of the yield stress fluid is described.

Design/methodology/approach

The ventilation in the enclosure of heated walls is created by an opening on one vertical wall through which cold fluid is injected and another opening on the opposite vertical wall through which fluid can flow out.

Findings

This study finds that the inclusion of Fe3O4 nanoparticles with the Al2O3-viscoplastic nanofluid augments the heat transfer. This rate of enhancement in heat transfer is higher than the rate by which the entropy generation is increased as well as the enhancement in the pressure drop. The yield stress has an adverse effect on the heat transfer; however, it favors thermal mixing. The magnetic field, which is acting opposite to the direction of the inlet jet, manifests heat transfer of the viscoplastic hybrid nanofluid. The horizontal jet of cold fluid produces the optimal heat transfer.

Originality/value

The objective of this study is to analyze the impact of the inclined cold jet of viscoplastic electrically conducting hybrid nanofluid on heat transfer from the enclosure in the presence of a uniform magnetic field. The combined effect of hybrid nanoparticles and a magnetic field to enhance heat transfer of a viscoplastic fluid in a ventilated enclosure has not been addressed before.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 32 no. 9
Type: Research Article
ISSN: 0961-5539

Keywords

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